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Cree en aquellos que buscan la verdad, duda de los que la han encontrado. (André Gide)
𝔖abc xyz y z (-4 b^2 c^2 (b^2-c^2) (-a^2+b^2+c^2) (a^6+b^6-b^4 c^2-b^2 c^4+c^6+a^4 (-b^2-c^2)+a^2 (-b^4+10 b^2 c^2-c^4)) x^5 y z+4 a^4 (b^2-c^2) (-a^2+b^2+c^2) (a^6+b^6-b^4 c^2-b^2 c^4+c^6+a^4 (-b^2-c^2)+a^2 (-b^4+10 b^2 c^2-c^4)) x y^3 z^3-8 b^2 c^2 (-a^2+b^2+c^2) x^6 (-c^2 (a^4 c^2-2 a^2 (b-c)^2 (b+c)^2+(b-c)^2 (b+c)^2 (2 b^2+c^2)) y+b^2 (a^4 b^2-2 a^2 (b-c)^2 (b+c)^2+(b-c)^2 (b+c)^2 (b^2+2 c^2)) z)+8 a^6 (-a^2+b^2+c^2) y^3 z^3 ((a^4 b^2+b^6-3 b^2 c^4+2 c^6+a^2 (-2 b^4+4 b^2 c^2-2 c^4)) y+(-2 b^6-a^4 c^2+3 b^4 c^2-c^6+a^2 (2 b^4-4 b^2 c^2+2 c^4)) z)-x^4 y z (c^2 (a^12+2 a^10 (b^2-c^2)-(b-c)^3 (b+c)^3 (b^2+c^2)^2 (3 b^2+c^2)+a^8 (-5 b^4+18 b^2 c^2-c^4)+2 a^2 (b^2-c^2) (b^2+c^2)^2 (b^4-10 b^2 c^2+c^4)-4 a^6 (b^2-c^2) (b^4-4 b^2 c^2+c^4)+a^4 (b^2-c^2) (7 b^6-13 b^4 c^2+21 b^2 c^4+c^6)) y-b^2 (a^12-2 a^10 (b^2-c^2)+(b-c)^3 (b+c)^3 (b^2+c^2)^2 (b^2+3 c^2)+a^8 (-b^4+18 b^2 c^2-5 c^4)-2 a^2 (b^2-c^2) (b^2+c^2)^2 (b^4-10 b^2 c^2+c^4)+4 a^6 (b^2-c^2) (b^4-4 b^2 c^2+c^4)-a^4 (b^2-c^2) (b^6+21 b^4 c^2-13 b^2 c^4+7 c^6)) z)-2 (a^2+b^2+c^2) x^5 (-c^4 (a^8-4 a^6 c^2-4 a^2 (b-c)^2 (b+c)^2 (2 b^2+c^2)+(b-c)^2 (b+c)^2 (5 b^4+2 b^2 c^2+c^4)+2 a^4 (b^4+3 c^4)) y^2+b^4 (a^8-4 a^6 b^2-4 a^2 (b-c)^2 (b+c)^2 (b^2+2 c^2)+2 a^4 (3 b^4+c^4)+(b-c)^2 (b+c)^2 (b^4+2 b^2 c^2+5 c^4)) z^2)+4 a^6 y^2 z^2 ((a^8+b^8+2 b^6 c^2-10 b^2 c^6+7 c^8+a^6 (-4 b^2+2 c^2)+a^4 (6 b^4-2 b^2 c^2)+a^2 (-4 b^6-2 b^4 c^2+16 b^2 c^4-10 c^6)) y^3+(-a^8-7 b^8+10 b^6 c^2-2 b^2 c^6-c^8+a^6 (-2 b^2+4 c^2)+a^4 (2 b^2 c^2-6 c^4)+a^2 (10 b^6-16 b^4 c^2+2 b^2 c^4+4 c^6)) z^3)) = 0.
)Q = u (((b^2-c^2) u+a^2 (u-2 v)) ((a^2-c^2) v+b^2 (2 u+v))^2 ((-b^2+c^2) u+a^2 (u-2 w)) ((a^2-b^2) w+c^2 (2 u+w))^2 ((-b^2+c^2) (v-w)+a^2 (v+w))+((a^2-c^2) v+b^2 (-2 u+v)) ((a^2-c^2) v+b^2 (2 u+v))^2 ((b^2-c^2) u-a^2 (u-2 w)) ((b^2-c^2) (v-w)-a^2 (v+w)) ((-a^2+b^2) w+c^2 (2 v+w))^2+((-b^2+c^2) u-a^2 (u-2 v)) ((a^2-b^2) w+c^2 (-2 u+w)) ((a^2-b^2) w+c^2 (2 u+w))^2 ((b^2-c^2) (v-w)-a^2 (v+w)) (-a^2 v+c^2 v+b^2 (v+2 w))^2) : ... : ...
Pares {P, Q}: {incentro, }, {circuncentro, X41005} y {ortocentro, X6525}.El 29 de diciembre de 1874 el general Martínez Campos realiza el «Pronunciamiento de Sagunto» a favor de la monarquía de Alfonso XII, que supuso la Restauración borbónica en España y el fin del Sexenio Democrático (1868-1874) y de la Primera República Española (1873-1874).
Ab = (-(a - b - c) (a + b - c) (a - b + c) (a + b + c) : -a^4 + b^4 +
2 a^2 c^2 - c^4 : 0),
Ac = ((a-b-c) (a+b-c) (a-b+c) (a+b+c):0:a^4-2 a^2 b^2+b^4-c^4).
W = ( (a^4-(b^2-c^2)^2) (3 a^18 (b^2+c^2)-2 a^16 (10 b^4+13 b^2 c^2+10 c^4)-a^2 (b^2-c^2)^6 (8 b^6+13 b^4 c^2+13 b^2 c^4+8 c^6)+a^14 (55 b^6+78 b^4 c^2+78 b^2 c^4+55 c^6)+(b^2-c^2)^6 (b^8-b^6 c^2-2 b^4 c^4-b^2 c^6+c^8)+a^8 (b^2-c^2)^2 (7 b^8-9 b^6 c^2-18 b^4 c^4-9 b^2 c^6+7 c^8)-7 a^12 (11 b^8+15 b^6 c^2+14 b^4 c^4+15 b^2 c^6+11 c^8)+a^4 (b^2-c^2)^4 (25 b^8+37 b^6 c^2+42 b^4 c^4+37 b^2 c^6+25 c^8)-a^6 (b^2-c^2)^2 (35 b^10+24 b^8 c^2+21 b^6 c^4+21 b^4 c^6+24 b^2 c^8+35 c^10)+a^10 (49 b^10+62 b^8 c^2+33 b^6 c^4+33 b^4 c^6+62 b^2 c^8+49 c^10)) : ... : ...),
que tiene números de búsqueda en (-12.1295732106015, 11.2956361699589, 1.41887323067506).El 16 de diciembre de 1959 falleció, a los 83 años, el matemático alemán Erhard Schmidt. Sus trabajos versan esencialmente sobre los aspectos geométricos del álgebra lineal (espacios vectoriales de dimensión finita) y el desarrollo de la teoría de espacios de Hilbert completando los resultados de este último en el estudio de ecuaciones integrales, ecuaciones funcionales donde la función buscada aparece bajo el símbolo de integración En uno de sus artículos sobre ecuaciones integrales enuncia el algoritmo de ortonormalización de una base de un espacio vectorial igualmente atribuida al danés Gram y llamado precisamente método de Gram Schmidt
M1 = (2 a^2 (b^2 - c^2)^2 - a^4 (b^2 + c^2) - (b^2 - c^2)^2 (b^2 + c^2) : b^2 (-a + b - c) (a + b - c) (-a + b + c) (a + b + c) : -(a + b - c) c^2 (a - b + c) (-a + b + c) (a + b + c)}).
Ecuación de la circunferencia Γa, de centro Ma y tangente a MbMc:
𝔖abc xyz
(a^4+(b^2-c^2)^2-2 a^2 (b^2+c^2))^2 (a^8-2 a^4 (b^2-c^2)^2+(b^4-c^4)^2)x^2+
2 (a^16+4 a^12 (b^2-c^2)^2-4 a^14 (b^2+c^2)+4 a^10 (b^2-c^2)^2 (b^2+c^2)+(b^2-c^2)^6 (b^2+c^2)^2-2 a^8 (b^2-c^2)^2 (5 b^4-28 b^2 c^2+5 c^4)+4 a^6 (b^2-c^2)^2 (b^6-13 b^4 c^2-13 b^2 c^4+c^6)-4 a^2 (b^2-c^2)^4 (b^6-5 b^4 c^2-5 b^2 c^4+c^6)+4 a^4 (b^2-c^2)^2 (b^8-6 b^6 c^2+26 b^4 c^4-6 b^2 c^6+c^8))y z = 0.
𝔖abc xyz
(a^16-4 a^14 (b^2+c^2)-4 a^2 (b^2-c^2)^6 (b^2+c^2)+4 a^12 (b^2+c^2)^2+(b^2-c^2)^6 (b^2+c^2)^2+4 a^10 (b^2+c^2)^3+4 a^4 (b^2-c^2)^2 (b^8-10 b^6 c^2-14 b^4 c^4-10 b^2 c^6+c^8)-2 a^8 (5 b^8+26 b^6 c^2+34 b^4 c^4+26 b^2 c^6+5 c^8)+4 a^6 (b^10+17 b^8 c^2+14 b^6 c^4+14 b^4 c^6+17 b^2 c^8+c^10))x^2+
2 (a^16-4 a^14 (b^2+c^2)+4 a^10 (b^2-c^2)^2 (b^2+c^2)-4 a^2 (b^2-c^2)^6 (b^2+c^2)+4 a^12 (b^2+c^2)^2+(b^2-c^2)^6 (b^2+c^2)^2+4 a^4 (b^2-c^2)^4 (b^4-4 b^2 c^2+c^4)+4 a^6 (b^2-c^2)^2 (b^6+7 b^4 c^2+7 b^2 c^4+c^6)-2 a^8 (5 b^8+2 b^6 c^2+18 b^4 c^4+2 b^2 c^6+5 c^8))y z = 0.
Z389 = ( a^2 (-a^12 (b^2+c^2)-2 a^2 (b^2-c^2)^4 (2 b^4+b^2 c^2+2 c^4)+a^10 (4 b^4+6 b^2 c^2+4 c^4)+(b^2-c^2)^4 (b^6+b^4 c^2+b^2 c^4+c^6)+a^4 (b^2-c^2)^2 (5 b^6-17 b^4 c^2-17 b^2 c^4+5 c^6)-a^8 (5 b^6+17 b^4 c^2+17 b^2 c^4+5 c^6)+4 a^6 (7 b^6 c^2+2 b^4 c^4+7 b^2 c^6)) : ... : ...),
que tiene números de búsqueda en (1.70213804045450, 2.02906356578353, 1.45032599461678).a Pablo, por su cumpleaños
Q = (1/((a-b-c) ((a-b-c) u+(a-b+c) v+(a+b-c) w)^2) : ... : ...).
Pares {P=Xi, Q=Xj}, para {i,j}: {1, 8}, {7, 7}, {2, 16078}, {56, 1118}, {57, 479}, {65, 56}, {145, 6049}, {174, 7002}, {177, 1}, {222, 7055}, {226, 6063}, {234, 1088}, {354, 55}, {481, 1336}, {482, 1123}, {497, 5423}, {513, 59}, {517, 1318}, {553, 552}, {942, 60}, {1071, 1259}, {1122, 7023}, {1401, 1397}, {1439, 1804}, {1565, 34387}, {1836, 1857}, {2089, 7022}, {2091, 269}, {3057, 33963}, {3309, 6065}, {3638, 14358}, {3639, 14359}, {3649, 12}, {3663, 3596}, {3664, 261}, {3665, 41283}, {3666, 18021}, {3667, 4076}, {3676, 4998}, {3782, 40363}, {4014, 3271}, {4854, 6057}, {4890, 7064}, {4897, 6064}, {4934, 4092}, {7178, 7340}, {7198, 41284}, {7217, 41289}, {7317, 8}, {10391, 6061}, {10499, 10489}, {11570, 4996}, {12723, 6059}, {14100, 480}, {16888, 41287}, {20053, 3635}, {21746, 2175}, {24471, 7341}, {30493, 7335}, {39787, 202}, {39788, 203}, {39791, 7066}, {39793, 181}, {39794, 1124}, {39795, 1335}, {39796, 6056}, {40617, 41292}, {40961, 7337}, {41003, 34388}, {41004, 1264}, {43909, 7336}.Q3 = ( (a-b-c) (a^6-4 a b (b-c)^2 c (b+c)-a^4 (b+c)^2+(b-c)^4 (b+c)^2-a^2 (b^4-6 b^2 c^2+c^4))^2 : ... : ...),
que tiene números de búsqueda en (0.0821307968585268, 5.19170297165521, 0.00850205682683410).Q4 = ( (a-b-c) (a^6-3 a^4 (b-c)^2-(b-c)^2 (b+c)^4+a^2 (b-c)^2 (3 b^2+2 b c+3 c^2))^2 : ... : ...),
que tiene números de búsqueda en ETC (3.77434787991551, 2.17393984513875, 0.393622490696548).Q8 = ( (a^2-(b-c)^2) (a^4-4 a^3 (b+c)-4 a (b+c)^3+(b+c)^4-2 a^2 (5 b^2-22 b c+5 c^2))^2 : ... : ...),
que tiene números de búsqueda en ETC (2.00422673295215, 1.92940226825527, 1.37989672713743).El 10 de diciembre de 1977, la dictadura de Videla secuestra en Buenos Aires (Argentina) a Azucena Villaflor (53 años), una de las fundadoras de las Madres de Plaza de Mayo. Esa tarde, Villaflor había publicado en los periódicos la lista de varios jóvenes desaparecidos. El 20 de diciembre, tras diez días de tortura, será dejada caer viva desde un avión al Río de la Plata (Vuelos de la Muerte).
W = ( a (a^5 (b+c)+5 a^3 b c (b+c)+5 b c (b^2-c^2)^2+2 a^4 (b^2-8 b c+c^2)+a^2 (-2 b^4+11 b^3 c-10 b^2 c^2+11 b c^3-2 c^4)-a (b^5+6 b^4 c-3 b^3 c^2-3 b^2 c^3+6 b c^4+c^5)) : ... : ...),
que tiene números de búsqueda en (-2.77660310658974, -15.7702682448838, 15.8400516237146).El ocho de diciembre ee 1982, en la aldea Las Dos Erres, en el departamento guatemalteco de La Libertad (Petén), el Gobierno del dictador Efraín Ríos Montt lleva a cabo el tercer y último día de la Masacre de Las Dos Erres, en que torturaron y asesinaron a toda la población de la aldea (más de 400 personas).
Ab = (2 a c:a^2-b^2-c^2:,2 c^2),
Ac = (2 a b:2 b^2:a^2-b^2-c^2).
ℓa: ((b-c)^2-a^2) x+2 a c y+2 a b z = 0.
A' = (a^4-2 a^3 (b+c)+2 a (b-c)^2 (b+c)-(b^2-c^2)^2:-2 b c (a^2-4 a b+b^2-c^2):2 b c (-a^2+b^2+4 a c-c^2)).
ℓ'a: (a^2 + (b - c)^2) x - 2 a b y - 2 a c z = 0.
A" = (a^4-2 a^3 (b+c)+2 a^2 (b+c)^2+(b^2-c^2)^2-2 a (b^3+b^2 c+b c^2+c^3):
2 a b (a^2-2 a b+b^2+3 c^2) : 2 a c (a^2+3 b^2-2 a c+c^2)).
𝔖abc xyz -2 a b (b-c) c (-a^13+7 a^12 (b+c)+(b-c)^8 (b+c)^3 (b^2+c^2)-2 a^11 (10 b^2+23 b c+10 c^2)+2 a^10 (14 b^3+53 b^2 c+53 b c^2+14 c^3)-a (b-c)^8 (7 b^4+26 b^3 c+30 b^2 c^2+26 b c^3+7 c^4)-a^9 (13 b^4+90 b^3 c+210 b^2 c^2+90 b c^3+13 c^4)-a^8 (21 b^5+3 b^4 c-112 b^3 c^2-112 b^2 c^3+3 b c^4+21 c^5)+4 a^7 (12 b^6+b^5 c+48 b^4 c^2-34 b^3 c^3+48 b^2 c^4+b c^5+12 c^6)-4 a^6 (12 b^7-19 b^6 c+85 b^5 c^2-6 b^4 c^3-6 b^3 c^4+85 b^2 c^5-19 b c^6+12 c^7)+3 a^5 (7 b^8-12 b^7 c+60 b^6 c^2+140 b^5 c^3-134 b^4 c^4+140 b^3 c^5+60 b^2 c^6-12 b c^7+7 c^8)-2 a^3 (b-c)^2 (14 b^8-41 b^7 c-34 b^6 c^2+9 b^5 c^3-280 b^4 c^4+9 b^3 c^5-34 b^2 c^6-41 b c^7+14 c^8)+2 a^2 (b-c)^2 (10 b^9-23 b^8 c-27 b^7 c^2+71 b^6 c^3-95 b^5 c^4-95 b^4 c^5+71 b^3 c^6-27 b^2 c^7-23 b c^8+10 c^9)+a^4 (13 b^9-95 b^8 c+56 b^7 c^2-368 b^6 c^3+266 b^5 c^4+266 b^4 c^5-368 b^3 c^6+56 b^2 c^7-95 b c^8+13 c^9)) x^2-a (b-c) (-a^15+9 a^14 (b+c)-5 a^13 (7 b^2+16 b c+7 c^2)+3 a^12 (25 b^3+97 b^2 c+97 b c^2+25 c^3)+(b-c)^8 (b+c)^3 (b^4+2 b^3 c+6 b^2 c^2+2 b c^3+c^4)-a (b-c)^6 (b+c)^4 (9 b^4-2 b^3 c+6 b^2 c^2-2 b c^3+9 c^4)-a^11 (89 b^4+548 b^3 c+930 b^2 c^2+548 b c^3+89 c^4)+a^10 (33 b^5+525 b^4 c+1454 b^3 c^2+1454 b^2 c^3+525 b c^4+33 c^5)+a^9 (77 b^6-124 b^5 c-937 b^4 c^2-2032 b^3 c^3-937 b^2 c^4-124 b c^5+77 c^6)+a^7 (b+c)^2 (165 b^6+14 b^5 c+1235 b^4 c^2-2060 b^3 c^3+1235 b^2 c^4+14 b c^5+165 c^6)-a^8 (165 b^7+265 b^6 c+499 b^5 c^2-1393 b^4 c^3-1393 b^3 c^4+499 b^2 c^5+265 b c^6+165 c^7)-a^6 (77 b^9+277 b^8 c+1052 b^7 c^2+1676 b^6 c^3-714 b^5 c^4-714 b^4 c^5+1676 b^3 c^6+1052 b^2 c^7+277 b c^8+77 c^9)+a^5 (-33 b^10+248 b^9 c+283 b^8 c^2+976 b^7 c^3+1606 b^6 c^4-2064 b^5 c^5+1606 b^4 c^6+976 b^3 c^7+283 b^2 c^8+248 b c^9-33 c^10)-a^3 (b+c)^2 (75 b^10-290 b^9 c+331 b^8 c^2+432 b^7 c^3-2262 b^6 c^4+3172 b^5 c^5-2262 b^4 c^6+432 b^3 c^7+331 b^2 c^8-290 b c^9+75 c^10)+a^2 (b-c)^2 (35 b^11+5 b^10 c-139 b^9 c^2+131 b^8 c^3+58 b^7 c^4-346 b^6 c^5-346 b^5 c^6+58 b^4 c^7+131 b^3 c^8-139 b^2 c^9+5 b c^10+35 c^11)+a^4 (89 b^11-215 b^10 c-83 b^9 c^2+397 b^8 c^3-2310 b^7 c^4+842 b^6 c^5+842 b^5 c^6-2310 b^4 c^7+397 b^3 c^8-83 b^2 c^9-215 b c^10+89 c^11)) y z = 0.
)«Muchas veces las palabras que tendríamos que haber dicho no se presentan ante nuestra mente hasta que ya es demasiado tarde» (André Gide)
A" = (2 a^2 b c : b^2 (a^2-b^2+c^2) : c^2 (a^2+b^2-c^2)).
El 1 de diciembre de 1792 nació el matemático ruso Niclaï Ivanovitch Lobatchevsky, fue uno de los primeros matemáticos que aplicó un tratamiento crítico a los postulados fundamentales de la geometría euclidiana. Informó, por primera vez, de su nueva geometría no euclidiana el 23 de febrero de 1826, con una conferencia en la sesión del departamento de física y matemáticas de la Universidad de Kazán. Publicó un artículo "Geometría Imaginaria" en la cual desarrollaba una geometría no euclidea llamada geometría hiperbólica, con independencia del húngaro János Bolyai y del alemán Carl Friedrich Gauss. Antes de Lobachevski, los matemáticos intentaban deducir el quinto postulado de Euclides a partir de los otros axiomas; sin embargo, Lobachevski se dedicó a desarrollar una geometría en la cual el quinto postulado puede no ser cierto o, mejor dicho, ser diferente.
W = (a^10 (3 u+v+w)-a^4 (b^4 c^2 (4 u+v)+c^6 (v-2 w)+b^2 c^4 (4 u+w)+b^6 (-2 v+w))-a^8 (c^2 (7 u+2 v)+b^2 (7 u+2 w))-(b^2-c^2)^4 (b^2 (u+2 v+w)+c^2 (u+v+2 w))+a^2 (b^2-c^2)^2 (b^4 (u+3 v+2 w)+c^4 (u+2 v+3 w)-b^2 c^2 (u+2 (v+w)))+a^6 (c^4 (4 u+v-4 w)+b^4 (4 u-4 v+w)+b^2 c^2 (11 u+4 (v+w))): ... : ....).
A' = (-2 (b^2-c^2)^4 (b^2+c^2)^2+a^12 (1+t)-2 a^10 (b^2+c^2) (2+t)+a^8 (-2 b^4 (-2+t)-2 c^4 (-2+t)+9 b^2 c^2 (1+t))+a^2 (b^2-c^2)^2 (b^2+c^2) (5 b^2 c^2 (-1+t)+2 b^4 (4+t)+2 c^4 (4+t))-a^4 (4 b^4 c^4 (1-4 t)+b^6 c^2 (-15+t)+b^2 c^6 (-15+t)+b^8 (11+7 t)+c^8 (11+7 t))+a^6 (b^2+c^2) (4 c^4 (1+2 t)+b^4 (4+8 t)-b^2 c^2 (15+17 t)) :
-b^2 (a^4+b^4+b^2 c^2-2 c^4+a^2 (-2 b^2+c^2)) ((b^2-c^2)^2 (b^2+c^2) (-1+t)+2 a^6 t-a^4 (b^2+c^2) (1+3 t)+2 a^2 (b^4+c^4+b^2 c^2 (-1+2 t))) :
-c^2 (a^4-2 b^4+b^2 c^2+c^4+a^2 (b^2-2 c^2)) ((b^2-c^2)^2 (b^2+c^2) (-1+t)+2 a^6 t-a^4 (b^2+c^2) (1+3 t)+2 a^2 (b^4+c^4+b^2 c^2 (-1+2 t)))),
W = (2 (b^2-c^2)^4 (b^2+c^2)-a^8 (b^2+c^2) (-5+t)+a^10 (-3+t)-a^2 (b^2-c^2)^2 (5 b^2 c^2 (-1+t)+2 b^4 (1+t)+2 c^4 (1+t))+a^4 (b^2+c^2) (2 b^2 c^2 (4-5 t)+b^4 (-3+5 t)+c^4 (-3+5 t))+a^6 (b^4 (1-3 t)+c^4 (1-3 t)+b^2 c^2 (-13+7 t)) :
2 a^10-a^2 (b^2-c^2) (-6 c^6+2 b^4 c^2 (4-3 t)+b^6 (-5+t)-b^2 c^4 (-3+t))+(b^2-c^2)^3 (-2 c^4+b^4 (-3+t)+2 b^2 c^2 (-2+t))-2 a^8 (3 c^2+b^2 (1+t))+a^4 (4 c^6+b^6 (1-3 t)-5 b^4 c^2 (-1+t)+2 b^2 c^4 (-7+3 t))+a^6 (4 c^4-b^2 c^2 (-9+t)+b^4 (-3+5 t)) :
2 a^10+(b^2-c^2)^3 (2 b^4-c^4 (-3+t)-2 b^2 c^2 (-2+t))-2 a^8 (3 b^2+c^2 (1+t))+a^4 (4 b^6+c^6 (1-3 t)-5 b^2 c^4 (-1+t)+2 b^4 c^2 (-7+3 t))-a^2 (b^2-c^2) (6 b^6-c^6 (-5+t)+b^4 c^2 (-3+t)+2 b^2 c^4 (-4+3 t))+a^6 (4 b^4-b^2 c^2 (-9+t)+c^4 (-3+5 t))).
Pt=O + t H ↦ Ft*= 8 (1+t) O -(4 S^2OH² + a²b²c² + 8t SASBSC) H
es una involución sobre la recta de EulerF+, F- SBSC(SA(3SBSC-S²) ± 2 OH S √- SASBSC) : :
a Lolilla, por su cumpleaños
A' = (-a^4 + (b^2 - c^2)^2 : -2 b^2 (-a^2 + b^2 - c^2) : -2 c^2 (-a^2 - b^2 +
c^2)),
A" = (a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) : b (b-c) (-a+b+c) (a+b+c) (a^2+b^2-c^2) : (a-b-c) (b-c) c (a+b+c) (a^2-b^2+c^2),
ta: (b-c)^2 (-a+b+c)^2 (a+b+c)^2 x+a^2 (a^2-b^2+c^2)^2 y+a^2 (a^2+b^2-c^2)^2 z = 0.
A1 = (a (a^6+a^5 (b+c)-2 b c (b^2-c^2)^2+a^2 (b^2+c^2)^2-2 a^4 (b^2-b c+c^2)-2 a^3 (b^3+c^3)+a (b^5-b^4 c-b c^4+c^5)) :
-b^2 (a^5+b^5+a^4 (b-c)+b^4 c-b c^4-c^5-2 a^3 (b^2+c^2)+a (b^2+c^2)^2-2 a^2 (b^3-c^3)) :
-c^2 (a^5-b^5-b^4 c+b c^4+c^5+a^4 (-b+c)-2 a^3 (b^2+c^2)+a (b^2+c^2)^2+2 a^2 (b^3-c^3))).
X2178 = ( a^2(a^3+a^2 (b+c)-a (b^2+c^2)-(b-c)^2 (b+c)): ... : ...).
NOTA:El 18 de noviembre de 1922 falleció (a los 51 años) Marcel Proust, novelista, ensayista y crítico francés cuya obra maestra, la novela "En busca del tiempo perdido" está compuesta de siete partes publicadas entre 1913 y 1927.
Fo = ( 21 a^8 -12 a^6 (b^2+c^2)+2 a^4 (b^4-14 b^2 c^2+c^4) +28 a^2 (b^2-c^2)^2 (b^2+c^2) -(b^2-c^2)^2 (7 b^4-22 b^2 c^2+7 c^4) : ... : ...),
que tiene números de búsqueda en (0.855064707936612, 1.75820343733889, 2.02880146777902).V = ( a^8+8 a^6 (b^2+c^2)-2 a^4 (b^2+c^2)^2-8 a^2 (b^2-c^2)^2 (b^2+c^2)+(b^2-c^2)^2 (b^4-10 b^2 c^2+c^4) : ... : ...),
que tiene números de búsqueda en ETC (-46.2674456459368, -55.3441871404062, 63.3100766464672).El 13 de noviembre de 2014 falleció, a los 86 años, Alexander Grothendieck, matemático apátrida, nacionalizado francés en los años 1980. Recibió la medalla Fields en 1966 por sus contribuciones al Álgebra Homológica y la Geometría Algebraica.
(a^2 (-q+r)+(b^2-c^2) (q+r)) x+2 ((-b^2+c^2) p+a^2 (p+r)) y-2 ((b^2-c^2) p+a^2 (p+q)) z = 0.
ABC y A'B'C' son ortológicos si y solo si las coordenadas de P satisfacen a la ecuación:𝔖abc xyz y z (a^2 (y-z)-3 (b^2-c^2) (y+z)) = 0,
que es la ecuación de K117.U = ( 1/((3 a^4-2 a^2 b^2-b^4-2 a^2 c^2+2 b^2 c^2-c^4) (3 a^4-6 a^2 b^2+3 b^4-6 a^2 c^2+2 b^2 c^2+3 c^4)) : ... : ...),
que tiene números de búsqueda en (0.519598388237994, 0.919646961594628, 2.76417117546287).V = ( (4 a^2-b^2-c^2)/(27 a^4+3 b^4+26 b^2 c^2+3 c^4-30 a^2 (b^2+c^2)) : ... : ...),
punto sobre la rectas X3146X11008, que tiene números de búsqueda en ETC (47.6607923560715, 110.191003918725, -94.6427039338584).W = ( (3 a^4-5 a^2 (b^2+c^2)+2 b^4-b^2 c^2+2 c^4)/(a^8-a^6 (b^2+c^2)-a^4 (3 b^4+b^2 c^2+3 c^4)+a^2 (5 b^6+b^4 c^2+b^2 c^4+5 c^6)-(b^2-c^2)^2 (2 b^4+3 b^2 c^2+2 c^4)) : ... : ...),
punto sobre la recta X3146X15619, que tiene números de búsqueda en ETC (-0.468912595906691, 5.62506509968115, -0.0371901582225602).Z = ( (a^2+b^2-4 c^2) (a^2-4 b^2+c^2) (4 a^12-8 a^10 (b^2+c^2)+a^8 (3 b^4+14 b^2 c^2+3 c^4) +(b^2-c^2)^4 (2 b^4-b^2 c^2+2 c^4) +a^4 (b^2-c^2)^2 (11 b^4+9 b^2 c^2+11 c^4)-a^2 (b^2-c^2)^2 (9 b^6-7 b^4 c^2-7 b^2 c^4+9 c^6)-3 a^6 (b^2+c^2)^3) : ... : ...),
que tiene números de búsqueda en ETC (-61.5836245195268, -69.4524767401615, 80.1463596956470).El 8 de noviembre de 1868 nació, Felix Hausdorff, matemático alemán, considerado uno de los fundadores de la Topología moderna. Axiomatizó el concepto topológico de entorno e introdujo los espacios topológicos conocidos como espacios de Hausdorff.
A* = ( -a (a^4 (b+c)+6 a^2 (b-c)^2 (b+c)+(b-c)^4 (b+c)-4 a^3 (b^2+c^2)-4 a (b-c)^2 (b^2+c^2)) :
b (a-b+c)^2 (a^3-a^2 (2 b+3 c)+c (b^2-c^2)+a (b^2+2 b c+3 c^2)) :
(a+b-c)^2 c (a^3-b^3+b c^2-a^2 (3 b+2 c)+a (3 b^2+2 b c+c^2))),
Ab = (-a (a+b-c)^2 : b (a+b-c)^2 : a^3-b (b-c)^2-a^2 (3 b+2 c)+a (3 b^2-4 b c+c^2)),
Ac = (-a (a-b+c)^2 : a^3-(b-c)^2 c-a^2 (2 b+3 c)+a (b^2-4 b c+3 c^2) : c (a-b+c)^2),
A' = (-a (a^4 (b+c)+6 a^2 (b-c)^2 (b+c)+(b-c)^4 (b+c)-4 a^3 (b^2+c^2)-4 a (b-c)^2 (b^2+c^2)):
b (a^5-(b-c)^3 c (b+c)-a^4 (4 b+3 c)+a (b-c)^2 (b^2-3 c^2)+2 a^3 (3 b^2+b c+c^2)+a^2 (-4 b^3+4 b^2 c-2 b c^2+2 c^3)) :
c (a^5+b (b-c)^3 (b+c)-a^4 (3 b+4 c)-a (b-c)^2 (3 b^2-c^2)+2 a^3 (b^2+b c+3 c^2)+2 a^2 (b^3-b^2 c+2 b c^2-2 c^3))),
D' = (-2 a (b-c)^2+a^2 (b+c)+(b-c)^2 (b+c) : -b (a^2+(b-c)^2-2 a (b+c)) : -c (a^2+(b-c)^2-2 a (b+c))).
El 5 de noviembre de 2012 falleció, a los 74 años, Leonardo Favio, director de cine, cantautor, productor cinematográfico, guionista y actor argentino. Es considerado un director de culto, y uno de los más brillantes cineastas de su país. Sus películas Crónica de un niño solo y El romance del Aniceto y la Francisca suelen ser evaluadas entre las mejores de la historia del cine argentino.
μ(x y+x z+y z) +
λ ((b^2-c^2)^2 x+(a^2-c^2)^2 y+(a^2-b^2)^2 z) ((b^2-c^2) (-c^2-b^2 t+a^2 (1+t)) x+(a^2-b^2) (a^2-c^2) t y-(a^2-b^2) (a^2-c^2) z) = 0.
Γ: 𝔖abc xyz a^2 y z-((2 a^2-b^2-c^2) (b^2-c^2)^4 x (x+y+z))/(a^4+b^4-b^2 c^2+c^4-a^2 (b^2+c^2))^2 = 0.
Contiene a los centros X99 y X892 (que es el otro punto de su intersección con la elipse circunscrita de Steiner).D = (3 a^12-8 a^10 (b^2+c^2)+2 a^8 (4 b^4+9 b^2 c^2+4 c^4)-a^6 (5 b^6+13 b^4 c^2+13 b^2 c^4+5 c^6) +a^4 (2 b^8+6 b^6 c^2+3 b^4 c^4+6 b^2 c^6+2 c^8)+a^2 (b^10-6 b^8 c^2+3 b^6 c^4+3 b^4 c^6-6 b^2 c^8+c^10) -(b^2-c^2)^2 (b^8-b^6 c^2-b^4 c^4-b^2 c^6+c^8) : ... : ...).
El 3 de noviembre de 1940 fallece, a los 60 años, en su exilio de Montauban, Manuel Azaña Díaz, escritor, político y uno de los oradores más importantes de la política española del siglo XX. Fue Jefe del Gobierno español de 1931 a 1933, y algunos meses en el año 1936. También fue Presidente de la Segunda República Española desde 1936 hasta 1939.
Ab = ((a^2+b^2-c^2)^2 : 0 : (-a+b+c) (a+b-c) (a-b+c) (a+b+c)),
Ac = ((a^2-b^2+c^2)^2 : (-a+b+c) (a+b-c) (a-b+c) (a+b+c) : 0),
A' = (2 (a^6 (b^2+c^2)+a^2 (b^2-c^2)^2 (b^2+c^2)-2 a^4 (b^4+c^4)) :
-a^8-(b^2-c^2)^4+2 a^6 (b^2+2 c^2)-2 a^4 (b^4+3 c^4)+2 a^2 (b^6-3 b^2 c^4+2 c^6) :
-a^8-(b^2-c^2)^4+2 a^6 (2 b^2+c^2)-2 a^4 (3 b^4+c^4)+2 a^2 (2 b^6-3 b^4 c^2+c^6),
A" = (2 a^2 (-b^2+c^2) : -a^4+2 a^2 c^2-(b^2-c^2)^2 : a^4-2 a^2 b^2+(b^2-c^2)^2).
X2165 = (1/(a^4+b^4+c^4-2 a^2 (b^2+c^2)):...:...).
W = ( 1/(a^4-2 a^2 (b^2+c^2)+b^4-4 b^2 c^2+c^4) : ... : ...),
que tiene números de búsqueda en (1.52383127282490, 1.74722266792601, 1.72774204742411).X15805 = (a^2 (a^8-4 a^6 (b^2+c^2)+(b^2-c^2)^2 (b^4-6 b^2 c^2+c^4)+a^4 (6 b^4-4 b^2 c^2+6 c^4)-4 a^2 (b^6-4 b^4 c^2-4 b^2 c^4+c^6)) : ... : ... )
No se conocen centros en ETC[1-44066], salvo X15805, cuya imagen mediante σ estén en ETC.
σ(x:y:z)= ((-a^24 - (b^2 - c^2)^12 + 16 a^22 (b^2 + c^2) +
16 a^2 (b^2 - c^2)^10 (b^2 + c^2) -
2 a^20 (53 b^4 + 104 b^2 c^2 + 53 c^4) +
80 a^18 (5 b^6 + 13 b^4 c^2 + 13 b^2 c^4 + 5 c^6) -
2 a^4 (b^2 - c^2)^6 (53 b^8 + 6 b^6 c^2 - 126 b^4 c^4 + 6 b^2 c^6 +
53 c^8) -
a^16 (975 b^8 + 2756 b^6 c^2 + 3338 b^4 c^4 + 2756 b^2 c^6 +
975 c^8) +
16 a^6 (b^2 - c^2)^4 (25 b^10 + 21 b^8 c^2 - 50 b^6 c^4 -
50 b^4 c^6 + 21 b^2 c^8 + 25 c^10) +
32 a^14 (51 b^10 + 133 b^8 c^2 + 140 b^6 c^4 + 140 b^4 c^6 +
133 b^2 c^8 + 51 c^10) +
32 a^10 (b^2 - c^2)^2 (51 b^10 + 140 b^8 c^2 + 143 b^6 c^4 +
143 b^4 c^6 + 140 b^2 c^8 + 51 c^10) -
4 a^12 (483 b^12 + 928 b^10 c^2 + 345 b^8 c^4 + 376 b^6 c^6 +
345 b^4 c^8 + 928 b^2 c^10 + 483 c^12) -
a^8 (b^2 - c^2)^2 (975 b^12 + 1030 b^10 c^2 - 1487 b^8 c^4 -
1228 b^6 c^6 - 1487 b^4 c^8 + 1030 b^2 c^10 + 975 c^12))x+
2 a^2 c^2 (a^20 -
2 a^18 (8 b^2 + 5 c^2) + (b^2 - c^2)^8 (b^4 - 6 b^2 c^2 + c^4) +
a^16 (101 b^4 + 114 b^2 c^2 + 45 c^4) -
24 a^14 (14 b^6 + 17 b^4 c^2 + 14 b^2 c^4 + 5 c^6) -
2 a^2 (b^2 - c^2)^5 (8 b^8 - 51 b^6 c^2 + 33 b^4 c^4 +
23 b^2 c^6 - 5 c^8) +
a^12 (666 b^8 + 392 b^6 c^2 + 388 b^4 c^4 + 504 b^2 c^6 +
210 c^8) +
a^4 (b^2 - c^2)^3 (101 b^10 - 553 b^8 c^2 + 90 b^6 c^4 +
470 b^4 c^6 + 129 b^2 c^8 - 45 c^10) -
4 a^10 (208 b^10 - 169 b^8 c^2 - 264 b^6 c^4 - 138 b^4 c^6 +
84 b^2 c^8 + 63 c^10) +
2 a^8 (333 b^12 - 970 b^10 c^2 - 577 b^8 c^4 - 748 b^6 c^6 -
693 b^4 c^8 - 42 b^2 c^10 + 105 c^12) -
8 a^6 (42 b^14 - 233 b^12 c^2 + 174 b^10 c^4 + 105 b^8 c^6 +
50 b^6 c^8 - 111 b^4 c^10 - 42 b^2 c^12 + 15 c^14))y+
2 a^2 b^2 (a^20 -
2 a^18 (5 b^2 + 8 c^2) + (b^2 - c^2)^8 (b^4 - 6 b^2 c^2 + c^4) +
a^16 (45 b^4 + 114 b^2 c^2 + 101 c^4) -
24 a^14 (5 b^6 + 14 b^4 c^2 + 17 b^2 c^4 + 14 c^6) -
2 a^2 (b^2 - c^2)^5 (5 b^8 - 23 b^6 c^2 - 33 b^4 c^4 +
51 b^2 c^6 - 8 c^8) +
a^12 (210 b^8 + 504 b^6 c^2 + 388 b^4 c^4 + 392 b^2 c^6 +
666 c^8) +
a^4 (b^2 - c^2)^3 (45 b^10 - 129 b^8 c^2 - 470 b^6 c^4 -
90 b^4 c^6 + 553 b^2 c^8 - 101 c^10) -
4 a^10 (63 b^10 + 84 b^8 c^2 - 138 b^6 c^4 - 264 b^4 c^6 -
169 b^2 c^8 + 208 c^10) +
2 a^8 (105 b^12 - 42 b^10 c^2 - 693 b^8 c^4 - 748 b^6 c^6 -
577 b^4 c^8 - 970 b^2 c^10 + 333 c^12) -
8 a^6 (15 b^14 - 42 b^12 c^2 - 111 b^10 c^4 + 50 b^8 c^6 +
105 b^6 c^8 + 174 b^4 c^10 - 233 b^2 c^12 + 42 c^14))z : ... : ...).
El 31 de octubre de 1992, Juan Pablo II, en la sesión plenaria de la Academia Pontificia de las Ciencias, reconoce claramente los errores de ciertos teólogos del siglo XVII en el caso de Galileo, sobre el que había propuesto una revisión honrada y sin prejuicios en 1979, pero la comisión que nombró al efecto en 1981 y que dio por concluidos sus trabajos en 1992, confirmó una vez más la tesis de que Galileo Galilei carecía de argumentos científicos para demostrar el heliocentrismo y sostuvo la inocencia de la Iglesia como institución y la obligación de Galileo de reconocer y prestar obediencia a su magisterio, justificando la condena y evitando una rehabilitación plena.
U = (1/(c^2 p q+b^2 p r+a^2 q r+(a^2+b^2+c^2) q r t) : ... : ...).
La C(P, U) de P y U tiene de ecuación:
𝔖abc pqr xyz
q r (a^2 q r (1+t)+b^2 r (p+q t)+c^2 q (p+r t)) x^2
-p (a^2 q r (q+r+2 p t)+b^2 p r (q+r+2 q t)+c^2 p q (q+r+2 r t)) y z = 0.
Q = (p(q-r)^2 : q(p-r)^2 : r(p-q)^2).
t = -(2 (c^2 p q+b^2 p r+a^2 q r)^2/((a^2+b^2+c^2) (c^2 p q ((q-r) r+p (q+r))+r (a^2 q (-p^2+q r+p (q+r))+b^2 p (q (-q+r)+p (q+r)))).
Su ecuación es:
𝔖abc pqr xyz
q r (-c^2 p q (p-r) (q+r)+(p-q) r (a^2 q (p-r)-b^2 p (q+r))) x^2
+p (c^2 p q (q-r) (p (q-r)+r (q+r))+r (-b^2 p (q-r) (p (-q+r)+q (q+r))+a^2 q (p (q-r)^2-p^2 (q+r)+q r (q+r)))) y z = 0.
a Raquel, por su "cumple"
BA1:A1C = CA2:A2B = AD':D'A'.
Procediendo cíclicamente se definen los puntos B1, B2 y C1, C2.P1 - P2 = (p(q^2-r^2) : q (r^2-p^2) : r (p^2-q^2)).
NOTA: La diferencia baricéntrica de un par baricéntrico solo tiene sentido cuando sus coordenadas se toman en la forma:(f(a,b,c) : f(b,c,a) : f(c,a,b)) y (f(a,c,b) : f(b,a,c) : f(c,b,a)).
Si (0:1:t) son las coordenadas del punto de intersección de ℓ con BC, se tiene que:λ (1 - t : t : -1) = (p, q, r), p+q+r = 0 ⇒ p = λ- t λ, q = t λ, r = -λ.
Entonces, P1 - P2 = ((-1+t)^2 (1+t):(-2+t) t^2:1-2 t), que es una ecuación paramétrica de K219, cuya ecuación baricéntrica es:3 x y z + 𝔖xyz x^3 - y z (y + z) = 0.
El 12 de octubre de 1935 nació el tenor italiano Luciano Pavarotti, uno de los más destacados a nivel mundial.
u^2 (a^2 v w-(v+w) (c^2 v+b^2 w)) y z + ... = 0.
Fo = (u^2 (-a^2 v w+c^2 v (v+w)+b^2 w (v+w)) (-b^2 u (v+t (u+v)) w+a^2 v w (u-t u-t v+w)+c^2 u v (u+w+t w)) :
v^2 (-b^2 u w+c^2 u (u+w)+a^2 w (u+w)) (c^2 u (u (v+w)+w (-t v+w))+w (b^2 u (u+t u+t v-w)-a^2 (u^2+u (-t v+w)+v (-t v+w)))) :
-(-c^2 u v+b^2 u (u+v)+a^2 v (u+v)) w^2 (c^2 u v (u+t u-t v+w)-a^2 v (-w (u+w)+t (u^2+u v+v w))+b^2 u (-v w+t (v^2+u (v+w)))).
T(P) = (u (-w (a^2 (u-v+w)+b^2 (-u+v+w))+c^2 (w (v+w)+u (2 v+w))) (a^2 v (u+v-w)+c^2 v (-u+v+w)-b^2 (v (v+w)+u (v+2 w))) : ... : ...).
𝔖abc xyz (a-b) (a-c) (b-c) (a^5-b^5+b^4 c+b c^4-c^5-a^4 (b+c)+a (b-c)^2 (b^2+c^2)-2 a^3 (b^2-b c+c^2)+2 a^2 (b^3+c^3))x^2 + 2 a (b-c) (a^6-2 a^5 (b+c)+(b^2-c^2)^2 (b^2+c^2)-a^4 (b^2-7 b c+c^2)-a^2 (b-c)^2 (b^2+5 b c+c^2)-a (b-c)^2 (2 b^3+b^2 c+b c^2+2 c^3)+a^3 (4 b^3-5 b^2 c-5 b c^2+4 c^3))y z = 0.
)Se estima que 330 mil niños fueron víctimas de abuso sexual dentro de la Iglesia Católica de Francia durante los últimos 70 años, según un informe publicado este martes (5 de octubre de 2021) que representa el primer informe importante del país sobre el fenómeno mundial. La cifra incluye abusos cometidos por unos 3 mil sacerdotes y otras personas involucradas en la iglesia, delitos que las autoridades católicas encubrieron durante décadas de manera “sistémica”, según el presidente de la comisión que emitió el informe, Jean-Marc Sauvé. El documento de 2 mil 500 páginas se publicó cuando la Iglesia católica en Francia, como en otros países, busca hacer frente a vergonzosos secretos que durante mucho tiempo estuvieron encubiertos.
Las rectas AA', BB', CC' son concurrentes, en el punto Q, del complemento del de P.
(2 (u^2+v^2+w^2) + 5 (u v + u w + v w)))/(4 (u + v + w)^2) área (ABC).
Po = (u (u^2+u (v+w)-2 (v^2+v w+w^2)) : ... : ...).
La matriz asociada a 𝒞(P) es:Q = ((u+2 v+w) (u+v+2 w) : (2 u+v+w) (u+v+2 w) : (2 u+v+w) (u+2 v+w)),
conjugado isotómico del complemeto, (2 u + v + w : u + 2 v + w : u + v + 2 w), del complemento, (v + w : u + w : u + v), de P=(u:v:w).El 4 de octubre de 1873 nació Gheorghe Titeica, matematico rumano especialista en geometría diferencial. En 1907 publica, en Comptes Rendues, un trabajo en el que aparece el siguiente resultado: "Una transformación lineal que no cambia ni el plano en el infinito, ni el origen, deja invariante la relación entre la curvatura gaussiana de la superficie y la cuarta potencia de la distancia del origen al plano tangente en un punto de la superficie." Las superficies en las que esta relación es constante se les conoce como superficies de Titeica.
A" = ((b^2-c^2) (-c^2 v+b^2 w)-a^2 (c^2 v+b^2 w) : -b^2 (-a^2+b^2+c^2) w : -c^2 (-a^2+b^2+c^2) v).
Las rectas AA", BB", CC" concurren en el de P (Euclid#2579, Tran Quang Hung, Elias M. Hagos)Q = (a^2 (a^2 (c^2 v + b^2 w)-(b^2 - c^2) (b^2 w-c^2 v)) : ... : ...).
a Silvia, por su "cumple"
D = (2 a^2 v w - b^2 (v - w) w - c^2 v (-v + w) : ... : ...),
Ab = (-2 a^2 v w + b^2 (v - w) w + c^2 v (-v + w) : 0 : w (c^2 v - b^2 w)),
Ac = ({-2 a^2 v w + b^2 (v - w) w + c^2 v (-v + w) : v (-c^2 v + b^2 w) : 0).
-3 (a-b) (a+b) (a-c) (a+c) (b^2-c^2) x^2 y^2 z^2
+
𝔖abc xyz
y z (-3 b^2 c^2 (b^2-c^2) x^4-a^4 (b^2-c^2) y^2 z^2-a^4 (2 a^2-b^2-c^2) y (y-z) z (y+z)-x^3 (c^2 (a^4-b^4+6 b^2 c^2-2 c^4+a^2 (-4 b^2-c^2)) y-b^2 (a^4-2 b^4+6 b^2 c^2-c^4+a^2 (-b^2-4 c^2)) z)-a^4 (c y^2-b z^2) (c y^2+b z^2))= 0,
W = ( 2 a^2-b^2-c^2)(2 a^6-2 a^4 (b^2+c^2)-a^2 (b^4-4 b^2 c^2+c^4)+3 (b^2-c^2)^2 (b^2+c^2)) : ... : ...),
que tiene números de búsqueda en (17.2982498688915, 4.11531659681015, -7.19220848614178).El 28 de septiembre de 1761 nació, François Budan de Boislaurent, matemático aficionado y médico francés conocido por haber formulado el teorema de Budan-Fourier; es un teorema para acotar el número de raíces reales de un polinomio en un intervalo y calcular la paridad de este número. Fue publicado en 1807 por François Budan de Boislaurent. Un teorema similar fue publicado independientemente por Joseph Fourier en 1820. Cada uno de estos teoremas es un corolario del otro. La afirmación de Fourier aparece con más frecuencia en la literatura del siglo XIX y se la conoce como teorema de Fourier, Budan-Fourier, Fourier-Budan e incluso Budan. La formulación original de Budan se utiliza en algoritmos modernos y rápidos para el aislamiento de raíces reales de polinomios.
Ab = (-a^4 - b^4 - 3 c^4 +
2 a^2 (b^2 + 2 c^2) : 0 : (-a^2 + b^2 + c^2) (-a^2 + b^2 + 3 c^2)),
Ac = (-a^4 - 3 b^4 - c^4 +
2 a^2 (2 b^2 + c^2) : (-a^2 + b^2 + c^2) (-a^2 + 3 b^2 + c^2) : 0),
A' = (-18 a^6 (b^2-c^2)^2+2 a^2 (b^2-c^2)^4+9 a^8 (b^2+c^2)+8 a^4 (b^2-c^2)^2 (b^2+c^2)-(b^2-c^2)^4 (b^2+c^2) :
-3 a^8 (b^2+2 c^2)-2 a^6 (b^4+12 b^2 c^2-10 c^4)+(b^2-c^2)^3 (3 b^4-7 b^2 c^2+2 c^4)+2 a^4 (8 b^6-11 b^4 c^2+27 b^2 c^4-12 c^6)+a^2 (-14 b^8+36 b^6 c^2+6 b^4 c^4-40 b^2 c^6+12 c^8) :
-3 a^8 (2 b^2+c^2)+a^6 (20 b^4-24 b^2 c^2-2 c^4)-(b^2-c^2)^3 (2 b^4-7 b^2 c^2+3 c^4)+a^4 (-24 b^6+54 b^4 c^2-22 b^2 c^4+16 c^6)+2 a^2 (6 b^8-20 b^6 c^2+3 b^4 c^4+18 b^2 c^6-7 c^8)).
W = ( 2 a^10-7 a^8 (b^2+c^2)+2 a^6 (5 b^4+18 b^2 c^2+5 c^4)-8 a^4 (b^6+b^4 c^2+b^2 c^4+c^6) +4 a^2 (b^2-c^2)^2 (b^4-4 b^2 c^2+c^4)-(b^2-c^2)^4 (b^2+c^2) : ... : ...),
que tiene números de búsqueda en (-13.6012455235066, -13.2487802883968, 19.0903949231853).El 19 de septiembre de 1888 nació James Waddell Alexander, matemático y topólogo estadounidense, que formó parte de la escuela de topología Princeton. Colaboró en los inicios de la teoría de nudos por la invención de la invariante de Alexander de un nudo. A partir de esta invariante, definió el primero de los invariantes de nudos polinomio. Hacia el final de su vida, Alejandro se convirtió en un recluso. Era conocido como socialista y su prominencia llamó la atención de los macartistas. La atmósfera de la era McCarthy lo empujó a un mayor aislamiento. No se le vio en público después de 1954, cuando apareció para firmar una carta apoyando a J. Robert Oppenheimer, físico teórico estadounidense de origen judío y profesor de física en la Universidad de California en Berkeley, que participó en el Proyecto Manhattan, el proyecto que consiguió desarrollar las primeras armas nucleares de la historia.
b^2 c^2 (b^2 - c^2) (a^4 (-2 b^4 + b^2 c^2 - 2 c^4) + a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2)-b^2 c^2 (b^2 - c^2)^2) x + ... = 0.
(b^2-c^2) (b^4 c^4 (b^2-c^2)^6 (b^6+c^6)-a^20 (b^6-2 b^4 c^2-2 b^2 c^4+c^6)+a^18 (6 b^8-6 b^6 c^2-19 b^4 c^4-6 b^2 c^6+6 c^8)+a^12 b^2 c^2 (-88 b^10+14 b^8 c^2+103 b^6 c^4+103 b^4 c^6+14 b^2 c^8-88 c^10)-a^16 (14 b^10+4 b^8 c^2-51 b^6 c^4-51 b^4 c^6+4 b^2 c^8+14 c^10)-2 a^2 b^2 c^2 (b^2-c^2)^4 (b^12+b^10 c^2-b^8 c^4+2 b^6 c^6-b^4 c^8+b^2 c^10+c^12)+a^14 (14 b^12+44 b^10 c^2-53 b^8 c^4-108 b^6 c^6-53 b^4 c^8+44 b^2 c^10+14 c^12)+a^4 (b^2-c^2)^4 (b^14+10 b^12 c^2+2 b^10 c^4-2 b^8 c^6-2 b^6 c^8+2 b^4 c^10+10 b^2 c^12+c^14)+a^8 (b^2-c^2)^2 (14 b^14-16 b^12 c^2-82 b^10 c^4-85 b^8 c^6-85 b^6 c^8-82 b^4 c^10-16 b^2 c^12+14 c^14)+a^10 (-14 b^16+88 b^14 c^2+17 b^12 c^4-64 b^10 c^6-62 b^8 c^8-64 b^6 c^10+17 b^4 c^12+88 b^2 c^14-14 c^16)+a^6 (-6 b^20+4 b^18 c^2+49 b^16 c^4-76 b^14 c^6+29 b^12 c^8+29 b^8 c^12-76 b^6 c^14+49 b^4 c^16+4 b^2 c^18-6 c^20))x + ... =0,
e interseca a la recta de Euler en:
W = ( 2 a^18 (b^2-c^2)^2
+a^16 (-9 b^6+13 b^4 c^2+13 b^2 c^4-9 c^6)
+a^14 (14 b^8-5 b^6 c^2-44 b^4 c^4-5 b^2 c^6+14 c^8)
-a^12 (5 b^10+30 b^8 c^2-47 b^6 c^4-47 b^4 c^6+30 b^2 c^8+5 c^10)
-a^10 (10 b^12-48 b^10 c^2+25 b^8 c^4+30 b^6 c^6+25 b^4 c^8-48 b^2 c^10+10 c^12)
+a^8 (b^2-c^2)^2 (13 b^10+3 b^8 c^2-19 b^6 c^4-19 b^4 c^6+3 b^2 c^8+13 c^10)
-a^6 (b^2-c^2)^2 (6 b^12+17 b^10 c^2-18 b^8 c^4+14 b^6 c^6-18 b^4 c^8+17 b^2 c^10+6 c^12)
+a^4 (b^2-c^2)^4 (b^10+12 b^8 c^2+9 b^6 c^4+9 b^4 c^6+12 b^2 c^8+c^10)
-a^2 b^2 c^2 (b^2-c^2)^4 (2 b^8+3 b^6 c^2-6 b^4 c^4+3 b^2 c^6+2 c^8)
+b^4 c^4 (b^2-c^2)^6 (b^2+c^2)
: ... : ...),
El 4 de septiembre de 1967 es la fecha oficial en la que se creó el grupo Les Luthiers, fundado por Gerardo Masana, Marcos Mundstock, Jorge Maronna y Daniel Rabinovich. Los espectáculos de Les Luthiers combinan parodias de géneros musicales clásicos y populares con escenas teatrales humorísticas cuidadosamente elaboradas y dotadas de múltiples sentido. Incorporan instrumentos inventados y construidos por sus propios integrantes, de ahí su nombre: la palabra francesa "luthier" designa a los artesanos encargados de construir instrumentos
Ab = (u ((a^2-c^2) v+b^2 (u-w)) : v ((a^2-c^2) v+b^2 (u-w)) : c^2 v^2+b^2 (u+v) w),
Ac = (u (c^2 (-u+v)+(-a^2+b^2) w) : -b^2 w^2-c^2 v (u+w) : w (c^2 (-u+v)+(-a^2+b^2) w)),
A' = (u (b^4 (u-w) w-(a^2-c^2) v (c^2 (u-v)+a^2 w)+b^2 (a^2 w (-u+v+w)+c^2 (-u^2-2 v w+u (v+w)))) :
b^4 w^2 (-u+w)+c^2 (-a^2+c^2) v^2 (u+w)-b^2 v (a^2 w^2+c^2 (u^2-2 w^2)):
c^4 v^2 (-u+v)-c^2 (a^2 v^2+b^2 (u^2-2 v^2)) w+b^2 (-a^2+b^2) (u+v) w^2).
a^2 b^2 x y-b^4 x y-2 a^2 c^2 x y+b^2 c^2 x y+a^4 y^2-a^2 b^2 y^2+a^2 c^2 y^2-a^2 b^2 x z-b^4 x z+b^2 c^2 x z-2 a^4 y z=0.
La cónica 𝒞a2 vuelve a corta a BC en D2=(0 : 2a^2 : a>^2 - b^2 + c^2).a^2 c^2 x y-b^2 c^2 x y+c^4 x y+2 a^2 b^2 x z-a^2 c^2 x z-b^2 c^2 x z+c^4 x z+2 a^4 y z-a^4 z^2-a^2 b^2 z^2+a^2 c^2 z^2=0.
La cónica 𝒞a3 vuelve a corta a BC en D3=(0 : a^2 + b^2 - c^2 : 2a^2).El 30 de agosto de 1871 nació Ernest Rutherford, físico y químico neozelandés. Premio Nobel de Química en 1908 en reconocimiento a sus investigaciones relativas a la desintegración de los elementos. Estudió las emisiones radioactivas descubiertas por H. Becquerel, y logró clasificarlas en rayos alfa, beta y gamma. En 1911, describió un nuevo modelo atómico (modelo atómico de Rutherford), que posteriormente sería perfeccionado por N. Bohr. Durante la Primera Guerra Mundial estudió la detección de submarinos mediante ondas sonoras, de modo que fue uno de los precursores del sonar.
El 26 de agosto de 1964 muere, a los 86 años, Sixto Cámara Tecedor matemático español. En 1911 colabora en la fundación de la Sociedad Matemática Española, de la que llegó a ser secretario en 1914, bajo la presidencia del ingeniero matemático y autor de melodramas José Echegaray. Entre sus obras cabe destacar: Elementos de Geometría Analítica (1941).
𝔖abc xyz
(-a^2 q r+c^2 q (q+r)+b^2 r (q+r)) (b^4 r (-p^3-2 p^2 (q+r)+2 p r (q+r)+q (q+r)^2)+q (a^4 r (q^2-q r+r^2+p (q+r))+c^4 (-p^3-2 p^2 (q+r)+2 p q (q+r)+r (q+r)^2)+a^2 c^2 (p^3+p^2 (3 q+2 r)+2 r (q^2-r^2)+p (2 q^2-q r-r^2)))+b^2 (a^2 r (p^3-2 q^3+2 q r^2+p^2 (2 q+3 r)-p (q^2+q r-2 r^2))+c^2 (p^4+p^3 (q+r)-2 p^2 (q+r)^2-2 q r (q+r)^2-2 p (q^3+q^2 r+q r^2+r^3))))x^2
+a^6 q r (3 p^4+7 p^3 (q+r)+5 p^2 (q^2+4 q r+r^2)+2 q r (q^2+5 q r+r^2)+p (q^3+15 q^2 r+15 q r^2+r^3))+p^2 (b^6 r (p^3-q^3+p^2 (q-3 r)+q^2 r+3 q r^2+r^3-p (q^2+2 q r-3 r^2))+c^6 q (p^3+q^3+3 q^2 r+q r^2-r^3+p^2 (-3 q+r)+p (3 q^2-2 q r-r^2))+b^4 c^2 (q^4+5 q^3 r-q^2 r^2-7 q r^3-2 r^4+p^3 (3 q+4 r)+p^2 (7 q^2+q r-2 r^2)+p (5 q^3+2 q^2 r+q r^2-8 r^3))+b^2 c^4 (-2 q^4-7 q^3 r-q^2 r^2+5 q r^3+r^4+p^3 (4 q+3 r)+p^2 (-2 q^2+q r+7 r^2)+p (-8 q^3+q^2 r+2 q r^2+5 r^3)))+a^2 p (b^4 r (-2 p^4+q^4+7 q^3 r+5 q^2 r^2-3 q r^3-2 r^4+p^3 (q+4 r)+p^2 (9 q^2+3 q r+4 r^2)+p (7 q^3+6 q^2 r+9 q r^2-4 r^3))+c^4 q (-2 p^4-2 q^4-3 q^3 r+5 q^2 r^2+7 q r^3+r^4+p^3 (4 q+r)+p^2 (4 q^2+3 q r+9 r^2)+p (-4 q^3+9 q^2 r+6 q r^2+7 r^3))-2 b^2 c^2 (-q^5-q^4 r+6 q^3 r^2+6 q^2 r^3-q r^4-r^5+2 p^4 (q+r)+3 p^3 (q^2+r^2)-p^2 (q^3-5 q^2 r-5 q r^2+r^3)+p (-3 q^4+6 q^3 r+4 q^2 r^2+6 q r^3-3 r^4)))+a^4 (-b^2 r (-p^5+p^4 (5 q+r)+p^3 (15 q^2+8 q r+7 r^2)+2 q r (q^3+5 q^2 r+6 q r^2+2 r^3)+p^2 (11 q^3+27 q^2 r+17 q r^2+7 r^3)+2 p (q^4+11 q^3 r+10 q^2 r^2+9 q r^3+r^4))-c^2 q (-p^5+p^4 (q+5 r)+p^3 (7 q^2+8 q r+15 r^2)+2 q r (2 q^3+6 q^2 r+5 q r^2+r^3)+p^2 (7 q^3+17 q^2 r+27 q r^2+11 r^3)+2 p (q^4+9 q^3 r+10 q^2 r^2+11 q r^3+r^4)))y z = 0.
W = ( a (5 a^2 - 2 a (b + c)+ b^2 - 6 b c + c^2) : ... : ...),
que tiene números de búsqueda en (14.1563337667027, 5.28221409205323, -6.54994547414600).U1, U2 ( a (b-c) (a^2-b c±Sqrt[b^2 c^2-a b c (b+c)+a^2 (b^2-b c+c^2)]) : ... : ...),
que tienen números de búsqueda en ETC (-2.08691289941282, -8.18006199222680, 10.2669748916396) y (-10.9526098878272, 7.33490773749828, 3.61770215032887), respectivamente.𝔖abc xyz y z ((3 a^4+2 b^4+2 c^4+a^2 (-5 b^2-5 c^2)) x^2+2 a^2 (2 a^2-b^2-c^2) y z-a^2 ((a^2-b^2+3 c^2) y^2+(a^2+3 b^2-c^2) z^2)) = 0.
La cuártica 𝒬 pasa por el foco de la y las tangentes en los vértices de ABC son perpendiculares a las .El 24 de agosto de 1670 falleció, cuando solo tenía 32 años, el matemático inglés William Neile. Calculó en 1657 la longitud del arco de la parábola semicúbica (y2=a2 x3), hoy conocida como parábola de Neile. Aunque las longitudes de algunas otras curvas no algebraicas, incluidas la espiral logarítmica y la cicloide, ya se habían calculado (es decir, estas curvas se rectificaron), la parábola semicúbica fue la primera curva algebraica (excluyendo la línea y el círculo) en ser rectificada. Una propiedad adicional de la parábola semicúbica es que es una curva isócrona, lo que significa que una partícula que sigue su camino mientras es atraida hacia abajo por la gravedad viaja a intervalos verticales iguales en períodos de tiempo iguales.
AB'a/AC = AC'a/AB = t.
Similarmente, se consideran los puntos C'b, A'c sobre BA, BC, respectivamente, tales que BC'b/BA = BA'b/BC = t, y los puntos A'c, B'c on CB, CA, resp such that CA'c/CB = CB'c/CA = t.El lugar gemétrico del punto de concurrencia, cuando t varía, es la .
(a^2 + b^2 - c^2) (a^4 t + (b^2 - c^2)^2 t +
2 a^2 (c^2 - b^2 t)) y
- (a^2 - b^2 +
c^2) (a^4 t + (b^2 - c^2)^2 t + 2 a^2 (b^2 - c^2 t)) z = 0.
Pt = ((a^2-b^2-c^2) (-2 a^6 (b^2+c^2) (-1+t) t-2 a^2 (b^2-c^2)^2 (b^2+c^2) (-1+t) t+a^8 t^2+(b^2-c^2)^4 t^2+2 a^4 (2 b^2 c^2+b^4 (-2+t) t+c^4 (-2+t) t)):
-(a^2-b^2+c^2) (a^8 t^2-2 a^6 t (b^2 (-1+t)+2 c^2 t)+(b^2-c^2)^2 t (2 b^2 c^2+b^4 t+c^4 t)+2 a^4 t (b^4 (-2+t)+b^2 c^2 (-1+t)+3 c^4 t)-2 a^2 (-2 b^4 c^2+b^6 (-1+t) t-b^2 c^4 (-1+t) t+2 c^6 t^2)) :
-(a^2+b^2-c^2) (a^8 t^2-2 a^6 t (c^2 (-1+t)+2 b^2 t)+2 a^4 t (c^4 (-2+t)+b^2 c^2 (-1+t)+3 b^4 t)+(b^2-c^2)^2 t (2 b^2 c^2+b^4 t+c^4 t)-2 a^2 (-2 b^2 c^4-b^4 c^2 (-1+t) t+c^6 (-1+t) t+2 b^6 t^2)),
Bao = (-(a^2 - b^2 + c^2) (2 a^8 - (b^2 - c^2)^3 (2 b^2 + c^2) -
a^6 (3 b^2 + 7 c^2) + a^4 (-2 b^4 + 3 b^2 c^2 + 9 c^4) +
a^2 (5 b^6 - b^4 c^2 + b^2 c^4 - 5 c^6)) :
-b^2 (-a^8 +
c^2 (b^2 - c^2)^3 + a^6 (3 b^2 + 2 c^2) -
a^4 (3 b^4 + 3 b^2 c^2 + 2 c^4) +
a^2 (b^6 - 3 b^2 c^4 + 2 c^6)) :
c^2 (a^8 -
a^2 (b^2 - 2 c^2) (b^2 - c^2)^2 + c^2 (b^2 - c^2)^3 -
a^6 (3 b^2 + 2 c^2) + a^4 (3 b^4 + 5 b^2 c^2))).
Cao = (-(a^2+b^2-c^2) (2 a^8+(b^2-c^2)^3 (b^2+2 c^2)-a^6 (7 b^2+3 c^2)+a^4 (9 b^4+3 b^2 c^2-2 c^4)+a^2 (-5 b^6+b^4 c^2-b^2 c^4+5 c^6)) :
b^2 (a^8-b^2 (b^2-c^2)^3+a^2 (b^2-c^2)^2 (2 b^2-c^2)-a^6 (2 b^2+3 c^2)+a^4 (5 b^2 c^2+3 c^4)) :
-c^2 (-a^8-b^2 (b^2-c^2)^3+a^6 (2 b^2+3 c^2)-a^4 (2 b^4+3 b^2 c^2+3 c^4)+a^2 (2 b^6-3 b^4 c^2+c^6))).
∗ ∗ ∗ ∗ ∗
∗ ∗ ∗ ∗ ∗
B'ao = ((a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^6-5 a^4 (b^2+c^2)-(b^2-c^2)^2 (b^2+c^2)+2 a^2 (2 b^4+b^2 c^2+2 c^4)) :
b^2 (a^2+b^2-c^2) (-a^2+b^2+c^2) (a^4-2 a^2 b^2+(b^2-c^2)^2) :
c^2 (-a^8-6 a^4 b^2 (b^2+c^2)-(b^2-c^2)^3 (b^2+c^2)+2 a^6 (2 b^2+c^2)+a^2 (4 b^6-6 b^4 c^2+4 b^2 c^4-2 c^6))).
C'ao = ((a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^6-5 a^4 (b^2+c^2)-(b^2-c^2)^2 (b^2+c^2)+2 a^2 (2 b^4+b^2 c^2+2 c^4)) :
b^2 (-a^8-6 a^4 c^2 (b^2+c^2)+(b^2-c^2)^3 (b^2+c^2)+2 a^6 (b^2+2 c^2)-2 a^2 (b^6-2 b^4 c^2+3 b^2 c^4-2 c^6)) :
c^2 (a^2-b^2+c^2) (-a^2+b^2+c^2) (a^4-2 a^2 c^2+(b^2-c^2)^2)).
A' = (a^8 (b^2+c^2)-4 a^4 b^2 c^2 (b^2+c^2)-(b^2-c^2)^4 (b^2+c^2)+2 a^2 (b^4-c^4)^2-2 a^6 (b^4+c^4) :
a^10-a^8 (4 b^2+3 c^2)+(b^2-c^2)^3 (2 b^4+b^2 c^2-c^4)+2 a^6 (2 b^4+3 b^2 c^2+c^4)+2 a^4 (b^6-2 b^4 c^2-2 b^2 c^4+c^6)+a^2 (-5 b^8+6 b^6 c^2-4 b^4 c^4+6 b^2 c^6-3 c^8) :
&esmp;
a^10-a^8 (3 b^2+4 c^2)+(b^2-c^2)^3 (b^4-b^2 c^2-2 c^4)+2 a^6 (b^4+3 b^2 c^2+2 c^4)+2 a^4 (b^6-2 b^4 c^2-2 b^2 c^4+c^6)+a^2 (-3 b^8+6 b^6 c^2-4 b^4 c^4+6 b^2 c^6-5 c^8)).
𝔖abc xyz (-a^2 + b^2 + c^2) ((2 b^18 - 13 b^16 c^2 + 35 b^14 c^4 - 47 b^12 c^6 + 23 b^10 c^8 + 23 b^8 c^10 - 47 b^6 c^12 + 35 b^4 c^14 - 13 b^2 c^16 + 2 c^18 + a^16 (b^2 + c^2) + a^14 (-5 b^4 - 11 b^2 c^2 - 5 c^4) + a^12 (7 b^6 + 32 b^4 c^2 + 32 b^2 c^4 + 7 c^6) + a^10 (3 b^8 - 37 b^6 c^2 - 56 b^4 c^4 - 37 b^2 c^6 + 3 c^8) + a^8 (-15 b^10 + 16 b^8 c^2 + 27 b^6 c^4 + 27 b^4 c^6 + 16 b^2 c^8 - 15 c^10) + a^6 (9 b^12 + 11 b^10 c^2 - 25 b^8 c^4 + 10 b^6 c^6 - 25 b^4 c^8 + 11 b^2 c^10 + 9 c^12) + a^4 (5 b^14 - 36 b^12 c^2 + 82 b^10 c^4 - 51 b^8 c^6 - 51 b^6 c^8 + 82 b^4 c^10 - 36 b^2 c^12 + 5 c^14) + a^2 (-7 b^16 + 37 b^14 c^2 - 90 b^12 c^4 + 139 b^10 c^6 - 158 b^8 c^8 + 139 b^6 c^10 - 90 b^4 c^12 + 37 b^2 c^14 - 7 c^16)) x^2 - 2 (b^18 - 8 b^16 c^2 + 25 b^14 c^4 - 37 b^12 c^6 + 19 b^10 c^8 + 19 b^8 c^10 - 37 b^6 c^12 + 25 b^4 c^14 - 8 b^2 c^16 + c^18 + a^16 (2 b^2 + 2 c^2) + a^14 (-7 b^4 - 13 b^2 c^2 - 7 c^4) + a^12 (5 b^6 + 22 b^4 c^2 + 22 b^2 c^4 + 5 c^6) + a^10 (9 b^8 - 17 b^6 c^2 - 28 b^4 c^4 - 17 b^2 c^6 + 9 c^8) + a^8 (-15 b^10 + 14 b^8 c^2 + 21 b^6 c^4 + 21 b^4 c^6 + 14 b^2 c^8 - 15 c^10) + a^6 (3 b^12 + b^10 c^2 - 11 b^8 c^4 + 14 b^6 c^6 - 11 b^4 c^8 + b^2 c^10 + 3 c^12) + a^4 (7 b^14 - 30 b^12 c^2 + 44 b^10 c^4 - 21 b^8 c^6 - 21 b^6 c^8 + 44 b^4 c^10 - 30 b^2 c^12 + 7 c^14) + a^2 (-5 b^16 + 29 b^14 c^2 - 66 b^12 c^4 + 83 b^10 c^6 - 82 b^8 c^8 + 83 b^6 c^10 - 66 b^4 c^12 + 29 b^2 c^14 - 5 c^16)) y z = 0,
cuyo centro es el punto medio de X2 y X24:W = ( 4 a^10-9 a^8 (b^2+c^2)+2 a^6 (b^4+6 b^2 c^2+c^4)+4 a^4 (2 b^6-3 b^4 c^2-3 b^2 c^4+2 c^6)-6 a^2 (b^2-c^2)^2 (b^4+c^4)+(b^2-c^2)^4 (b^2+c^2) : ... : ...),
que tiene números de búsqueda en (2.11026735344037, 1.23518049198081, 1.81156997817903).El 21 de Agosto del 2012, falleció, a los 65 años, William Paul Thurston, matemático estadounidense Estas son unas palabras suyas: "No lo hago por el resultado final. La fuerza interior que impulsa a los matemáticos no es la búsqueda de aplicaciones, sino comprender la estructura y la belleza interior de las matemáticas mismas". Thurston recibió la Medalla Fields en el Congreso Internacional de Matemáticos en Varsovia en 1983 por su trabajo en la topología de dos y tres dimensiones. Las Notas de Thurston [http://www.msri.org/publications/books/gt3m/] son las notas que escribió Thurston para los seminarios que impartió en la Universidad de Princeton (1976-1981) sobre geometría y topología de variedades de dimensión tres.
In a triangle ABC, the common internal tangents of the incircle and the A-excircle touch them in four concyclic points. Let Γa be the circle through these touchpoints. Build Γb and Γc cyclically. X(3057) is the radical center of circles Γa, Γb, Γc. (Randy Hutson, June 27, 2018)
Let be the excentral triangle. X(3057) is the radical center of the of triangles A'BC, B'CA, C'AB. (Randy Hutson, June 27, 2018)
W = ( a (a^9-9 a^5 b (b-c)^2 c-a^6 b c (b+c)-b (b-c)^4 c (b+c)^3+a^7 (-2 b^2+9 b c-2 c^2)+3 a^4 b c (3 b^3-7 b^2 c-7 b c^2+3 c^3)-a (b^2-c^2)^2 (b^4-b^3 c+12 b^2 c^2-b c^3+c^4)-a^2 b c (7 b^5-5 b^4 c+30 b^3 c^2+30 b^2 c^3-5 b c^4+7 c^5)+a^3 (2 b^6-b^5 c-22 b^4 c^2+58 b^3 c^3-22 b^2 c^4-b c^5+2 c^6)) : ... : ...),
que tiene números de búsqueda en (3.14737297491916, 2.98666262486684, 0.120341291652340).a Clara, por su "cumple"
A'=BC∩AbAc, B'=CA∩BcBa, C'=AB∩CaCb.
Los puntos A', B', C' están alineados en la del , X2052, del , X577, del circuncentro.W = ( b^2 c^2 (a^4-(b^2-c^2)^2)^2 (a^6 (b^2+c^2)+a^4 (-2 b^4+b^2 c^2-2 c^4)+a^2 (b^2-c^2)^2 (b^2+c^2)-b^2 c^2 (b^2-c^2)^2) : ... : ...),
que tiene números de búsqueda en (-1.15533135169705, -0.591435591258595, 4.58334974586974).El 14 de agosto de 1084 el Cid, al mando del ejército de la Taifa de Zaragoza, gobernado por Al-Mu’tamin, vence a la coalición del rey Al-Mundir de Lérida y Sancho Ramírez de Aragón en la Batalla de Morella. Tras ser desterrado por Alfonso VI, el Cid había pasado al servicio de al-Muqtadir, padre de Al-Mu’tamin. A al-Mu’tamín se debe la primera formulación conocida del teorema de Ceva, que no sería conocido en Europa hasta 1678 en la obra De lineis rectis del geómetra italiano Giovanni Ceva.
X(759) is Ψ(X(6), X(661)), i.e. X(759) is the point where the line that passes through X(2) ( of X(6)) and through the isogonal conjugate of the point of infinity of line X(6)X(661) intersects again at the circumcircle.
Las rectas AA2, BB2 y CC2 concurren en X661.
Bb=(-a^2 - b^2 + c^2 : 0 : (a - c) (a + c)),
Bc=(-a : a - c : 0),
B'c=(-a : a + c : 0),
Cc=(-a^2 + b^2 - c^2 : (a - b) (a + b) : 0),
Cb=(-a : 0 : a - b),
C'b=(-a : 0 : a + b).
A1=(a^2 b c+a^3 (b+c)+(b^2-c^2)^2 :-b (a^3+b^3-a c^2-b c^2):-c (a^3-a b^2-b^2 c+c^3)),
A2=({a^2 (b - c) : b (-a^2 + c^2) : c(a^2 - b^2)).
El 6 de agosto 1925 falleció (a los 72 años) Gregorio Ricci-Curbastro matemático italiano. En el trabajo "Méthodes de calcul différentiel absolu et leurs aplicaciones", publicado conjuntamente con Tullio Levi-Civita en 1900, Ricci introdujo una exposición sistemática sobre lo que llamó "cálculo diferencial absoluto". Las ideas de Ricci fueron una inspiración importante para Albert Einstein en su trabajo en relatividad general. El tensor de Ricci aparece en las Ecuaciones de Einstein.
((a^2+b^2-c^2) (a^2-b^2+c^2) (b^2+c^2) : b^6+4 a^2 c^4+b^2 c^4-2 c^6-a^4 (b^2+2 c^2) : 4 a^2 b^4-2 b^6+b^4 c^2+c^6-a^4 (2 b^2+c^2)).
El 4 de agoato de 1874 falleció, a los 63 años de edad, Ludwig Otto Hesse, matemático alemán. Trabajó en la teoría de invariantes y estudio curvas de tercer y cuarto grado. La matriz hessiana (matriz cuadrada formada por las segundas derivadas parciales de una función escalar) y la forma normal de Hesse (de una recta, plano o hiperplano) son nombrados en su honor.
Ab = (u((b^2-c^2)u+a^2(u+2v)) : v((b^2-c^2)u+a^2(u+2v)) : -u(c^2(-u+v)+a^2(u+v)-b^2(u+v))),
Ac = (u((-b^2+c^2)u+a^2(u+2 w)) : -u(b^2(-u+w)+a^2 (u+w)-c^2(u+w)) : w((-b^2+c^2)u+a^2(u+2w)).
(a^6 (u+v) (v-w) (u+w)+(b^2-c^2)^3 u^2 (u+v+w)-a^4 (c^2 (u^3+u^2 (2 v-w)-2 u w^2-v w (v+w))+b^2 (-u^3+2 u v^2+u^2 (v-2 w)+v w (v+w)))-a^2 (b^2-c^2) u (c^2 (2 u^2+v^2-w^2+u (2 v+w))+b^2 (2 u^2-v^2+w^2+u (v+2 w)))) x -
-a^2 ((b^2-c^2) u+a^2 (u+2 v)) (-b^2 u w+c^2 u (u+w)+a^2 w (u+w)) y +
a^2 (-c^2 u v+b^2 u (u+v)+a^2 v (u+v)) ((-b^2+c^2) u+a^2 (u+2 w)) z = 0.
𝔖abc xyz (-b^4+c^4+a^2 (b^2-c^2))^2 (-4 a^2 (b^2-c^2)^4 (b^2+c^2)-4 a^6 (b^2+c^2)^3+(b^2-c^2)^4 (b^4+6 b^2 c^2+c^4)+a^8 (b^4+14 b^2 c^2+c^4)+2 a^4 (3 b^8-8 b^6 c^2+18 b^4 c^4-8 b^2 c^6+3 c^8))x^2-2 (a^2-b^2) (a^2-c^2) (a^16-b^2 c^2 (b^2-c^2)^6-a^14 (b^2+c^2)+15 a^10 (b^2-c^2)^2 (b^2+c^2)+a^12 (-7 b^4+15 b^2 c^2-7 c^4)-a^8 (b^2-c^2)^2 (5 b^4+41 b^2 c^2+5 c^4)+a^4 (b^2-c^2)^4 (11 b^4+29 b^2 c^2+11 c^4)-a^2 (b^2-c^2)^4 (3 b^6+13 b^4 c^2+13 b^2 c^4+3 c^6)-a^6 (b^2-c^2)^2 (11 b^6-27 b^4 c^2-27 b^2 c^4+11 c^6))y z = 0,
de foco X1304 (punto de intersección de las circunferencias (AB'C'), (BC'A'), (CA'B'), siendo A', B', C' los puntos de intersección de la recta de Euler con los lados BC, CA, AB, respectivamente. Randy Hutson, Feb. 10, 2016) y directriz la recta que pasa por la reflexión, X107, de su foco en la recta de Euler, y por el foco de la parábola de Kiepert. X110.
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𝔖abc xyz (b^2-c^2) (a^20-7 a^18 (b^2+c^2)-(b^2-c^2)^6 (b^2+c^2)^2 (2 b^4-b^2 c^2+2 c^4)+a^16 (18 b^4+31 b^2 c^2+18 c^4)-4 a^14 (3 b^6+7 b^4 c^2+7 b^2 c^4+3 c^6)-a^12 (42 b^8+82 b^6 c^2+97 b^4 c^4+82 b^2 c^6+42 c^8)+a^2 (b^2-c^2)^4 (17 b^10+25 b^8 c^2+16 b^6 c^4+16 b^4 c^6+25 b^2 c^8+17 c^10)+a^10 (126 b^10+226 b^8 c^2+269 b^6 c^4+269 b^4 c^6+226 b^2 c^8+126 c^10)-a^4 (b^2-c^2)^2 (63 b^12+68 b^10 c^2+33 b^8 c^4+23 b^6 c^6+33 b^4 c^8+68 b^2 c^10+63 c^12)-a^8 (168 b^12+208 b^10 c^2+191 b^8 c^4+189 b^6 c^6+191 b^4 c^8+208 b^2 c^10+168 c^12)+a^6 (132 b^14+44 b^12 c^2-15 b^10 c^4+b^8 c^6+b^6 c^8-15 b^4 c^10+44 b^2 c^12+132 c^14))x^2 + 2 (b^2-c^2) (a^20-6 a^18 (b^2+c^2)+(b^2-c^2)^8 (b^4+b^2 c^2+c^4)+5 a^16 (3 b^4+5 b^2 c^2+3 c^4)-8 a^2 (b^2-c^2)^6 (b^6+b^4 c^2+b^2 c^4+c^6)-2 a^14 (11 b^6+23 b^4 c^2+23 b^2 c^4+11 c^6)+a^12 (28 b^8+60 b^6 c^2+71 b^4 c^4+60 b^2 c^6+28 c^8)-2 a^10 (21 b^10+29 b^8 c^2+29 b^6 c^4+29 b^4 c^6+29 b^2 c^8+21 c^10)-2 a^6 (b^2-c^2)^2 (25 b^10+15 b^8 c^2+9 b^6 c^4+9 b^4 c^6+15 b^2 c^8+25 c^10)+a^4 (b^2-c^2)^2 (27 b^12-30 b^10 c^2-2 b^8 c^4+9 b^6 c^6-2 b^4 c^8-30 b^2 c^10+27 c^12)+a^8 (56 b^12+6 b^10 c^2+5 b^6 c^6+6 b^2 c^10+56 c^12))y z = 0,
que pasa por X5, X143, X5944, X6343, X10285, X27683, X27684.El 3 de agosto de 1917 falleció (a los 67 años) Ferdinand Georg Frobenius, matemático alemán reconocido por sus aportes a la teoría de las ecuaciones diferenciales y a la teoría de grupos. Fue profesor en la Universidad de Berlín. Exigía un nivel muy alto, sospechaba a cada oportunidad que el gobierno trataba de bajar el nivel académico. Se consideraba un profesor cuya obligación era contribuir al conocimiento de las matemáticas puras. La matemática aplicada, en su opinión pertenecía a las escuelas técnicas. El punto de vista de la universidad de Göttingen era muy diferente. El 'Método de Frobenius', que se debe a él, es una forma de hallar una solución expresada como serie infinita para una ecuación diferencial ordinaria de segundo orden de cierto tipo.
D' = (u (c^2 (a^2-c^2) v-b^4 w+b^2 (a^2 w+c^2 (2 u+v+w))) : -b^2 (-a^2+b^2-c^2) v w : -c^2 (-a^2-b^2+c^2) v w).
Q = a^2 u (-a^6 v w (c^2 v (u + 3 v + w) + b^2 w (u + v + 3 w)) +
a^4 (-c^4 v^2 (u - 2 w) (u + 3 v + w) -
b^4 (u - 2 v) w^2 (u + v + 3 w) +
b^2 c^2 v w (-u^2 - 5 u (v + w) + 2 (v + w)^2)) +
a^2 (c^6 v^2 (2 u - w) (u + 3 v + w) +
b^6 (2 u - v) w^2 (u + v + 3 w) +
b^4 c^2 w (-2 u^2 (v + w) + v (v^2 + v w + 2 w^2) +
u (5 v^2 + 14 v w + 2 w^2)) +
b^2 c^4 v (-2 u^2 (v + w) + w (2 v^2 + v w + w^2) +
u (2 v^2 + 14 v w + 5 w^2))) +
u (-c^8 v^2 (u + 3 v + w) - b^8 w^2 (u + v + 3 w) +
b^2 c^6 v (2 v^2 - v w + w^2 + 3 u (2 v + w)) +
b^6 c^2 w (v^2 - v w + 2 w^2 + 3 u (v + 2 w)) +
b^4 c^4 (v^3 + v^2 w + v w^2 + w^3 +
u (3 v^2 + 10 v w + 3 w^2)))) : ... : ...
Un aniversario de importante significado personal
(a^4 (b^2 - c^2)^2 - (b^2 - c^2)^4 - a^6 (b^2 + c^2) +
a^2 (b^2 - c^2)^2 (b^2 + c^2) :
a^6 (b^2 + 2 c^2) + (b^2 - c^2)^3 (b^2 + 2 c^2) -
a^4 (b^4 + b^2 c^2 + 6 c^4) - a^2 (b^6 + 5 b^2 c^4 - 6 c^6) :
a^6 (2 b^2 + c^2) - (b^2 - c^2)^3 (2 b^2 + c^2) -
a^4 (6 b^4 + b^2 c^2 + c^4) - a^2 (-6 b^6 + 5 b^4 c^2 + c^6)).
(b^2 - c^2) (a^6 - a^2 (b^2 - c^2)^2 - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2))x + (-a^6 (b^2 + c^2) + (b^2 - c^2)^3 (3 b^2 + c^2) + a^4 (5 b^4 + 2 b^2 c^2 + c^4) + a^2 (-7 b^6 + 7 b^4 c^2 - b^2 c^4 + c^6))y + (a^6 (b^2 + c^2) + (b^2 - c^2)^3 (b^2 + 3 c^2) - a^4 (b^4 + 2 b^2 c^2 + 5 c^4) + a^2 (-b^6 + b^4 c^2 - 7 b^2 c^4 + 7 c^6))z = 0.
El 1 de agosto de 1744 nació el naturalista francés Jean Baptiste de Monet, quien estudiará la evolución zoológica fundamentándola en el principio de adaptación al medio ambiente y la herencia de caracteres adquiridos. Influirá a Charles Darwin en su teoría de selección natural.
D' = (a^2 u : (-b^2 + c^2) u + a^2 (-u + v) : (b^2 - c^2) u + a^2 (-u + w)).
El 30 de julio de 2007 falleció (a los 89 años) Ingmar Bergman, guionista y director de teatro y cine sueco. Con la comedia "Sonrisas de una noche de verano", el nombre de Bergman empezó a ser internacionalmente conocido. El cine de Bergman destaca por su gran sentido plástico, casi pictórico, y el aprovechamiento de las posibilidades del blanco y negro. Sus filmes giran en torno de una serie de constantes temáticas, en especial la muerte y el amor, abordados con un tono metafísico y una densidad de diálogos motivada por sus inicios en el teatro. Entre sus películas estan: ‘Un verano con Mónica’ (1953), ‘Sonrisas de una noche de verano’ (1955), ‘El séptimo sello’ (1957), ‘Fresas salvajes’ (1957). ‘El manantial de la doncella’ (1960), ‘La hora del lobo’ (1968) ‘Gritos y susurros’ (1972), ‘Secretos de un matrimonio’ (1974), 'Sonata de otoño' (1978), ‘Fanny y Alexander’ (1982),
a^14 (x+y) (x+z)
-a^12 (c^2 (3 x+2 y-2 z) (x+z)+b^2 (x+y) (3 x-2 y+2 z))
-a^10 (b^4 (x+y) (x+5 (2 y+z))+c^4 (x+z) (x+5 (y+2 z))-2 b^2 c^2 (9 x^2+10 x (y+z)+3 (y^2+3 y z+z^2)))
+a^8 (-b^2 c^4 (23 x^2+29 x y+12 y^2+26 x z+20 y z+8 z^2)-b^4 c^2 (23 x^2+26 x y+8 y^2+29 x z+20 y z+12 z^2)+5 b^6 (x+y) (3 x+4 (y+z))+5 c^6 (x+z) (3 x+4 (y+z)))
-a^6 (b^2-c^2) (-5 c^6 (x+z) (5 x+5 y+4 z)+5 b^6 (x+y) (5 x+4 y+5 z)+b^4 c^2 (37 x^2+69 x y+32 y^2+57 x z+53 y z+20 z^2)-b^2 c^4 (37 x^2+57 x y+20 y^2+69 x z+53 y z+32 z^2))
+a^4 (b^2-c^2)^2 (c^6 (x+z) (19 x+14 y+10 z)+b^6 (x+y) (19 x+10 y+14 z)+b^4 c^2 (77 x^2+116 x y+44 y^2+113 x z+82 y z+42 z^2)+b^2 c^4 (77 x^2+113 x y+42 y^2+116 x z+82 y z+44 z^2))
-a^2 (b^2-c^2)^2 (c^8 (x+z) (7 x+3 y+2 z)+b^8 (x+y) (7 x+2 y+3 z)+2 b^2 c^6 (18 x^2+29 x y+9 y^2+23 x z+14 y z+7 z^2)+2 b^6 c^2 (18 x^2+23 x y+7 y^2+29 x z+14 y z+9 z^2)+2 b^4 c^4 (21 x^2+38 x (y+z)+3 (5 y^2+11 y z+5 z^2)))
+(b^2-c^2)^4 x (b^6 (x+y)+c^6 (x+z)+b^2 c^4 (7 x+9 y+6 z)+b^4 c^2 (7 x+6 y+9 z)) = 0.
A' = (a^10-6 a^6 (b^2-c^2)^2+8 a^4 (b^2-c^2)^2 (b^2+c^2)-a^2 (b^2-c^2)^2 (3 b^4+10 b^2 c^2+3 c^4):
-(a^4-3 b^4+2 b^2 c^2+c^4+2 a^2 (b^2-c^2)) (a^6-a^4 (2 b^2+c^2)+(-b^2 c+c^3)^2+a^2 (b^4+4 b^2 c^2-c^4)):
-(a^4+b^4+2 b^2 c^2-3 c^4-2 a^2 (b^2-c^2)) (a^6-a^4 (b^2+2 c^2)+(b^3-b c^2)^2+a^2 (-b^4+4 b^2 c^2+c^4)).
X2883 = ( : ... : ...).
El 27 de julio de 1844 falleció en Manchester (a los 77 años) John Dalton, químico y matemático inglés, estudioso de la enfermedad de la visión que padecía, defecto genético consistente en la imposibilidad de distinguir los colores, conocida también como acromatopsia y más tarde llamada daltonismo en su honor.
𝔖abc xyz b^4 (b-c)^4 c^4 (b+c)^4 (a^2-b^2-c^2) x^2+2 a^6 (a-b)^2 b^2 (a+b)^2 (a-c)^2 c^2 (a+c)^2 y z = 0.
*** center of 𝒞:Ta = (a^2 v w : -a^2 v w + c^2 v (v + w) : -a^2 v w + b^2 w (v + w)).
Los puntos Tb y Tc se determinan cíclicamente.
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𝔖abc xyz y z (2 b^2 c^2 (-a^2+b^2+c^2) x^3-a^2 (-b^4+2 b^2 c^2-c^4+a^2 (b^2+c^2)) x y z-a^2 (b^2-c^2) y z ((a^2-b^2+c^2) y+(-a^2-b^2+c^2) z)) = 0,
que tiene cuatro puntos dobles: A, B, C (nodales) y H (acnodal). Pasa por los pies de las alturas.
A' = (a^2 (-c^2 v^2+b^2 (u+v)^2) (b^2 w^2-c^2 (u+w)^2)+b^2 c^2 u^2 (u+v+w) (b^2 (u+v-w)+c^2 (u-v+w)):
-b^2 (c^4 u^2 v^2+a^2 b^2 (u+v)^2 w^2-c^2 (b^2 u^2+a^2 v^2) w^2):
-c^2 (b^2 u^2 (-c^2 v^2+b^2 w^2)+a^2 v^2 (-b^2 w^2+c^2 (u+w)^2))).
W = (a^2/(a^4 v^2 w^2 - a^2 u^2 (c^2 v^2 + b^2 w^2) + b^2 c^2 u^2 (v + w)^2) : ... : ...).
Si U está en la circunferencia circunscrita, también W=τ(U) está sobre esta circunferencia. Se denota por U' y W' los puntos diametralmente opuestos a U y a W, respectivamente. Sean U*, U'*, W*, W'* sus conjugados isogonales (en la recta del infinito). Se tiene que:W = τ(U) = τ(U'), W'* = τ(U*) = τ(U'*).
En este caso, W es el SR(U,U') (único punto sobre la circunferencia circunscrita tal que su sW es perpendicular a UU'), es la reflexión de H en el punto RS(U,U') (intersección de las rectas de Simson de U y U', que por ser diametralmente opuestos, está en la ).
∗ ∗ ∗ ∗ ∗
∗ ∗ ∗ ∗ ∗
Q106 is a bicircular curve of degree 10. It has 6 real asymptotes namely the parallels at X(5562) to the cevian lines of O and the parallels at X(5) to the asymptotes of the McCay cubic.
Q106 meets the circumcircle (O) at 20 points namely the vertices of ABC (each counting for 4), the circular points at infinity (each counting for 2), X(953) and its extraversions labelled X953a, X953b, X953c.
The orthocenter H = X(4) is a quadruple point on the curve. Q106 has 8 other double points namely :
El 23 de julio de 1912 nació Rafael Artzy, quién participó activamente en el movimiento zionista con anterioridad a 1933. No pudo finalizar su tesis con Kurt Reidemeister en Königsberg debido al cese de este en 1933. Emigró a Palestina, y residió temporalmente en EE.UU, y finalmente estableció su residencia en Haifa (Israel). A finales de la década de 1970 fundó una conferencia de geometría en Haifa, que se celebró cada cuatro años hasta finales de la década de 1990. Editó junto a Izu Vaisman las actas Geometría y geometría diferencial celebradas en 1979. El réferi en Mathematical Reviews, MR0188842 (32 #6274), de su "Geometría lineal" (1965) está escrito por H. S. M. Coxeter.
ψp(U)= P× c(X÷X1) = a(v/b+w/c): :
𝒞ℓ: 𝔖abc xyz (a-b-c)^2 (b-c)^2 (-a^2 c^2-b^2 c^2+c^4+a^2 b^2 τ-b^4 τ+b^2 c^2 τ)^2x^2-2 a^4 (a-b) (a-c) (a+b-c) (a-b+c) (a^2-b^2-c^2)^2 τy z = 0.
El lugar geométrico de los puntos de tangencia de ℓ con 𝒞ℓ, cuando ℓ gira alrededor de O, es la cónica circunscrita que pasa por I, O. Su centro es X38983.𝓅: (a^8 - a^7 (b + c) + a^6 (-2 b^2 + 3 b c - 2 c^2) + a^5 (3 b^3 - b^2 c - b c^2 + 3 c^3)+ a^4 b c (-5 b^2 + 8 b c - 5 c^2) - a^3 (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3) + a^2 (b - c)^2 (2 b^4 + 5 b^3 c + 4 b^2 c^2 + 5 b c^3 + 2 c^4) + a (b - c)^2 (b^5 - b^4 c - 4 b^3 c^2 - 4 b^2 c^3 - b c^4 + c^5)- (b - c)^4 (b + c)^2 (b^2 + b c + c^2) - (b - c)^4 (b + c)^2 (b^2 + b c + c^2) )x + ... =0.
Contiene a los centros del triángulo X6718, cuando ℓ pasa por el y X24025, cuando ℓ es IO; en este caso la cónica 𝒞IO es cuadrado trilineal de IO.El 20 de julio de 1822 nació Gregor Mendel en la actual República Checa. Fue un fraile y naturalista. Formuló, por medio de los trabajos que llevó a cabo con diferentes variedades del guisante, las hoy llamadas leyes de Mendel que dieron origen a la herencia genética.
IA*/IIa = IB*/IIb = IC*/IIc = t
(Ka), (Kb), (Kc) = the circles (I, IA*), (I, IB*), (I, IC*), resp.IP/PO = ID/DIa = IE/EIb = IF/FIc = t.
Γa es la circunferencia simétrica, respecto a BC, de la circunferencia de centro I y radio ID,
IQ/QO = 4abct^2/(a^3(1+t)^2-a^2(b+c)(1+t)^2-a(b^2(1+t)^2+c^2(1+t)^2+2bc(-1-2t+t^2))+(b-c)^2(b+c)(1+t)^2).
Si P' es la reflexión de P en I, entonces f(P)=f(P').El 14 de julio de 1800 falleció, a los 50 años de edad, Lorenzo Mascheroni, matemático italiano. En su libro "Geometria del Compás" (1797, publicado en verso y dedicado a Napoleón Bonaparte) probó que cualquier construcción geométrica que pueda ser hecha con regla y compás, puede ser hecha únicamente con compás; aunque el primero en probar este resultado fue el danés Georg Mohr, quien publicó sus investigaciones en 1672.
A' = (2 a b c : b (-a^2 + b^2 + c^2) : c (-a^2 + b^2 + c^2)),
y el eje de perspectividad de ABC y A'B'C' es:
b c (-a + b + c) (-a^2 + b^2 + c^2)x + a c (a - b + c) (a^2 - b^2 +
c^2)y + a b (a + b - c) (a^2 + b^2 - c^2)z = 0.
El 6 de julio de 1907, nació Frida Kahlo, pintora mexicana. Su obra gira temáticamente en torno a su biografía y a su propio sufrimiento. La obra de Frida y la de su marido, el pintor Diego Rivera, se influyeron mutuamente. Ambos compartieron el gusto por el arte popular mexicano de raíces indígenas, inspirando a otros pintores mexicanos del periodo pos-revolucionario.
Ab=A1C2∩A2C1, Ac=A1B2∩A2B1, Abc=A1C2∩A2B1, Acb=A1B2∩A2C1,
Bc=B2A1∩B1A2, Ba=B2C1∩B1C2, Bca=B2A1∩B1C2, Bac=B2C1∩B1A2,
Ca=C2B1∩C1B2, Cb=C2A1∩C1A2, Cab=C1B2∩C2A1, Cba=C1A2∩C2B1.
𝒞a: v w (u (b^2 (u+v-w)+c^2 (u-v+w))-a^2 (u^2+2 v w+u (v+w)))x^2 +
u^2 (u (b^2 (u+v-w)+c^2 (u-v+w))-a^2 (u^2+2 v w+u (v+w)))y z-2 u w(-c^2 u v+b^2 u (u+v)+a^2 v (u+v))z x-2 u v (-b^2 u w+c^2 u (u+w)+a^2 w (u+w))x y = 0.
Ta = (u (-u (b^2 (u+v-w)+c^2 (u-v+w))+a^2 (u^2+2 v w+u (v+w))) :
-2 (-c^2 u v+b^2 u (u+v)+a^2 v (u+v)) w : -2 v (-b^2 u w+c^2 u (u+w)+a^2 w (u+w))).
Ao = (u ((-b^2-c^2) u^2+a^2 (u^2-2 v w)) (-u (b^2 (u+v-w)+c^2 (u-v+w))+a^2 (u^2+2 v w+u (v+w))) :
2 w (a^4 v (u^2+2 u v+2 v^2) w-a^2 u (c^2 v (u v+2 u w+2 v w)+b^2 (u^3+2 u^2 v+u v^2-2 v^2 w))+u^2 (c^4 v (v+w)+b^2 c^2 (u^2-2 u v-2 v (v+w))+b^4 (u^2+2 u v+v (v+w)))), :
2 v (a^4 v w (u^2+2 u w+2 w^2)-a^2 u (b^2 w (2 u v+u w+2 v w)+c^2 (u^3+2 u^2 w+u w^2-2 v w^2))+u^2 (b^4 w (v+w)+b^2 c^2 (u^2-2 u w-2 w (v+w))+c^4 (u^2+2 u w+w (v+w))))).
𝔖abc xyz y z (2 (b^2-c^2) (-a^2+b^2+c^2) (a^4+b^4-5 b^2 c^2+c^4+a^2 (-2 b^2-2 c^2)) x^5 y^2 z^2-(b^2-c^2) (-4 a^6+b^6-b^4 c^2-b^2 c^4+c^6+a^4 (9 b^2+9 c^2)+a^2 (-6 b^4-4 b^2 c^2-6 c^4)) x^3 y^3 z^3-2 a^4 (b^2-c^2) (-a^2+b^2+c^2) x y^4 z^4-2 b^2 c^2 (-a^2+b^2+c^2) x^7 (-c y+b z) (c y+b z)-2 a^6 y^4 z^4 ((a^2-b^2+c^2) y+(-a^2-b^2+c^2) z)+x^6 y z (c^2 (a^6+a^4 (-4 b^2-3 c^2)-(b^2-c^2) (2 b^4+3 b^2 c^2-c^4)+a^2 (5 b^4+3 c^4)) y-b^2 (a^6+a^4 (-3 b^2-4 c^2)-(b^2-c^2) (b^4-3 b^2 c^2-2 c^4)+a^2 (3 b^4+5 c^4)) z)+x^5 y z (c^2 (2 a^6+a^4 (-7 b^2-5 c^2)-(b^2-c^2) (3 b^4-c^4)+2 a^2 (4 b^4-b^2 c^2+2 c^4)) y^2-b^2 (2 a^6+a^4 (-5 b^2-7 c^2)-(b^2-c^2) (b^4-3 c^4)+2 a^2 (2 b^4-b^2 c^2+4 c^4)) z^2)-2 x^6 (c^4 (a^4-b^4-2 a^2 c^2+2 b^2 c^2+c^4) y^3-b^4 (a^4-2 a^2 b^2+b^4+2 b^2 c^2-c^4) z^3)) = 0,
con puntos cuádruples en los vértices de ABC y que pasa por los centros X2 (baricentro), X13, X14 (), X110 (foco de la ), X39162, X39163 (focos de la ).P2 = ( 25 a^8-35 a^6 (b^2+c^2)+3 a^4 (15 b^4-7 b^2 c^2+15 c^4)+a^2 (-29 b^6+15 b^4 c^2+15 b^2 c^4-29 c^6)+10 b^8-35 b^6 c^2+54 b^4 c^4-35 b^2 c^6+10 c^8 : ... : ...),
que tiene números de búsqueda en (-0.774039984833567, -0.812449860198048, 4.56037899350621).T = (1/(u (c^2 v^2 - a^2 v w + b^2 v w + c^2 v w + b^2 w^2)) : ... : ...).
Cuando P está sobre la circunferencia circunscrita, T es el () de la parábola inscrita en ABC de foco P y queda sobre la , ℰ.
da:
w^2 (-a^2 v (u+v-w)-c^2 v (-u+v+w)+b^2 (v (v+w)+u (v+2 w))) y
-v^2 (-w (a^2 (u-v+w)+b^2 (-u+v+w))+c^2 (w (v+w)+u (2 v+w))) z = 0.
𝔖abc xyz (c^2 v (u v+w (v+w))+w (a^2 v (v-w)-b^2 (v^2+(u+v) w)))^2x^2+2 (a^4 v w (u^3 (u+v)+u (u^2+u v-v^2) w-v (u+v) w^2)+u^2 (b^4 w (u v (u+v)+(u^2+u v+v^2) w-u w^2)+c^4 v (u (u-v) v+u (u+v) w+(u+v) w^2)+b^2 c^2 (-2 v^2 w^2+u (v+w) (v^2-3 v w+w^2)+u^2 (v^2+v w+w^2)))-a^2 u (b^2 w (v^2 w (-v+w)+u^3 (2 v+w)+u v w (2 v+3 w)+u^2 (2 v^2+2 v w+w^2))+c^2 v (v (v-w) w^2+u^3 (v+2 w)+u v w (3 v+2 w)+u^2 (v^2+2 v w+2 w^2))))y z = 0.
En particular, cuando P es el foco de la , la cónica es la de la con respecto a la . Cuyo centro es X34968.El 4 de Julio de 1986 falleció (a los 87 años de edad) el matemático ruso Oscar Zariski. Sus trabajos versan sobre geometría algebraica, en la que desarrolla una teoría abstracta de invariantes donde los conceptos algebraicos de álgebra conmutativa priman sobre la intuición geométrica.
c^2 x y+b^2 x z+a^2 y z+(x+y+z) (-((c^2 (a-b+c-a t-b t+c t) y)/(2 c-a t-b t+c t))-(b^2 (-a+b-c+a t+b t-c t) z)/(-a+b-c+2 b t))=0,
y su punto de tangencia con la A-circunferencia de Mannheim es:
Ta = (a^5 t+a^4 (c (-3+t)+b (1-3 t) t)+(b-c)^2 (b+c) (1+t) (c^2+b^2 t-3 b c (1+t))-2 a^3 (-8 b c t+c^2 (2+t)+b^2 t (1+2 t))+a (b-c) (-c^3 (4+t)+b^3 t (1+4 t)-3 b^2 c t (5+4 t)+3 b c^2 (4+5 t))+2 a^2 (-c^3 (-1+t)+b^3 (-1+t) t+3 b^2 c (1+t-2 t^2)+3 b c^2 (-2+t+t^2)) :
2 b^2 (-a+b-c) ((a+b) t-c (2+t))^2 :
-2 (a+b-c) c^2 (a+c-b (1+2 t))^2).
T' = (-a^2 (a-b+c-2 b t)^2 (-2 c+a t+b t-c t)^2 :
b^2 (-a+b-c) (-a+b+c) (1+t)^2 (-2 c+a t+b t-c t)^2 :
c^2 (-a-b+c) (-a+b+c) (1+t)^2 (a-b+c-2 b t)^2).
𝒬: 𝔖abc xyz y z (2 b^2 (-a+b-c) (a+b-c) c^2 x^2+a^4 (a^2+b^2+a (-2 b-2 c)+2 b c+c^2) y z) = 0.
Contiene a los centros del triángulo X(59), X(1318), X(4076), X(6065). Las tangentes en los vértices de ABC (puntos de retroceso) concurren es X(55), centro de homotecia interior de las circunferencias inscrita y circunscrita.𝔖abc xyz 4 a b c (-a+b+c)^4 ((b-c)^2+a (b+c))^2x^2-a (a^2-(b-c)^2)^2 (a^6-2 a^5 (b+c)-a^4 (b^2-14 b c+c^2)+4 a^3 (b^3-3 b^2 c-3 b c^2+c^3)+(b+c)^2 (b^4-4 b^3 c-2 b^2 c^2-4 b c^3+c^4)-a^2 (b^4+12 b^3 c-50 b^2 c^2+12 b c^3+c^4)-2 a (b^5-7 b^4 c-2 b^3 c^2-2 b^2 c^3-7 b c^4+c^5))y z = 0,
cuyo centro es el , X(3333).A1 = (4 a^2 : (b+c-a)(a-b+c) : (b+c-a)(a+b-c)) , ...
que están sobre las cevianas del . Los otros puntos en los que estas cevianas vuelven a cortar a la circunferencia inscrita son:A2 = (4 (b - c)^2 : -a^2 + 2 a b - b^2 + c^2 : -a^2 + b^2 + 2 a c - c^2) , ...
El punto fijo finito de la transformación afín que aplica ABC en es el incentro.La mañana del 30 de junio de 1908, ocurrió una devastadora explosión conocida como el evento de Tunguska. Una enorme bola de fuego atravesó el cielo de la meseta de Siberia central. En cuestión de segundos, un calor abrasador hizo arder el cielo y una explosión ensordecedora derribó más de 80 millones de árboles en un área de 2100 kilómetros cuadrados de bosque.
Hab = (a^6 (-1+t)^2-(b^2-c^2)^2 (b^2 (-1+t)-c^2 t)+a^2 (b^2-c^2) (-1+t) (-c^2 (-1+t)+b^2 (1+t))-a^4 (b^2 (1-3 t+2 t^2)+c^2 (2-3 t+2 t^2)) :
-(a^2-b^2-c^2) (-b^2 c^2+c^4+a^2 (c^2 (-2+t)+b^2 (-1+t))-a^4 (-1+t)):
-c^2 (-a^2+b^2+c^2) (-b^2+c^2+a^2 (-1+2 t))),
Hac = (a^6 t^2+a^2 (b^2-c^2) t (-c^2 (-2+t)+b^2 t)-(b^2-c^2)^2 (b^2 (-1+t)-c^2 t)-a^4 (c^2 t (-1+2 t)+b^2 (1-t+2 t^2)):
-b^2 (-a^2+b^2+c^2) (b^2-c^2+a^2 (1-2 t)):
-(a^2-b^2-c^2) (b^4-b^2 c^2+a^4 t-a^2 (c^2 t+b^2 (1+t)))).
𝔖abc xyz (-a^2+b^2+c^2)^2 (b^2 c^2 (b^2-c^2)^2+a^8 (-1+t) t+a^2 (b^4-c^4) (b^2 (-1+t)^2-c^2 t^2)+a^6 (-c^2 (-2+t) t-b^2 (-1+t^2))-a^4 (c^4 t (1+t)+b^2 c^2 (1+2 t-2 t^2)+b^4 (2-3 t+t^2)))x^2 +(a^4-(b^2-c^2)^2)^2 (b^4 (-1+t)-c^4 t+a^4 (-1+t) t+b^2 c^2 (-1-2 t+2 t^2)+a^2 (-c^2 (-2+t) t-b^2 (-1+t^2)))y z = 0,
degenera (en el producto de dos rectas) cuando P coincide con los vértices de ABC. Estas rectas son las alturas y los respectivos lados del , A'B'C', de los triángulos , , () y , , del triángulo órtico.Z = ( : ... : ...),
que tiene números de búsqueda en (1.09789418806845, -0.463499047670596, 3.45482804349397).W = ((a^2+b^2-c^2) (a^2-b^2+c^2) (a^4-2 (b^2-c^2)^2+a^2 (b^2+c^2)) (-b^8+b^6 c^2+b^2 c^6-c^8+a^6 (b^2+c^2)+3 a^2 (b^2-c^2)^2 (b^2+c^2)+a^4 (-3 b^4+b^2 c^2-3 c^4)) : ... : ...),
que tiene números de búsqueda en ETC (-1.44655374773501, -2.74246092746355, 6.20693146910607).La teoría de Galois es una serie de resultados que conectan la teoría de cuerpos con la teoría de grupos. La teoría de Galois tiene aplicación a diversos problemas de la teoría de cuerpos que pueden reducirse a problemas más sencillos de la teoría de grupos. La teoría de Galois debe su nombre al matemático francés Évariste Galois, matemático francés (25 de octubre de 1811 - 31 de mayo de 1832).
Ab = ((a - c) (a + c) : 0 : -a^2 + b^2 + c^2),
Ac = ((a - b) (a + b) : -a^2 + b^2 + c^2 : 0),
A' = (-b^2 + c^2 : -a^2 + c^2 : a^2 - b^2).
ℳ[1,1] = (a^2-b^2) (a^2-c^2) (b^2-c^2),
ℳ[1,2] = (a^2-b^2) (b^2-c^2)^2,
ℳ[1,3] = -(a^2-c^2) (b^2-c^2)^2.
λ = -(b^2-c^2) (a^4-a^2 b^2-a^2 c^2+b^2 c^2),
esX523 = (b^2-c^2 : c^2-a^2 : a^2-b^2).
Y la recta de puntos fijos, correspondiente al valor propio, λ= 2 (b^2-c^2) (a^4-a^2 b^2-a^2 c^2+b^2 c^2) es(a^2-b^2) (a^2-c^2) x+(-a^2+b^2) (b^2-c^2) y-(b^2-c^2) (-a^2+c^2) z = 0.
Si X, X' son dos puntos homólogos y Xo es el punto de intersección de XX' con el eje de homología, se tiene que XoX' = -(1/2)XoX. Es decir, (-1/2) es la razón de la homología.Puntos homólogos mediante σ, {Xi, Xj=σ(Xi)}, para los índices {i, j}: {2, 10278}, {99, 13187}, {115, 115}, {125, 125}, {148, 9293}, {245, 245}, {246, 246}, {247, 247}, {338, 7668}, {351, 9979}, {512, 525}, {523, 523}, {525, 3566}, {526, 45147}, {647, 2501}, {661, 3700}, {669, 33294}, {686, 686}, {690, 690} (punto del infinito del eje de homogía), {764, 4647}, {804, 9479}, {826, 512}, {850, 23301}, {868, 868}, {1109, 11}, {1116, 1116}, {1365, 8286}, {1562, 1562}, {1577, 21051}, {1637, 1637}, {1640, 1640}, {1648, 1648}, {1649, 5466}, {2081, 2081}, {2088, 2088}, {2501, 6587}, {2514, 23285}, {2610, 2610}, {2611, 1109}, {2632, 38357}, {2643, 1086}, {2799, 804}, {3005, 850}, {3120, 3120}, {3124, 3124}, {3125, 3125}, {3258, 12079}, {3269, 3269}, {3569, 3569}, {3700, 14321}, {3708, 1146}, {3906, 1499}, {4010, 18004}, {4024, 661}, {4036, 31946}, {4041, 7178}, {4088, 4010}, {4092, 8287}, {4120, 4120}, {4122, 4806}, {4155, 918}, {4466, 21045}, {4516, 16732}, {4705, 1577}, {4730, 4707}, {4838, 4841}, {4934, 4092}, {4983, 7265}, {4988, 4024}, {5027, 14316}, {5489, 4}, {5664, 15543}, {5972, 12064}, {6070, 3154}, {6089, 6370}, {6328, 33967}, {6367, 514}, {6368, 924}, {6370, 900}, {6388, 6388}, {6545, 21020}, {6627, 6627}, {6791, 6791}, {7927, 826}, {7950, 3800}, {8029, 2}, {8034, 321}, {8288, 8288}, {8371, 8371}, {8663, 25259}, {8901, 8902}, {9148, 9148}, {9178, 18310}, {9200, 9200}, {9201, 9201}, {9979, 32193}, {10278, 10189}, {10413, 10413}, {11123, 8029}, {11182, 11182}, {12071, 14838}, {12072, 17069}, {12073, 3906}, {12075, 30476}, {12076, 620}, {12077, 647}, {13291, 13291}, {13636, 13636}, {13722, 13722}, {14270, 24978}, {14277, 14279}, {14417, 9134}, {14420, 14420}, {14431, 14431}, {14443, 671}, {14444, 14444}, {14446, 14446}, {14447, 14447}, {15357, 15357}, {15359, 15359}, {15451, 14618}, {15475, 14566}, {16230, 6130}, {16278, 16278}, {16280, 16280}, {16282, 16282}, {16732, 2486}, {17436, 8599}, {18007, 9183}, {18314, 34964}, {20975, 338}, {21044, 21044}, {21053, 21053}, {21124, 2533}, {21131, 1213}, {21132, 2292}, {21134, 1834}, {21141, 4854}, {21731, 41079}, {21950, 21950}, {22260, 141}, {23099, 76}, {23105, 5}, {23616, 1853}, {23775, 21677}, {23991, 31644}, {24290, 24290}, {30465, 30465}, {30468, 30468}, {30574, 30574}, {31945, 12065}, {31953, 31953}, {33919, 524}, {35443, 20578}, {35444, 20579}, {36197, 36197}, {36255, 36255}, {36642, 2487}, {36955, 12076}, {38356, 38356}, {39691, 39691}.
Los pares de color azul están en la recta del infinito y los pares en “negrita” están sobre el eje de homología.W = ( (b^2-c^2) (a^5-a^2 ((a+b-c) c^2+b^2 (a-b+c))-b^5-c^5+b^2 c^2 (a+b+c)) : ... : ...),
que tiene números de búsqueda en (-1.89699591310576, 5.30478948067561, 0.843654493642388).El 18 de mayo de 1911, falleció a los 51 años de edad, Gustav Mahler, compositor y director de orquesta austríaco, valorado en su tiempo más como director de orquesta que como compositor, hoy es considerado uno de los más grandes y originales sinfonistas. Son diez las sinfonías de su catálogo, si bien la última quedó inacabada a su muerte. De ellas, las números 2, 3, 4 y 8 incluyen la voz humana.
a^2 v w - c^2 v (v + w) - b^2 w (v + w) x + a^2 v w - b^2 w (v + w) + c^2 (u^2 + 2 u (v + w) + w (v + w)) y + a^2 v w - c^2 v (v + w) + b^2 (u^2 + 2 u (v + w) + v (v + w)) z = 0.
D = (a^2 u (b^2 (u + v - w) + c^2 (u - v + w)) -
a^4 (u^2 + 2 v w + u (v + w)) :
-a^4 v (u + v) + (b^2 -
c^2) u (c^2 v + b^2 w) +
a^2 (c^2 v (2 u + v) + b^2 (u (v + w) + v (v + 2 w))) :
-a^4 w (u +
w) - (b^2 - c^2) u (c^2 v + b^2 w) +
a^2 (b^2 w (2 u + w) + c^2 (u (v + w) + w (2 v + w))).
El 16 de mayo de 1830, falleció a los 62 años de edad, el matemático e ingeniero francés Jean-Baptiste Joseph Fourier, conocido por las Series de Fourier y Transformada de Fourier.
Then A4B4C4 is perspective to A2B2C2, and the perspector is the point V(P), here named the Vu 1st PCC perspector, given by
V(P) = a^2 (2 b^2 c^2 p^2 + a^2 c^2 p q + b^2 c^2 p q - c^4 p q + a^2 b^2 p r - b^4 p r + b^2 c^2 p r + a^4 q r - a^2 b^2 q r - a^2 c^2 q r) : :
Given a point P, let A'B'C' be the pedal triangle of P. Let O' be the circumcenter of A'B'C', and let A"B"C" be the reflection of A'B'C' in O'. A"B"C" is perspective to ABC at a point denominate the 'pedal antipodal perspector of P' , or PA(P) (Randy Hudson, Hyacinthos#20403, Nov 21, 2011).a^2 v w - c^2 v (v + w) - b^2 w (v + w) x + a^2 v w - b^2 w (v + w) + c^2 (u^2 + 2 u (v + w) + w (v + w)) y + a^2 v w - c^2 v (v + w) + b^2 (u^2 + 2 u (v + w) + v (v + w)) z = 0.
La proyección ortogonal de P sobre esta recta es:
A' = (a^4 (b^2 + c^2) v w - (b^2 - c^2)^2 u (c^2 v + b^2 w) +
a^2 (c^4 v (u - w) + b^4 (u - v) w +
b^2 c^2 (2 u^2 + 2 v w + 3 u (v + w))) :
b^2 (-a^4 v w + (b^2 -
c^2) u (c^2 v + b^2 w) +
a^2 (b^2 (-u + v) w + c^2 v (u + 2 v + w))) :
c^2 (-a^4 v w - (b^2 -
c^2) u (c^2 v + b^2 w) +
a^2 (c^2 v (-u + w) + b^2 w (u + v + 2 w))).
V(P) = (a^2(v w a^4 + (c^2 v (u - w) + b^2 w(u - v))a^2 - u (c^4 v + b^4 w - b^2 c^2 (2 u + v + w))) : ... : ...).
Pares {P=Xi, V(P)=Xj}, para {i, j}: {1, 56}, {2, 1995}, {4, 24}, {5, 13621}, {6, 1384}, {7, 38900}, {8, 38901}, {9, 38902}, {10, 38903}, {13, 11142}, {14, 11141}, {15, 6}, {16, 6}, {20, 11413}, {21, 11101}, {22, 26283}, {23, 1995}, {31, 38904}, {32, 38905}, {35, 14882}, {36, 56}, {40, 10310}, {54, 25044}, {55, 37541}, {75, 38906}, {76, 38907}, {83, 38908}, {140, 22462}, {141, 38909}, {182, 11842}, {186, 24}, {187, 1384}, {371, 6423}, {372, 6424}, {484, 14882}, {501, 17104}, {560, 38910}, {561, 38911}, {858, 26283}, {1155, 37541}, {1157, 25044}, {1324, 38903}, {1325, 11101}, {1501, 38912}, {1502, 38913}, {1687, 32}, {1688, 32}, {1691, 38905}, {1928, 38914}, {2070, 13621}, {2071, 11413}, {2077, 10310}, {2080, 11842}, {2321, 38915}, {2459, 6423}, {2460, 6424}, {2887, 38916}, {3513, 1617}, {3514, 1617}, {3676, 38917}, {5004, 2}, {5005, 2}, {5127, 17104}, {5152, 38907}, {5161, 38904}, {5205, 26264}, {5899, 22462}, {5938, 38909}, {5980, 183}, {5981, 183}, {6104, 11142}, {6105, 11141}, {7598, 3124}, {7599, 3124}, {10419, 39379}, {14094, 15034}, {14538, 1350}, {14539, 1350}, {15035, 15034}, {15054, 15021}, {15055, 15021}, {17100, 38901}, {32622, 55}, {32623, 55}, {32624, 38900}, {32625, 38902}, {32751, 1078}, {32752, 1078}, {32753, 1486}, {32754, 1486}, {38001, 11284}, {38002, 11284}, {38011, 21309}, {38012, 21309}, {38013, 999}, {38014, 999}, {39377, 39380}, {39378, 39381}, {39556, 38906}, {39557, 38908}.a^2 b^2 c^2 (a^4+(b^2-c^2)^2-2 a^2 (b^2+c^2)) m^2 n^2x^2+a^2 (a^8 m^2 n^2+(b^2-c^2)^2 l^2 (c^4 m^2+b^4 n^2)-2 a^6 m n (b^2 (l+m) n+c^2 m (l+n))+a^4 (b^4 (l^2+4 l m+m^2) n^2+2 b^2 c^2 m n (2 l^2+m n)+c^4 m^2 (l^2+4 l n+n^2))-2 a^2 l (b^6 (l+m) n^2+c^6 m^2 (l+n)-b^2 c^4 m (l (m-2 n)+n^2)-b^4 c^2 n (m^2+l (-2 m+n))))y z + .... =0.
El 10 de mayo de 1822 falleció Paolo Ruffini médico y matemático italiano. Ganó la cátedra de análisis de la escuela militar de la Universidad de Módena, que hubo de abandonar en 1798 al ser expulsado por negarse a pronunciar el juramento de fidelidad a la República Cisalpina creada por Napoleón Bonaparte. Paolo Ruffini es conocido como el descubridor del llamado método de Ruffini que permite hallar los coeficientes del polinomio que resulta de la división de un polinomio cualquiera por el binomio x-a. Sin embargo, la gran aportación de Ruffini fue la demostración de la irresolubilidad de las ecuaciones de grado cinco. aunque cometió ciertas inexactitudes que serían corregidas por el matemático noruego Abel.
Q = (a^2(-b^4w(v+2w)-(a^2-c^2)v(a^2w-c^2(2v+w))+2b^2(a^2w(v+w)+c^2(2u^2+v^2+v w+w^2+4u(v+w)))) : ... : ...).
Pares {P=Xi, Q=σp(Q)=Xj}, correspondientes a los índices {i, j}Qt = (a^2(b^4t(1+t)+(a^2-c^2)t(a^2t-c^2(1+t))- b^2(a^2t(1+2t)+c^2(3+6t+2t^2))) : ... : ... ),
que queda sobre la hipérbola de Thomson-Gibert-Moses: (b^2-c^2)(2b^2c^2x^2+a^2 (b^2+c^2-a^2)y z) + ... = 0.Fp = (2 a^10 (b^2+c^2) t+a^12 t^2+b^2 c^2 (b^2-c^2)^4 t (1+2 t)+a^6 (b^2+c^2) (b^4 t (6+5 t)+c^4 t (6+5 t)-3 b^2 c^2 (1+4 t+3 t^2))+a^8 (-b^4 t (6+5 t)-c^4 t (6+5 t)+b^2 c^2 (3+6 t+7 t^2))-a^2 (b^2-c^2)^2 (b^2+c^2) (b^4 t^2+c^4 t^2-b^2 c^2 (3+9 t+7 t^2))-a^4 (2 b^8 t+2 c^8 t+b^6 c^2 (3+12 t+13 t^2)+b^2 c^6 (3+12 t+13 t^2)-b^4 c^4 (9+30 t+26 t^2) : ... : ...).
El lugar geométrico de Fp es la circunferencia Γ:(-a^8 b^4+3 a^6 b^6-3 a^4 b^8+a^2 b^10+a^6 b^4 c^2-a^4 b^6 c^2+a^8 c^4-a^6 b^2 c^4+a^2 b^6 c^4-3 a^6 c^6+a^4 b^2 c^6-a^2 b^4 c^6+3 a^4 c^8-a^2 c^10) x^2+(-a^10 b^2+2 a^8 b^4-2 a^4 b^8+a^2 b^10+3 a^8 b^2 c^2-7 a^6 b^4 c^2+7 a^4 b^6 c^2-3 a^2 b^8 c^2-2 a^8 c^4-2 a^6 b^2 c^4+2 a^2 b^6 c^4+2 b^8 c^4+6 a^6 c^6+2 a^4 b^2 c^6-2 a^2 b^4 c^6-6 b^6 c^6-6 a^4 c^8+6 b^4 c^8+2 a^2 c^10-2 b^2 c^10) x y+(-a^10 b^2+3 a^8 b^4-3 a^6 b^6+a^4 b^8+a^6 b^4 c^2-a^4 b^6 c^2-a^6 b^2 c^4+a^2 b^6 c^4-b^8 c^4+a^4 b^2 c^6-a^2 b^4 c^6+3 b^6 c^6-3 b^4 c^8+b^2 c^10) y^2+(2 a^8 b^4-6 a^6 b^6+6 a^4 b^8-2 a^2 b^10+a^10 c^2-3 a^8 b^2 c^2+2 a^6 b^4 c^2-2 a^4 b^6 c^2+2 b^10 c^2-2 a^8 c^4+7 a^6 b^2 c^4+2 a^2 b^6 c^4-6 b^8 c^4-7 a^4 b^2 c^6-2 a^2 b^4 c^6+6 b^6 c^6+2 a^4 c^8+3 a^2 b^2 c^8-2 b^4 c^8-a^2 c^10) x z+(2 a^10 b^2-6 a^8 b^4+6 a^6 b^6-2 a^4 b^8-2 a^10 c^2+2 a^6 b^4 c^2-2 a^4 b^6 c^2+3 a^2 b^8 c^2-b^10 c^2+6 a^8 c^4-2 a^6 b^2 c^4-7 a^2 b^6 c^4+2 b^8 c^4-6 a^6 c^6+2 a^4 b^2 c^6+7 a^2 b^4 c^6+2 a^4 c^8-3 a^2 b^2 c^8-2 b^4 c^8+b^2 c^10) y z+(a^10 c^2+a^6 b^4 c^2-a^4 b^6 c^2-b^10 c^2-3 a^8 c^4-a^6 b^2 c^4+a^2 b^6 c^4+3 b^8 c^4+3 a^6 c^6+a^4 b^2 c^6-a^2 b^4 c^6-3 b^6 c^6-a^4 c^8+b^4 c^8) z^2 = 0.
Esta circunferencia corta a la circunferencia circunscrita a ABC en el y en el . Γ corta a la en el circuncentro y en X34365. Otros centros del triángulo sobre Γ son el baricentro, X20126 (reflexión del foco de la en el punto medio del baricentro y circuncentro) y X34310.W = ( (b^2-c^2) (2 a^8-4 a^6 (b^2+c^2)-2 a^2 b^2 c^2 (b^2+c^2)+2 a^4 (b^4+3 b^2 c^2+c^4)+b^2 c^2 (b^2-c^2)^2) : ... : ...),
que tiene números de búsqueda en (-0.676186949215500, 9.24675764730299, -2.44885068197207).El campo de concentración de Mauthausen (desde el verano de 1938 Mauthausen-Gusen) fue un grupo de campos de concentración nazis situados en torno a la pequeña empresa y cantera, de la población de Mauthausen en Austria. Cuando el Ejército norteamericano entró en Mauthausen, el 5 de mayo de 1945, banderas republicanas habían sustituido a las banderas nazis y la puerta del campo estaba cubierta por una gran pancarta en la que se podía leer: «Los españoles antifascistas saludan a las fuerzas libertadoras».
W = ( 1/((a-b-c) (a^3+b^3-3 b^2 c-3 b c^2+c^3-a^2 (b+c)-a (b^2-8 b c+c^2))) : ... : ...),
que tiene números de búsqueda en (-1.41160206428087, 2.03789907211123, 2.88131992319085).El 4 de mayo de 1938, a los 49 años de edad, falleció Carl von Ossietzky, periodista y pacifista alemán. Se opuso a cualquier forma de militarismo y abanderó el movimiento pacifista alemán en las primeras décadas del siglo XX. En 1935 fue galardonado con el Premio Nobel de la Paz. Cuando el comité Nobel le comunicó el premio, el gobierno nazi impidió que abandonara Alemania para recoger el galardón, prohibió a la prensa nacional comentar la concesión del premio y dictaminó que, en el futuro, Alemania no aceptaría ningún Premio Nobel.
Ab(a^2:0:c^2), Ac(a^2:b^2:0),
A1(2 a^2:(1 - Sqrt[5]) b^2:(1 + Sqrt[5]) c^2),
A2(2 a^2:(1 + Sqrt[5]) b^2:(1 - Sqrt[5]) c^2),
A1b(2 a^2 + (1 - Sqrt[5]) (b^2 - c^2): 0: 2 c^2),
A1c(-2 a^2 + (1 + Sqrt[5]) (b^2 - c^2) : -2 b^2 : 0),
A2b(2 a^2 + (1 + Sqrt[5]) (b^2 - c^2) : 0 : 2 c^2),
A2c(-2 a^2 + (1 - Sqrt[5]) (b^2 - c^2) : -2 b^2 : 0),
A'(2 a^2 : b^2 : c^2), B'(a^2 : 2b^2 : c^2), C'(a^2 : b^2 : 2c^2).
ℳ[1,1] = -2 a^2 (a^2 + 2 b^2 + c^2) (a^2 + b^2 + 2 c^2), ,
ℳ[1,2] = -a^2 (2 a^2 + b^2 +
c^2) (a^2 + b^2 + 2 c^2),
ℳ[1,3] = -a^2 (2 a^2 + b^2 + c^2) (a^2 + 2 b^2 +
c^2) .
λ = -(2 a^2 + b^2 + c^2) (a^2 + 2 b^2 + c^2) (a^2 + b^2 + 2 c^2),
esX5007 = (a^2 (2 a^2 + b^2 + c^2) : ... : ...).
Algunos pares {Xi, Xj=σ(Xi)}, con los índices {i, j}: {428, 51}, {3589, 6}, {4030, 42}, {5007, 5007}, {6292, 5041}, {7198, 1475}, {7767, 39}, {8664, 669}, {10330, 20976}, {17469, 2308}, {22352, 13366}, {39998, 20965}.W = ( 2 a^8+3 a^6 (b^2+c^2)-a^4 (3 b^4+2 b^2 c^2+3 c^4)-2 a^2 (b^6+2 b^4 c^2+2 b^2 c^4+c^6) : ... : ...),
que tiene números de búsqueda en (19.9325777903025, 19.0104752239030, -18.7200850378573).El 2 de mayo de 1928, el papa Pío XI desaprueba la celebración de competiciones deportivas femeninas en Roma. Ya en el Congreso Gimnástico Femenino de Roma de 1928, pedía “que se evite cuanto se armonice mal con el recato y la compostura, que son tan grande ornato y sostén de la virtud”.
(b^2-c^2) ((b-c)^2+a (b+c))x + a (a^2 b+a (b-c)^2+(b-c)^2 c)y -a (a (b-c)^2+b (b-c)^2+a^2 c)z = 0.
Procediendo cíclicamente, se deducen las ecuaciones de las tangentes ℓb y ℓc en V y W a las hipérbolas ℋb y ℋc.L = ( a (a^6-a^5 (b+c)-2 a^4 (b^2-3 b c+c^2)+a^3 (2 b^3-b^2 c-b c^2+2 c^3)+a^2 (b^4-5 b^3 c+4 b^2 c^2-5 b c^3+c^4)-a (b-c)^2 (b^3+c^3)-b c (b^2-c^2)^2) : ... : ...),
que tiene números de búsqueda en (11.5531962891311, 11.2191888327421, -9.45871068958987).El 28 de abril de 1945 fueron fusilados en la aldea de Dongo, a orillas del lago de Como, el dictador fascista Benito Mussolini y su amante, Clara Petacci, que intentaban huir a Suiza en un convoy con soldados alemanes. Fueron capturados por partisanos italianos y fusilados por orden del Comité de Liberación Nacional. Sus cadáveres, colgados de los pies, serán expuestos públicamente en las calles de Milán. Las imágenes de sus cadáveres dieron la vuelta al mundo y se convirtieron en unas de las más emblemáticas de la derrota del fascismo.
Xo = (-(b^2-c^2)^8 (b^2+c^2)^3 t+3 a^22 t^2-a^20 (b^2+c^2) t (3+14 t)+a^2 (b^2-c^2)^6 (b^2+c^2)^2 (b^4 (-1+8 t)+c^4 (-1+8 t)-b^2 c^2 (2-2 t+t^2))+a^6 (b^2-c^2)^2 (b^6 c^6 (-37+88 t-134 t^2)+b^8 c^4 (5-34 t-51 t^2)+b^4 c^8 (5-34 t-51 t^2)+2 b^10 c^2 (1-57 t+11 t^2)+2 b^2 c^10 (1-57 t+11 t^2)+b^12 (-21+10 t+14 t^2)+c^12 (-21+10 t+14 t^2))-a^4 (b^2-c^2)^4 (b^2+c^2) (b^8 (-7+21 t+3 t^2)+c^8 (-7+21 t+3 t^2)+b^6 c^2 (-5-22 t+11 t^2)+b^2 c^6 (-5-22 t+11 t^2)+b^4 c^4 (4-23 t+24 t^2))+a^12 (b^2+c^2) (b^4 c^4 (-14+169 t-404 t^2)+7 b^8 (3+16 t+11 t^2)+7 c^8 (3+16 t+11 t^2)+b^6 c^2 (-23-242 t+69 t^2)+b^2 c^6 (-23-242 t+69 t^2))+a^18 (b^4 t (14+17 t)+c^4 t (14+17 t)+b^2 c^2 (3+16 t+76 t^2))+a^16 (b^2+c^2) (b^4 (1-15 t+21 t^2)+c^4 (1-15 t+21 t^2)-2 b^2 c^2 (5+18 t+80 t^2))-a^8 (b^2+c^2) (b^8 c^4 (-139+342 t-45 t^2)+b^4 c^8 (-139+342 t-45 t^2)+b^12 (-35-56 t+17 t^2)+c^12 (-35-56 t+17 t^2)-2 b^10 c^2 (-44+19 t+53 t^2)-2 b^2 c^10 (-44+19 t+53 t^2)+2 b^6 c^6 (87-244 t+138 t^2))-a^10 (b^6 c^6 (-77+168 t-474 t^2)+b^8 c^4 (19-214 t-31 t^2)+b^4 c^8 (19-214 t-31 t^2)+7 b^12 (5+18 t+3 t^2)+7 c^12 (5+18 t+3 t^2)+b^10 c^2 (-25-38 t+201 t^2)+b^2 c^10 (-25-38 t+201 t^2))-a^14 (-2 b^6 c^2 (3+55 t+26 t^2)-2 b^2 c^6 (3+55 t+26 t^2)+b^8 (7+34 t+77 t^2)+c^8 (7+34 t+77 t^2)-b^4 c^4 (36+56 t+349 t^2)):
-(a^6-a^4 (b^2+c^2)+(b^2-c^2)^2 (b^2+c^2)-a^2 (b^4-3 b^2 c^2+c^4))^2 (-b^2 c^2-b^4 (-1+t)+a^4 t+c^4 t-a^2 (b^2+2 c^2 t)) (a^4 (b^2+c^2) t+(b^2-c^2)^2 (b^2+c^2) t-2 a^2 (b^2 c^2+b^4 t+c^4 t))-((b^2-c^2)^3 (b^2+c^2) (-c^2+b^2 (-1+t))-a^10 t+a^8 c^2 (1+4 t)+a^6 (b^2 c^2 (1-4 t)-2 c^4 (2+3 t)+b^4 (1+5 t))+a^2 (b^2-c^2) (3 b^6+c^6 (4+t)+b^2 c^4 (1+3 t)+b^4 c^2 (-1+6 t))+a^4 (b^4 c^2 (1-4 t)+2 c^6 (3+2 t)-b^6 (3+5 t)+b^2 c^4 (-3+7 t))) ((b^2-c^2)^4 (b^2+c^2)^2-a^10 (b^2+c^2) t+a^8 (b^4+c^4) (1+4 t)+2 a^4 (b^4 c^4 (1-4 t)+b^6 c^2 (-3+t)+b^2 c^6 (-3+t)+b^8 (3+2 t)+c^8 (3+2 t))-a^2 (b^2-c^2)^2 (b^2+c^2) (b^4 (4+t)+c^4 (4+t)+b^2 c^2 (-2+3 t))-a^6 (b^2+c^2) (2 c^4 (2+3 t)+b^4 (4+6 t)-b^2 c^2 (6+7 t))):
-(a^6-a^4 (b^2+c^2)+(b^2-c^2)^2 (b^2+c^2)-a^2 (b^4-3 b^2 c^2+c^4))^2 (-b^2 c^2-c^4 (-1+t)+a^4 t+b^4 t-a^2 (c^2+2 b^2 t)) (a^4 (b^2+c^2) t+(b^2-c^2)^2 (b^2+c^2) t-2 a^2 (b^2 c^2+b^4 t+c^4 t))-((b^2-c^2)^3 (b^2+c^2) (b^2-c^2 (-1+t))-a^10 t+a^8 b^2 (1+4 t)+a^6 (b^2 c^2 (1-4 t)-2 b^4 (2+3 t)+c^4 (1+5 t))-a^2 (b^2-c^2) (3 c^6+b^6 (4+t)+b^4 c^2 (1+3 t)+b^2 c^4 (-1+6 t))+a^4 (b^2 c^4 (1-4 t)+b^6 (6+4 t)-c^6 (3+5 t)+b^4 c^2 (-3+7 t))) ((b^2-c^2)^4 (b^2+c^2)^2-a^10 (b^2+c^2) t+a^8 (b^4+c^4) (1+4 t)+2 a^4 (b^4 c^4 (1-4 t)+b^6 c^2 (-3+t)+b^2 c^6 (-3+t)+b^8 (3+2 t)+c^8 (3+2 t))-a^2 (b^2-c^2)^2 (b^2+c^2) (b^4 (4+t)+c^4 (4+t)+b^2 c^2 (-2+3 t))-a^6 (b^2+c^2) (2 c^4 (2+3 t)+b^4 (4+6 t)-b^2 c^2 (6+7 t)))).
(2 a^6 b^4-6 a^4 b^6+6 a^2 b^8-2 b^10+6 a^4 b^4 c^2-8 a^2 b^6 c^2+2 b^8 c^2-2 a^6 c^4-6 a^4 b^2 c^4+4 b^6 c^4+6 a^4 c^6+8 a^2 b^2 c^6-4 b^4 c^6-6 a^2 c^8-2 b^2 c^8+2 c^10) x+
(3 a^8 b^2-10 a^6 b^4+12 a^4 b^6-6 a^2 b^8+b^10+3 a^6 b^2 c^2-3 a^4 b^4 c^2+a^2 b^6 c^2-b^8 c^2+a^6 c^4-3 a^4 b^2 c^4+6 a^2 b^4 c^4-2 b^6 c^4-3 a^4 c^6-4 a^2 b^2 c^6+2 b^4 c^6+3 a^2 c^8+b^2 c^8-c^10) y+
(-a^6 b^4+3 a^4 b^6-3 a^2 b^8+b^10-3 a^8 c^2-3 a^6 b^2 c^2+3 a^4 b^4 c^2+4 a^2 b^6 c^2-b^8 c^2+10 a^6 c^4+3 a^4 b^2 c^4-6 a^2 b^4 c^4-2 b^6 c^4-12 a^4 c^6-a^2 b^2 c^6+2 b^4 c^6+6 a^2 c^8+b^2 c^8-c^10) z = 0.
Ga =(3 a^10-8 a^8 (b^2+c^2)+(b^2-c^2)^4 (b^2+c^2)-2 a^2 (b^2-c^2)^2 (2 b^4+b^2 c^2+2 c^4)+a^6 (5 b^4+13 b^2 c^2+5 c^4)+a^4 (3 b^6-8 b^4 c^2-8 b^2 c^4+3 c^6):
a^8 (-2 b^2+c^2)+(b^2-c^2)^4 (b^2+c^2)+a^6 (5 b^4+b^2 c^2-4 c^4)+a^4 (-3 b^6-5 b^4 c^2+b^2 c^4+6 c^6)-a^2 (b^8-6 b^6 c^2+4 b^4 c^4-3 b^2 c^6+4 c^8):
a^8 (b^2-2 c^2)+(b^2-c^2)^4 (b^2+c^2)+a^6 (-4 b^4+b^2 c^2+5 c^4)+a^4 (6 b^6+b^4 c^2-5 b^2 c^4-3 c^6)-a^2 (4 b^8-3 b^6 c^2+4 b^4 c^4-6 b^2 c^6+c^8)).
((b^2-c^2)^4 (b^2+c^2)^2+a^8 (b^4-b^2 c^2+c^4)-a^6 (4 b^6-3 b^4 c^2-3 b^2 c^4+4 c^6)-a^2 (b^2-c^2)^2 (4 b^6+3 b^4 c^2+3 b^2 c^4+4 c^6)-a^4 (-6 b^8+5 b^6 c^2+b^4 c^4+5 b^2 c^6-6 c^8)) x+
a^2 b^2 (a^2-b^2-b c-c^2) (a^2-b^2+b c-c^2) (a^2-b^2-a c+c^2) (a^2-b^2+a c+c^2) y+
a^2 c^2 (a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) (a^2-b^2-b c-c^2) (a^2-b^2+b c-c^2) z = 0.
X186 = (a^2((a^2-b^2-c^2)^2-b^2 c^2)/ (-a^2+b^2+c^2) : ... : ...).
∗ ∗ ∗ ∗ ∗
∗ ∗ ∗ ∗ ∗
(-a^4+a^2 (2 b^2-c^2-b^4-b^2 c^2+2 c^4) ±2(a^2-b^2)S Sqrt[3])y +
(a^4+a^2 (b^2-2 c^2)-2 b^4+b^2 c^2+c^4 ±2(a^2-c^2)S Sqrt[3])z=0.
λ^2 (-4 a^8 b^4+16 a^6 b^6-24 a^4 b^8+16 a^2 b^10-4 b^12+4 a^8 b^2 c^2-12 a^6 b^4 c^2+20 a^4 b^6 c^2-20 a^2 b^8 c^2+8 b^10 c^2-4 a^8 c^4-12 a^6 b^2 c^4+4 a^4 b^4 c^4+4 a^2 b^6 c^4+4 b^8 c^4+16 a^6 c^6+20 a^4 b^2 c^6+4 a^2 b^4 c^6-16 b^6 c^6-24 a^4 c^8-20 a^2 b^2 c^8+4 b^4 c^8+16 a^2 c^10+8 b^2 c^10-4 c^12+a^2 b^2 c^2 λ)=0,
que tiene una raíz doble (λ=0), por lo que se trata de un haz simplemente tangente, la cónica degenerada del haz, correspondiente a la otra raíz, consta de la recta tangente a Γ en A y la recta B1C1, con ecuación:
((b^2-c^2)^4 (b^2+c^2)^2+a^8 (b^4-b^2 c^2+c^4)+a^6 (-4 b^6+3 b^4 c^2+3 b^2 c^4-4 c^6)-a^2 (b^2-c^2)^2 (4 b^6+3 b^4 c^2+3 b^2 c^4+4 c^6)+a^4 (6 b^8-5 b^6 c^2-b^4 c^4-5 b^2 c^6+6 c^8)) x+
a^2 b^2 (a^8+b^8-b^6 c^2-b^2 c^6+c^8-a^6 (4 b^2+c^2)+a^4 b^2 (6 b^2+c^2)+a^2 (-4 b^6+b^4 c^2+b^2 c^4-c^6)) y+
a^2 c^2 (a^8+b^8-b^6 c^2-b^2 c^6+c^8-a^6 (b^2+4 c^2)+a^4 c^2 (b^2+6 c^2)+a^2 (-b^6+b^4 c^2+b^2 c^4-4 c^6)) z = 0.
El 26 de abril de 1832 nació Robert Tucker matemático inglés, hizo contribuciones a la investigación en geometría. Escribió más de 40 artículos de investigación que se publicaron en las principales revistas. Estos artículos contienen una serie de ideas interesantes. Destaca especialmente su trabajo en el círculo de proporción triplicada, Círculos de Tucker
c^2 x y + b^2 x z + a^2 y z + (x + y + z) (-((a c^2 y)/(a + b - c)) - (a b^2 z)/( a - b + c)) = 0.
Sean Oa(a (a^4-2 a^2 (b-c)^2-a^3 (b+c)+a (b-c)^2 (b+c)+(b-c)^2 (b^2+c^2)):-b^2 (b-c) (-a^2+(b-c)^2+2 a c):(-a^2+2 a b+(b-c)^2) (b-c) c^2), Ob, Oc los circuncentros de los triángulos AAbAc, BBcBa, CCaCb.
ℳ[1,1] =a (a^5-2 a^4 (b+c)+3 a^2 (b-c)^2 (b+c)-a^3 (b^2-6 b c+c^2)-b^5+b^4 c-2 a b (b-c)^2 c+b c^4-c^5),
ℳ[1,2] = a^2 (a-c) (a^3+b^3-3 b^2 c+b c^2+c^3-a^2 (b+c)-a (b^2-4 b c+c^2)),
ℳ[1,3] = a^2 (a-b) (a^3+b^3+b^2 c-3 b c^2+c^3-a^2 (b+c)-a (b^2-4 b c+c^2)).
λ = -(b+c-a)^2 (a+b-c)^2 (a-b c)^2,
esX109 = (a^2/((a - b - c) (b - c)) : ... : ...).
El 22 de abril de 1929 nació Michael Atiyah. Por el impacto de su trabajo, ganó los premios de matemáticas más importantes a nivel mundial: la Medalla Fields en 1966 (considerada el Premio Nobel de matemáticas, y otorgada solo una vez cada 4 años), y el Premio Abel en 2004. Su primera contribución importante fue el desarrollo, en 1959 y en colaboración con Hirzebruch, de la llamada “teoría K topológica” (o “K-teoría topológica”). Otro de los resultados notables de Atiyah fue la demostración en 1963, junto con Singer, del llamado “teorema del índice”, o “teorema de Atiyah-Singer”. Entre sus numerosos publicaciones figura "Introducción al Álgebra Conmutativa", este libro tuvo su origen en un curso de lecciones dadas a los alumnos de la Universidad de Oxford y está destinado a estudiantes que aparte de los estudios básicos de Algebra lineal y Calculo, hayan seguido un curso introductorio de Algebra, y que además tenga una cierta disposición para el razonamiento abstracto.
P'= 8t O + a²b²c² H.
Son pares de puntos conjugados {X3, X4} y {X1113, X1114}, puntos de intersección de la circunferncia circunscrita con la recta de Euler.F+, F- = ( a (b c SBSC ± Sqrt[2] a SA Sqrt[SASBSC]) : ... : ...),
que tienen números de búsqueda en ±(1.002451878044815, 1.123499353117659, -1.538169300646643).El 20 de abril de 1923, en Italia, Benito Mussolini suprime el recuerdo del Primero de Mayo (la masacre contra los obreros de Chicago, 1886). En España, la celebración del primero de mayo, sepultada con la guerra civil, reaparece en los años cincuenta transformada en Fiesta de San José Artesano, patrón de los trabajadores católicos. En 1955 Pío XII introduce en el calendario oficial la festividad de San José Obrero, como patrón de los trabajadores, el día 1 de mayo.
(c^2 (u^2+v^2) (u+w)^2-b^2 (u+v)^2 (u^2+w^2)) x+(-b^2 u (u+v)^2 (u-w)+(u+w) (-a^2 (u+v)^2 w+c^2 u (u^2-2 u v-v^2+2 u w))) y+(-(-c^2 u (u-v)-a^2 v (u+v)) (u+w)^2-b^2 u (u^3+u^2 (3 v-2 w)-v w^2+u (2 v^2-2 v w-w^2))) z =0
Q7 = ( a (a^3 - a^2 (b + c) - a (b^2 - 6 b c + c^2)+ b^3 - 3 b^2 c - 3 b c^2 + c^3) : ... : ...),
que tiene números de búsqueda en (14.0506894848616, 2.51433390781734, -4.58496183190220).ℓa: (c^2 (a^2-c^2)^2 v^2-b^6 w^2-b^2 (a^4 w^2+2 a^2 c^2 u (-v+w)+c^4 (2 u^2+2 v^2+w^2+2 u (v+w)))+b^4 (2 a^2 w^2+c^2 (2 u^2+v^2+2 w^2+2 u (v+w)))) x+(-b^6 w^2-(-a^2 c+c^3)^2 v (u+w)-b^2 (a^4 w^2-2 a^2 c^2 (2 u v+v^2-u w+v w)+c^4 (2 u^2+2 u w-2 v w+w^2))+b^4 (2 a^2 w^2+c^2 (2 u^2+u v+2 u w-v w+2 w^2))) y+(c^2 (a^2-c^2)^2 v^2+b^6 (u+v) w+b^4 (-2 a^2 (u+v) w+c^2 (2 u^2+2 u v+v^2-2 v w))+b^2 (a^4 (u+v) w+2 a^2 c^2 (u (v-2 w)-w (v+w))-c^4 (2 u^2+v (2 v-w)+u (2 v+w)))) z = 0.
Las rectas ℓa, ℓa, ℓa son concurrentes, para todo puntos P en el plano de ABC. El punto de concurrencia es:Q = (a^6 u v w+(b^2-c^2)^2 u^2 (c^2 v+b^2 w)+a^4 (c^2 v (u^2+2 u (v-w)+2 v (v+w))+b^2 w (u^2-2 u (v-w)+2 w (v+w)))-a^2 (c^4 v (2 u^2+u (2 v-w)+2 v (v+w))+b^4 w (2 u^2-u (v-2 w)+2 w (v+w))+2 b^2 c^2 (2 v w (v+w)-u (v^2-v w+w^2))): ...: ...).
Algunos pares {P=Xi, Q=Xj}, con {i,j}: {3, 3}, {4, 68}, {20, 20427}, {21, 16139}, {23, 32599}, {40, 1158}, {3098, 11178}, {3579, 22936}, {6194, 31958}, {7691, 6288}, {15062, 18442}.El 19 de abril de 1832, nació José Echegaray , ingeniero, dramaturgo, político y matemático español. Obtuvo el Premio Nobel de Literatura en 1904. Realizó importantes aportaciones a las matemáticas y a la física. Introdujo en España la geometría de Chasles, la teoría de Galois, las funciones elípticas. Fue autor de obras de carácter científico, especialmente de matemáticas, y literariamente de obras teatrales, sesenta y siete en total, de las que treinta y cuatro, fueron en verso.
t=(2SASBSC ± S Sqrt[2 (a^2+b^2+c^2)SASBSC])/(4 SA SBSC).
Pares {P=Xi, P"=Xj}, ambos sobre la recta de Euler, para {i, j}: {2, 427}, {3, 4}, {4, 5}, {5, 1594}, {20, 235}, {21, 429}, {22, 25}, {23, 468}, {24, 3}, {25, 2}, {26, 24}, {27, 3136}, {28, 442}, {29, 3142}, {30, 403}, {140, 15559}, {199, 27}, {237, 297}, {297, 2450}, {376, 1596}, {378, 381}, {381, 7577}, {382, 16868}, {403, 2072}, {404, 1883}, {405, 5142}, {411, 37368}, {419, 21531}, {420, 21536}, {427, 5133}, {428, 37990}, {429, 37983}, {458, 37988}, {468, 858}, {631, 1595}, {851, 37371}, {858, 37981}, {859, 860}, {862, 26019}, {1011, 469}, {1013, 1985}, {1113, 1313}, {1114, 1312}, {1325, 37982}, {1344, 1347}, {1345, 1346}, {1583, 3127}, {1584, 3128}, {1593, 3091}, {1594, 5576}, {1597, 3545}, {1598, 3090}, {1599, 32588}, {1600, 32587}, {1628, 454}, {1658, 6240}, {1995, 5094}, {2070, 186}, {2071, 10151}, {2073, 33329}, {2074, 30447}, {2075, 36195}, {2409, 3150}, {2915, 28}, {2937, 3518}, {3129, 470}, {3130, 471}, {3131, 473}, {3132, 472}, {3135, 467}, {3145, 29}, {3147, 23335}, {3148, 458}, {3155, 1585}, {3156, 1586}, {3515, 20}, {3516, 3832}, {3517, 631}, {3518, 140}, {3520, 546}, {3522, 1906}, {3523, 1907}, {3541, 7403}, {3542, 11585}, {3575, 13160}, {3627, 35487}, {3651, 15763}, {4184, 430}, {4185, 2476}, {4186, 4193}, {4189, 1904}, {4213, 34119}, {4214, 5141}, {4216, 1894}, {4219, 8226}, {4220, 37362}, {4222, 4187}, {4224, 25985}, {4225, 407}, {4227, 30444}, {4230, 868}, {4231, 37360}, {4232, 30739}, {4235, 3143}, {4238, 3140}, {4240, 3134}, {4241, 3138}, {4242, 867}, {4246, 3139}, {4247, 16052}, {5000, 5000}, {5001, 5001}, {5020, 8889}, {5064, 37353}, {5094, 5169}, {5198, 5056}, {5200, 1591}, {5899, 37943}, {6143, 33332}, {6240, 10024}, {6353, 1368}, {6617, 6619}, {6636, 428}, {6642, 3541}, {6644, 378}, {6660, 419}, {6756, 14788}, {6995, 37439}, {7387, 3542}, {7412, 6831}, {7414, 6841}, {7420, 37381}, {7428, 11105}, {7430, 15762}, {7452, 3137}, {7461, 14010}, {7464, 37984}, {7466, 37315}, {7473, 36189}, {7476, 37986}, {7480, 3154}, {7482, 14120}, {7484, 7378}, {7485, 5064}, {7487, 7399}, {7488, 3575}, {7492, 10301}, {7494, 15809}, {7497, 6829}, {7501, 6907}, {7502, 7576}, {7503, 7507}, {7505, 13371}, {7506, 37119}, {7512, 6756}, {7517, 7505}, {7520, 37376}, {7526, 7547}, {7556, 37458}, {7575, 10295}, {7576, 37347}, {7577, 39504}, {7580, 37372}, {9714, 3147}, {9715, 7487}, {9909, 6353}, {10295, 11799}, {10323, 1598}, {10594, 1656}, {11107, 27555}, {11325, 5025}, {11328, 5117}, {11334, 5136}, {11337, 4185}, {11340, 1889}, {11350, 4196}, {11403, 5068}, {11410, 3839}, {11413, 37197}, {11414, 3089}, {12084, 35488}, {12086, 10019}, {12088, 21841}, {12106, 37118}, {13564, 34484}, {13596, 5066}, {13619, 11563}, {13621, 6143}, {13730, 406}, {13738, 5125}, {13739, 27687}, {14015, 37346}, {14017, 405}, {14070, 18533}, {14118, 23047}, {14865, 3850}, {15247, 16246}, {15329, 35235}, {15750, 3146}, {16049, 431}, {16064, 14004}, {16372, 31909}, {16868, 10224}, {16876, 862}, {17506, 3853}, {17516, 5154}, {17523, 4197}, {17562, 8728}, {17928, 1593}, {18324, 35480}, {18378, 14940}, {18533, 15760}, {18535, 5071}, {19219, 15235}, {20831, 451}, {20832, 21}, {20833, 4222}, {20834, 4213}, {20835, 4207}, {20836, 3144}, {20837, 411}, {20838, 412}, {20850, 38282}, {20851, 4248}, {20854, 420}, {20857, 15149}, {20877, 423}, {20897, 11331}, {20918, 37168}, {21213, 22}, {21284, 23}, {21312, 6623}, {21525, 4230}, {21844, 3627}, {22467, 1885}, {26863, 35018}, {26874, 6755}, {27369, 6656}, {28348, 17555}, {30733, 21530}, {31384, 37361}, {31510, 37985}, {32534, 382}, {33849, 26020}, {34008, 463}, {34009, 462}, {34484, 3628}, {34797, 13406}, {35471, 15761}, {35472, 3830}, {35473, 3845}, {35475, 3858}, {35477, 3843}, {35478, 3856}, {35479, 1657}, {35480, 10254}, {35488, 10255}, {35501, 41106}, {35502, 3851}, {35988, 37432}, {36009, 6881}, {36176, 1316}, {37034, 475}, {37117, 6842}, {37122, 7405}, {37183, 460}, {37194, 6828}, {37245, 5177}, {37250, 37384}, {37257, 4200}, {37259, 11109}, {37289, 37447}, {37295, 37354}, {37305, 1532}, {37311, 1884}, {37387, 6991}, {37391, 6945}, {37440, 10018}, {37441, 8727}, {37453, 31074}, {37777, 5159}, {37814, 18560}, {37898, 37912}, {37908, 857}, {37917, 2071}, {37920, 5189}, {37921, 36191}, {37922, 13619}, {37925, 37942}, {37928, 37777}, {37932, 2070}, {37933, 7464}, {37937, 37987}, {37939, 37935}, {37940, 37931}, {37941, 13473}, {37943, 37938}, {37951, 10257}, {37953, 37934}, {37954, 3153}, {37969, 7426}, {37970, 18403}, {38444, 12173}, {39568, 6622}.El 16 de abril de 1889 nació en Londres, Charles Chaplin, actor cómico del cine mudo conocido por su interpretación de Charlot, y también productor y guionista cinematográfico. Chaplin y su alter ego, el Vagabundo, simbolizan la capacidad del cine para hacernos llorar y reír al mismo tiempo.
t' = ((a^2-(b-c)^2)(b+c-a)((b+c-a)(a+b-c)(a-b+c)+2abct))/
((b+c-a)(a+b-c)(a-b+c)(a^3-a^2(b+c)+(b-c)^2(b+c)-a(b^2+c^2))-4a^2b^2c^2t).
Pares {P=Xi, P'=σ(P)=Xj}, para los índices {i, j}: {1, 65}, {3, 56}, {35, 32636}, {36, 1319}, {40, 37566}, {55, 57}, {56, 1}, {57, 354}, {65, 942}, {354, 5173}, {517, 18838}, {940, 10473}, {999, 2099}, {1155, 3660}, {1214, 40959}, {1381, 2446}, {1382, 2447}, {1388, 5903}, {1402, 3666}, {1403, 982}, {1420, 3057}, {1429, 20358}, {1460, 940}, {1466, 3333}, {1470, 999}, {1617, 55}, {2078, 1155}, {2099, 5902}, {2223, 241}, {2283, 3675}, {2352, 1214}, {3295, 5221}, {3303, 3339}, {3304, 3340}, {3336, 13751}, {3361, 17609}, {3513, 3513}, {3514, 3514}, {3660, 18839}, {5078, 5061}, {5172, 36}, {5193, 5048}, {5204, 1420}, {5217, 3361}, {5221, 18398}, {5563, 11011}, {5584, 1467}, {7742, 37579}, {8069, 1470}, {8071, 26437}, {10267, 1454}, {11011, 31794}, {11492, 5597}, {11493, 5598}, {11509, 3338}, {11510, 46}, {13462, 5919}, {14882, 3337}, {16678, 1402}, {16878, 37593}, {17798, 1429}, {18838, 5570}, {20323, 13601}, {21010, 7146}, {23853, 1403}.
| Xn en IO |
Primera coordenada baricéntrica de σ(Xn) | σ(Xn) en IO |
|---|---|---|
| 1 | a (a + b - c) (a - b + c) (b + c) | X(65) |
| 3 | a^2 (a + b - c) (a - b + c) | X(56) |
| 35 | a (a + b - c) (a - b + c) (2 a + b + c) | X(32636) |
| 36 | a (2 a - b - c) (a + b - c) (a - b + c) | X(1319) |
| 40 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2) | X(37566) |
| 46 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 55 | a (a + b - c) (a - b + c) | X(57) |
| 56 | a | X(1) |
| 57 | -(a ((b - c)^2 - a (b + c))) | X(354) |
| 65 | a (2 a b c + a^2 (b + c) - (b - c)^2 (b + c)) | X(942) |
| 165 | a (a + b - c) (a - b + c) (-2 a (b - c)^2 + a^2 (b + c) + (b - c)^2 (b + c)) | *** |
| 171 | a (a + b - c) (a - b + c) (b c (b + c) + a (b^2 + c^2)) | *** |
| 241 | a (a^2 + (b - c)^2) (-b^2 - c^2 + a (b + c)) | *** |
| 354 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b - c)^2 (b + c) - 2 a (b^2 + b c + c^2)) | X(5173) |
| 484 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + c^3)) | *** |
| 517 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2)) | X(18838) |
| 559 | -(a (a + b - c) (a - b + c) (-2 a^3 + b^3 - a^2 (b - 2 c) + 2 b^2 c - b c^2 - 2 c^3 + 2 a (b^2 + b c + c^2) + b Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) (-2 a^3 - 2 b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 + c^3 + 2 a (b^2 + b c + c^2) + c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) (2 a^4 b c + 2 a^5 (b + c) - 5 a^3 (b^3 + b^2 c + b c^2 + c^3) - (b^2 - c^2)^2 (b^2 - 2 b c + c^2 - Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) + a (b - c)^2 (b + c) (3 b^2 + 4 b c + 3 c^2 + Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) + a^2 (b^4 - 2 b^3 c + c^4 - 2 c^2 Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] + b^2 (2 c^2 - 2 Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) - 2 b (c^3 + c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)])))) | *** |
| 940 | a (a + b - c) (a - b + c) (b c (b + c) + a (b^2 + b c + c^2)) | X(10473) |
| 942 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 + c^2)) | *** |
| 980 | a (a + b - c) (a - b + c) (2 a^2 b c (b + c) + a^3 (b + c)^2 + b c (b^3 + b^2 c + b c^2 + c^3) + a (b^4 + b^3 c + 2 b^2 c^2 + b c^3 + c^4)) | *** |
| 982 | a (a + b - c) (a - b + c) (b^3 + c^3 + a^2 (b + c) - a (b^2 + c^2)) | *** |
| 986 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c) + a b c (b + c)) | *** |
| 988 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b + c)^2 (b^2 + c^2) + a^2 (b^2 + 6 b c + c^2) + a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 999 | a (a + b - c) (a - b + c) (a - 2 (b + c)) | X(2099) |
| 1038 | a (2 a^2 b (b - c)^2 c + a^5 (b + c) + 2 a^3 b c (b + c) + a^4 (b + c)^2 - (b^2 - c^2)^2 (b^2 + c^2) - a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 1040 | a (a + b - c) (a - b + c) (-2 a^2 b (b - c)^2 c + a^5 (b + c) + 2 a^3 b c (b + c) - a^4 (b + c)^2 + (b^2 - c^2)^2 (b^2 + c^2) - a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 1060 | a (a + b - c) (a - b + c) (-4 a^3 b^2 c^2 + a^6 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 1062 | a (a + b - c) (a - b + c) (4 a^3 b^2 c^2 + a^6 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 1082 | -(a (a + b - c) (a - b + c) (2 a^3 - b^3 + a^2 (b - 2 c) - 2 b^2 c + b c^2 + 2 c^3 - 2 a (b^2 + b c + c^2) + b Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) (2 a^3 + 2 b^3 + b^2 c - 2 b c^2 - c^3 + a^2 (-2 b + c) - 2 a (b^2 + b c + c^2) + c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) (2 a^4 b c + 2 a^5 (b + c) - 5 a^3 (b^3 + b^2 c + b c^2 + c^3) + a (b - c)^2 (b + c) (3 b^2 + 4 b c + 3 c^2 - Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) - (b^2 - c^2)^2 (b^2 - 2 b c + c^2 + Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) + a^2 (b^4 - 2 b^3 c + c^4 + 2 c^2 Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] + 2 b^2 (c^2 + Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]) + 2 b (-c^3 + c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)])))) | *** |
| 1155 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b - c)^2 (b + c) - 2 a (b^2 - b c + c^2)) | X(3660) |
| 1159 | a (a + b - c) (a - b + c) (2 a^3 (b + c) + 2 (b^2 - c^2)^2 - a^2 (2 b^2 + b c + 2 c^2) - 2 a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 1214 | a (-b^5 + 2 a^3 b c + b^4 c + b c^4 - c^5 + a^4 (b + c)) | X(40959) |
| 1319 | -(a (2 a b c - a^2 (b + c) + (b - c)^2 (b + c))) | X(517) |
| 1385 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2)) | *** |
| 1388 | -(a (a b c - a^2 (b + c) + (b - c)^2 (b + c))) | X(5903) |
| 1402 | a (b^2 + c^2 + a (b + c)) | X(3666) |
| 1403 | a (b^2 - b c + c^2) | X(982) |
| 1420 | a (a - b - c) ((b - c)^2 + a (b + c)) | X(3057) |
| 1429 | -(a (b (b - c)^2 c - a^2 (b^2 + c^2) + a (b^3 + c^3))) | X(20358) |
| 1454 | -(a (a^4 (b - c)^2 - a^5 (b + c) + (b - c)^4 (b + c)^2 - a (b - c)^2 (b + c)^3 + 2 a^3 (b^3 + b^2 c + b c^2 + c^3) - 2 a^2 (b^4 - 2 b^3 c - 2 b c^3 + c^4))) | *** |
| 1460 | a (a^2 + 2 b c + a (b + c)) | X(940) |
| 1466 | a (a^3 + a^2 (b + c) - (b - c)^2 (b + c) - a (b^2 - 6 b c + c^2)) | X(3333) |
| 1467 | -(a (-(a^5 (b + c)) + 2 a^3 (b - c)^2 (b + c) - a (b - c)^4 (b + c) + a^4 (b + c)^2 + (b - c)^4 (b + c)^2 - 2 a^2 (b^4 + 6 b^2 c^2 + c^4))) | *** |
| 1470 | a^2 (a^2 - b^2 + 4 b c - c^2) | X(999) |
| 1482 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + b c + c^2)) | *** |
| 1617 | a^2 (a - b - c) | X(55) |
| 1622 | a^2 (a + b - c) (a - b + c) (a^3 + a^2 (b + c) - (b - c)^2 (b + c) - a (b + c)^2)^2 | *** |
| 1697 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 - 5 b^2 c - 5 b c^2 + c^3)) | *** |
| 1715 | a (a + b - c) (a - b + c) (-(a^7 (b - c)^2 (b + c)) + a^8 (b + c)^2 + b c (b^2 - c^2)^4 + a (b - c)^4 (b + c)^3 (b^2 + c^2) - a^2 (b - c)^2 (b + c)^4 (b^2 - b c + c^2) + a^4 (b + c)^2 (3 b^4 - 5 b^3 c + 8 b^2 c^2 - 5 b c^3 + 3 c^4) - a^6 (3 b^4 + 3 b^3 c + 4 b^2 c^2 + 3 b c^3 + 3 c^4) + 3 a^5 (b^5 - b^4 c - b c^4 + c^5) - a^3 (b - c)^2 (3 b^5 + 3 b^4 c + 2 b^3 c^2 + 2 b^2 c^3 + 3 b c^4 + 3 c^5)) | *** |
| 1735 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^5 (b^2 + c^2) + (b - c)^2 (b + c)^3 (b^2 - b c + c^2) - a (b^2 - c^2)^2 (b^2 - b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + a^3 (2 b^4 - b^3 c + 2 b^2 c^2 - b c^3 + 2 c^4) - a^2 (b^5 - b^3 c^2 - b^2 c^3 + c^5)) | *** |
| 1754 | a (a + b - c) (a - b + c) (-(a^3 (b - c)^2 (b + c)) + b c (b^2 - c^2)^2 + a^4 (b^2 + c^2) - a^2 (b^4 + b^3 c + b c^3 + c^4) + a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 1758 | -(a (a^3 (b - c)^2 - a^4 (b + c) + a^2 b c (b + c) - a (b - c)^2 (b^2 + c^2) + (b - c)^2 (b^3 + c^3))) | *** |
| 1764 | a (a + b - c) (a - b + c) (-(a^3 (b - c)^2 (b + c)) + a^4 (b + c)^2 + b c (b^2 - c^2)^2 - a^2 (b - c)^2 (b^2 + b c + c^2) + a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 1771 | a (a + b - c) (a - b + c) (-(a^2 b (b - c)^2 c (b + c)) + b (b - c)^2 c (b + c)^3 + a^5 (b^2 + c^2) + a (b^2 - c^2)^2 (b^2 - b c + c^2) + a^3 (-2 b^4 + b^3 c - 2 b^2 c^2 + b c^3 - 2 c^4)) | *** |
| 1936 | a (a + b - c) (a - b + c) (b c (b^2 - c^2)^2 + a^4 (b^2 + c^2) - a^2 (b - c)^2 (b^2 + b c + c^2) - a^3 (b^3 + c^3) + a (b - c)^2 (b^3 + c^3)) | *** |
| 2061 | a (a + b - c) (a - b + c) (2 a^16 + a^15 (b + c) - 3 a^13 (b - c)^2 (b + c) - 3 a^11 (b - c)^4 (b + c) + a^14 (-5 b^2 + 2 b c - 5 c^2) + a (b - c)^6 (b + c)^7 (3 b^2 - 10 b c + 3 c^2) - (b - c)^6 (b + c)^8 (5 b^2 - 6 b c + 5 c^2) - a^12 (b - c)^2 (17 b^2 + 18 b c + 17 c^2) - a^3 (b - c)^4 (b + c)^5 (17 b^4 - 76 b^3 c + 38 b^2 c^2 - 76 b c^3 + 17 c^4) + a^2 (b - c)^4 (b + c)^6 (37 b^4 - 48 b^3 c + 54 b^2 c^2 - 48 b c^3 + 37 c^4) + a^10 (b - c)^2 (95 b^4 + 116 b^3 c + 154 b^2 c^2 + 116 b c^3 + 95 c^4) + a^9 (b - c)^2 (25 b^5 - 43 b^4 c - 142 b^3 c^2 - 142 b^2 c^3 - 43 b c^4 + 25 c^5) - a^4 (b - c)^4 (b + c)^2 (115 b^6 + 270 b^5 c + 381 b^4 c^2 + 388 b^3 c^3 + 381 b^2 c^4 + 270 b c^5 + 115 c^6) - a^8 (b - c)^2 (185 b^6 + 278 b^5 c + 327 b^4 c^2 + 212 b^3 c^3 + 327 b^2 c^4 + 278 b c^5 + 185 c^6) - a^7 (b - c)^2 (45 b^7 - 97 b^6 c - 363 b^5 c^2 - 353 b^4 c^3 - 353 b^3 c^4 - 363 b^2 c^5 - 97 b c^6 + 45 c^7) + a^6 (b - c)^2 (193 b^8 + 368 b^7 c + 332 b^6 c^2 + 80 b^5 c^3 + 102 b^4 c^4 + 80 b^3 c^5 + 332 b^2 c^6 + 368 b c^7 + 193 c^8) + a^5 (b - c)^2 (39 b^9 - 81 b^8 c - 372 b^7 c^2 - 324 b^6 c^3 - 286 b^5 c^4 - 286 b^4 c^5 - 324 b^3 c^6 - 372 b^2 c^7 - 81 b c^8 + 39 c^9)) | *** |
| 2077 | a (a + b - c) (a - b + c) (2 a^4 - 3 a^2 (b - c)^2 - a^3 (b + c) + a (b - c)^2 (b + c) + (b^2 - c^2)^2) | *** |
| 2078 | -(a (-2 a^2 + (b - c)^2 + a (b + c))) | X(1155) |
| 2093 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + a^2 (-3 b^2 + 2 b c - 3 c^2) + 3 (b^2 - c^2)^2 - a (3 b^3 + b^2 c + b c^2 + 3 c^3)) | *** |
| 2095 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - a^5 (2 b^2 + b c + 2 c^2) - a^2 (b - c)^2 (b^3 + c^3) - a^4 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^3 (4 b^4 + b^3 c + 2 b^2 c^2 + b c^3 + 4 c^4)) | *** |
| 2098 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + b c + c^2) - a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 2099 | a (a b c + a^2 (b + c) - (b - c)^2 (b + c)) | X(5902) |
| 2223 | a (a + b - c) (a - b + c) (-b^2 - c^2 + a (b + c)) | X(241) |
| 2283 | a (b - c)^2 (-b^2 - c^2 + a (b + c)) | X(3675) |
| 2352 | a (a + b - c) (a - b + c) (b + c) (a^2 - b^2 - c^2) | X(1214) |
| 2446 | a (a + b - c) (a - b + c) (b^4 - b^3 c - b^2 c^2 + b c^3 + a^3 (b + c) - a^2 (b^2 + 5 b c - 2 c^2) + 4 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - 2 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - a (b^3 - 7 b^2 c + 5 b c^2 - c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) (b^3 c - b^2 c^2 - b c^3 + c^4 + a^3 (b + c) + a^2 (2 b^2 - 5 b c - c^2) - 2 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 4 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - a (-b^3 + 5 b^2 c - 7 b c^2 + c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) (a^7 (b + c) - 2 a^6 (b^2 + b c + c^2) - a^5 (b^3 - 16 b^2 c - 16 b c^2 + c^3) + a^4 (4 b^4 - 23 b^3 c - 36 b^2 c^2 - 23 b c^3 + 4 c^4 + 6 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 6 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) - a^3 (b^5 + 7 b^4 c - 44 b^3 c^2 - 44 b^2 c^3 + 7 b c^4 + c^5 + 8 b^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 8 b c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 8 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) + a (b + c)^2 (b^5 - 12 b^4 c + 11 b^3 c^2 + c^5 + 8 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + b^2 (11 c^3 + 8 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) - 12 b (c^4 + 2 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) + (b + c)^3 (b^4 c - b^3 c^2 - 2 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - b^2 (c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) + b (c^4 + 6 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) - 2 a^2 (b + c) (b^5 - 13 b^4 c + 15 b^3 c^2 + c^5 + 2 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + b^2 (15 c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) - b (13 c^4 + 11 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]))) | *** |
| 2447 | a (a + b - c) (a - b + c) (b^3 c - b^2 c^2 - b c^3 + c^4 + a^3 (b + c) + a^2 (2 b^2 - 5 b c - c^2) + 2 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - 4 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + a (b^3 - 5 b^2 c + 7 b c^2 - c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) (b^4 - b^3 c - b^2 c^2 + b c^3 + a^3 (b + c) - a^2 (b^2 + 5 b c - 2 c^2) - 4 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 2 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + a (-b^3 + 7 b^2 c - 5 b c^2 + c^3 + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) (a^7 (b + c) - 2 a^6 (b^2 + b c + c^2) - a^5 (b^3 - 16 b^2 c - 16 b c^2 + c^3) - a^4 (-4 b^4 + 23 b^3 c + 36 b^2 c^2 + 23 b c^3 - 4 c^4 + 6 b Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 6 c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) + a (b + c)^2 (b^5 - 12 b^4 c + 11 b^3 c^2 + 11 b^2 c^3 - 12 b c^4 + c^5 - 8 b^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 24 b c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - 8 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) - 2 a^2 (b + c) (b^5 - 13 b^4 c + 15 b^3 c^2 + 15 b^2 c^3 - 13 b c^4 + c^5 - 2 b^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 11 b c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - 2 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) + (b + c)^3 (b^4 c - b^3 c^2 - b^2 c^3 + b c^4 + 2 b^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] - 6 b c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 2 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]) + a^3 (-b^5 - 7 b^4 c + 44 b^3 c^2 + 44 b^2 c^3 - 7 b c^4 - c^5 + 8 b^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 8 b c Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))] + 8 c^2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])) | *** |
| 2564 | -(a (a + b - c) (a - b + c) (b^2 c^2 (b + c)^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + a^4 (3 b^3 + 7 b^2 c + 7 b c^2 + 3 c^3) Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + a^2 (b^5 - b^4 c - 5 b^3 c^2 - 5 b^2 c^3 - b c^4 + c^5) Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + a^5 (3 b^2 + 8 b c + 3 c^2) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] - a^3 (b^4 + 6 b^3 c + 9 b^2 c^2 + 6 b c^3 + c^4) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + a (b + c)^2 (2 b^4 - b^2 c^2 + 2 c^4) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) (a^4 (b^2 + c^2) + a^3 (-2 b^2 c + 2 c^3) + a^2 (b^4 - 5 b^2 c^2 + c^4) + 2 a b (2 b^3 c - b c^3 + Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)]) + b c (b^3 c + b c^3 + 2 Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)])) (a^4 (b^2 + c^2) + 2 a^3 (b^3 - b c^2) + a^2 (b^4 - 5 b^2 c^2 + c^4) + 2 a c (-(b^3 c) + 2 b c^3 + Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)]) + b c (b^3 c + b c^3 + 2 Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)]))) | *** |
| 2565 | a (a + b - c) (a - b + c) (-(b^2 c^2 (b + c)^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)]) - a^4 (3 b^3 + 7 b^2 c + 7 b c^2 + 3 c^3) Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + a^2 (-b^5 + b^4 c + 5 b^3 c^2 + 5 b^2 c^3 + b c^4 - c^5) Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + a^5 (3 b^2 + 8 b c + 3 c^2) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] - a^3 (b^4 + 6 b^3 c + 9 b^2 c^2 + 6 b c^3 + c^4) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + a (b + c)^2 (2 b^4 - b^2 c^2 + 2 c^4) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) (a^4 (b^2 + c^2) + 2 a^3 (b^3 - b c^2) + a^2 (b^4 - 5 b^2 c^2 + c^4) + b c (b^3 c + b c^3 - 2 Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)]) - 2 a c (b^3 c - 2 b c^3 + Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)])) (a^4 (b^2 + c^2) + a^3 (-2 b^2 c + 2 c^3) + a^2 (b^4 - 5 b^2 c^2 + c^4) + b c (b^3 c + b c^3 - 2 Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)]) - 2 a b (-2 b^3 c + b c^3 + Sqrt[a^6 (b^2 + c^2) + a^2 (b^2 - c^2)^2 (b^2 + c^2) + b^2 c^2 (b^4 - b^2 c^2 + c^4) - a^4 (b^4 + b^2 c^2 + c^4)])) | *** |
| 2646 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2) - a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 2662 | -(a (b^2 c^2 (b^2 - c^2)^4 + a b (b - c)^4 c (b + c)^3 (b^2 + b c + c^2) - a^9 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^3 (b - c)^2 (b + c)^3 (b^4 - 4 b^3 c + 3 b^2 c^2 - 4 b c^3 + c^4) - a^8 (b^4 + 2 b^3 c - 2 b^2 c^2 + 2 b c^3 + c^4) - a^4 (b^2 - c^2)^2 (3 b^4 + 2 b^3 c + 7 b^2 c^2 + 2 b c^3 + 3 c^4) + a^7 (3 b^5 + 3 b^4 c + b^3 c^2 + b^2 c^3 + 3 b c^4 + 3 c^5) - a^5 (b - c)^2 (3 b^5 + 5 b^4 c + 3 b^3 c^2 + 3 b^2 c^3 + 5 b c^4 + 3 c^5) + a^2 (b^2 - c^2)^2 (b^6 + 2 b^4 c^2 - 2 b^3 c^3 + 2 b^2 c^4 + c^6) + a^6 (3 b^6 + 4 b^5 c - 2 b^4 c^2 + 2 b^3 c^3 - 2 b^2 c^4 + 4 b c^5 + 3 c^6))) | *** |
| 3057 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 - 3 b^2 c - 3 b c^2 + c^3))) | *** |
| 3072 | a (a + b - c) (a - b + c) (a^4 b c (b + c) + b (b - c)^2 c (b + c)^3 + a^5 (b^2 + c^2) + a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^2 b c (b^3 + b^2 c + b c^2 + c^3) - 2 a^3 (b^4 + c^4)) | *** |
| 3075 | a (a + b - c) (a - b + c) (a^4 b c (b + c) - 2 a^2 b (b - c)^2 c (b + c) + b (b - c)^2 c (b + c)^3 + a^5 (b^2 + c^2) + a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^3 (b^2 + c^2)^2) | *** |
| 3245 | a (a + b - c) (a - b + c) (2 a^3 (b + c) + 2 (b^2 - c^2)^2 - 2 a^2 (b^2 - b c + c^2) + a (-2 b^3 + b^2 c + b c^2 - 2 c^3)) | *** |
| 3256 | a (2 a^2 - 3 (b - c)^2 + a (b + c)) | *** |
| 3295 | a (a + b - c) (a - b + c) (a + 2 (b + c)) | X(5221) |
| 3303 | a (a + b - c) (a - b + c) (a + 3 (b + c)) | X(3339) |
| 3304 | a (a + b - c) (a - b + c) (a - 3 (b + c)) | X(3340) |
| 3333 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + 7 b^2 c + 7 b c^2 + c^3)) | *** |
| 3336 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + 2 b^2 c + 2 b c^2 + c^3)) | X(13751) |
| 3337 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + 4 b^2 c + 4 b c^2 + c^3)) | *** |
| 3338 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 + 5 b^2 c + 5 b c^2 + c^3)) | *** |
| 3339 | -(a (8 a b c + 3 a^2 (b + c) - 3 (b - c)^2 (b + c))) | *** |
| 3340 | -(a (4 a b c + 3 a^2 (b + c) - 3 (b - c)^2 (b + c))) | *** |
| 3359 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - 2 a (b - c)^4 (b + c)^2 - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) + 4 a^3 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4)) | *** |
| 3361 | a (8 a b c + a^2 (b + c) - (b - c)^2 (b + c)) | X(17609) |
| 3428 | a (a + b - c) (a - b + c) (a^4 - 2 a^3 (b + c) + 2 a (b - c)^2 (b + c) - (b^2 - c^2)^2) | *** |
| 3503 | -(a (b^2 (b - c)^2 c^2 + a^2 (b - c)^2 (b^2 + c^2) - a^3 (b^3 + c^3) - a b c (b^3 + c^3))) | *** |
| 3513 | a (a + b - c) (a - b + c) (a Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - b Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) | X(3513) |
| 3514 | a (a + b - c) (a - b + c) (a Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - b Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) | X(3514) |
| 3550 | -(a (a + b - c) (a - b + c) (a (b - c)^2 + b c (b + c))) | *** |
| 3576 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 6 b c + c^2)) | *** |
| 3579 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 - 4 b c + c^2)) | *** |
| 3587 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^2 (b - c)^4 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^4 - 4 b^2 c^2 + c^4)) | *** |
| 3601 | -(a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 + 6 b c + c^2))) | *** |
| 3612 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 6 b c + c^2) - a (b^3 + b^2 c + b c^2 + c^3))) | *** |
| 3660 | -(a (a - b - c) ((b - c)^4 + a^3 (b + c) - a (b - c)^2 (b + c) - a^2 (b^2 + c^2))) | X(18839) |
| 3666 | a (a + b - c) (a - b + c) (b^3 + 2 a b c + b^2 c + b c^2 + c^3 + a^2 (b + c)) | *** |
| 3670 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c)) | *** |
| 3675 | -(a (a + b - c) (a - b + c) (-b^2 - c^2 + a (b + c)) (a^3 - a^2 (b + c) - (b - c)^2 (b + c) + a (b^2 - b c + c^2))) | *** |
| 3677 | a (a + b - c) (a - b + c) (3 b^3 + b^2 c + b c^2 + 3 c^3 + 3 a^2 (b + c) - 2 a (b^2 + c^2)) | *** |
| 3744 | a (a + b - c) (a - b + c) (b^3 - 2 a b c + b^2 c + b c^2 + c^3 + a^2 (b + c)) | *** |
| 3745 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b + c)^3 + 2 a (b^2 + b c + c^2)) | *** |
| 3746 | a (a + b - c) (a - b + c) (2 a + 3 (b + c)) | *** |
| 3748 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b - c)^2 (b + c) - 2 a (b^2 + 3 b c + c^2)) | *** |
| 3749 | a (a + b - c) (a - b + c) (b^3 - 4 a b c + b^2 c + b c^2 + c^3 + a^2 (b + c)) | *** |
| 3750 | a (a + b - c) (a - b + c) (b c (b + c) + a (b^2 + 4 b c + c^2)) | *** |
| 3931 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b + c)^2 (b^2 + c^2) + a^2 (b^2 + 4 b c + c^2) + a (b^3 + 5 b^2 c + 5 b c^2 + c^3)) | *** |
| 3953 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c) - 2 a b c (b + c)) | *** |
| 3976 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c) - 3 a b c (b + c)) | *** |
| 3999 | -(a (a + b - c) (a - b + c) (3 b^3 - b^2 c - b c^2 + 3 c^3 + 3 a^2 (b + c) - 2 a (2 b^2 + b c + 2 c^2))) | *** |
| 4003 | a (a + b - c) (a - b + c) (3 b^3 + b^2 c + b c^2 + 3 c^3 + 3 a^2 (b + c) - 2 a (b^2 - b c + c^2)) | *** |
| 4038 | a (a + b - c) (a - b + c) (3 b c (b + c) + a (3 b^2 + 4 b c + 3 c^2)) | *** |
| 4424 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c) + 2 a b c (b + c)) | *** |
| 4689 | -(a (a + b - c) (a - b + c) (b^3 + 6 a b c + b^2 c + b c^2 + c^3 + a^2 (b + c))) | *** |
| 4694 | a (a + b - c) (a - b + c) (b^4 + 2 a^2 b c + b^3 c + b c^3 + c^4 + a^3 (b + c) - 4 a b c (b + c)) | *** |
| 4860 | -(a (a + b - c) (a - b + c) (a^2 (b + c) + (b - c)^2 (b + c) - a (2 b^2 + b c + 2 c^2))) | *** |
| 4883 | -(a (a + b - c) (a - b + c) (b^3 - 3 b^2 c - 3 b c^2 + c^3 + a^2 (b + c) - 2 a (2 b^2 + 3 b c + 2 c^2))) | *** |
| 5010 | a (a + b - c) (a - b + c) (4 a + b + c) | *** |
| 5045 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + 7 b^2 c + 7 b c^2 + c^3))) | *** |
| 5048 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 4 b c + 3 c^2) + a (-3 b^3 + 5 b^2 c + 5 b c^2 - 3 c^3)) | *** |
| 5049 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + 11 b^2 c + 11 b c^2 + c^3)) | *** |
| 5061 | -(a (b (b - c)^2 c (b + c) - a^3 (b^2 + c^2) + a (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4))) | *** |
| 5078 | a (a + b - c) (a - b + c) (a^3 + a b c - b c (b + c)) | X(5061) |
| 5091 | a (a + b - c) (a - b + c) (b (b - c)^2 c (b + c) + a^3 (b^2 + c^2) - 2 a^2 (b^3 + c^3) + a (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4)) | *** |
| 5119 | -(a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 - 3 b^2 c - 3 b c^2 + c^3))) | *** |
| 5122 | -(a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 - 8 b c + c^2))) | *** |
| 5126 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 8 b c + c^2) - a (b^3 - 5 b^2 c - 5 b c^2 + c^3)) | *** |
| 5128 | -(a (a + b - c) (a - b + c) (-3 a^2 (b - c)^2 + 3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a (3 b^3 + b^2 c + b c^2 + 3 c^3))) | *** |
| 5131 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 - 6 b c + c^2) - a (b^3 + 2 b^2 c + 2 b c^2 + c^3))) | *** |
| 5137 | a (a + b - c) (a - b + c) (b c (b^2 - c^2)^2 + a^4 (b^2 + c^2) - a^3 (b^3 + c^3) - a^2 (b^4 + b^3 c + b c^3 + c^4) + a (b^5 + b^3 c^2 + b^2 c^3 + c^5)) | *** |
| 5143 | a (a + b - c) (a - b + c) (-b^3 + a (b - c)^2 - c^3 + a^2 (b + c)) | *** |
| 5172 | a^2 (a^2 - b^2 + b c - c^2) | X(36) |
| 5173 | -(a (-(a^4 (b + c)) + (b - c)^4 (b + c) + 2 a^2 b c (b + c) - 2 a (b^2 - c^2)^2 + 2 a^3 (b^2 + b c + c^2))) | *** |
| 5183 | -(a (a + b - c) (a - b + c) (3 a^3 (b + c) + a^2 (-3 b^2 + 4 b c - 3 c^2) + 3 (b^2 - c^2)^2 + a (-3 b^3 + b^2 c + b c^2 - 3 c^3))) | *** |
| 5193 | a (a - b - c) (2 a^2 - 3 (b - c)^2 - a (b + c)) | X(5048) |
| 5204 | -(a (3 a - b - c) (a + b - c) (a - b + c)) | X(1420) |
| 5217 | -(a (a + b - c) (a - b + c) (3 a + b + c)) | X(3361) |
| 5221 | -(a (3 a b c + a^2 (b + c) - (b - c)^2 (b + c))) | X(18398) |
| 5228 | -(a (-(b (b - c)^2 c) - a (b - c)^2 (b + c) + a^2 (b^2 + b c + c^2))) | *** |
| 5255 | a (a + b - c) (a - b + c) (b c (b + c)^2 + a^2 (b^2 + c^2) + a (b^3 + c^3)) | *** |
| 5264 | a (a + b - c) (a - b + c) (b c (b + c)^2 + a^2 (b^2 + c^2) + a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 5266 | a (a + b - c) (a - b + c) (a^3 (b + c) + a^2 (b^2 + c^2) + (b + c)^2 (b^2 + c^2) + a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 5269 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b + c)^3 + 2 a (b^2 + c^2)) | *** |
| 5285 | -(a (a + b - c) (a - b + c) (2 a^3 + a^2 (b + c) + (b - c)^2 (b + c))) | *** |
| 5329 | -(a (a + b - c) (a - b + c) (a^3 - b c (b + c))) | *** |
| 5337 | a (a + b - c) (a - b + c) (b^2 + c^2) (a^3 + b c (b + c) + a (b^2 + b c + c^2)) | *** |
| 5347 | -(a (a + b - c) (a - b + c) (a^3 - a b c - b c (b + c))) | *** |
| 5348 | -(a (a + b - c) (a - b + c) (b c (b^2 - c^2)^2 + a^4 (b^2 + c^2) - a^3 (b^3 + c^3) + a (b - c)^2 (b^3 + c^3) - a^2 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4))) | *** |
| 5363 | -(a (a + b - c) (a - b + c) (2 a^3 - 3 b c (b + c) - a (b^2 + c^2))) | *** |
| 5425 | a (a + b - c) (a - b + c) (2 a^3 (b + c) + 2 (b^2 - c^2)^2 - 2 a^2 (b^2 + b c + c^2) - a (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3)) | *** |
| 5482 | a (a + b - c) (a - b + c) (2 a^4 b c (b + c) + a^5 (b + c)^2 + b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (b^2 + b c + c^2) - a^2 b c (b^3 + b^2 c + b c^2 + c^3) - a^3 (2 b^4 + b^3 c + 6 b^2 c^2 + b c^3 + 2 c^4)) | *** |
| 5535 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - a (b^2 - c^2)^2 (2 b^2 - b c + 2 c^2) - a^2 (b - c)^2 (b^3 + c^3) - a^4 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^3 (4 b^4 - b^3 c + 2 b^2 c^2 - b c^3 + 4 c^4)) | *** |
| 5536 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 + 2 a^2 (b - c)^2 (b^2 + b c + c^2) - a^4 (3 b^2 + 2 b c + 3 c^2) + a^3 (2 b^3 + b^2 c + b c^2 + 2 c^3) - a (b - c)^2 (3 b^3 + 2 b^2 c + 2 b c^2 + 3 c^3)) | *** |
| 5537 | a (a + b - c) (a - b + c) (2 a^3 - 4 a (b - c)^2 - a^2 (b + c) + 3 (b - c)^2 (b + c)) | *** |
| 5538 | a (a + b - c) (a - b + c) (a^6 (b + c) - 2 a^5 (b + c)^2 + (b - c)^4 (b + c)^3 - a (b^2 - c^2)^2 (2 b^2 - b c + 2 c^2) - a^4 (b^3 - 2 b^2 c - 2 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 4 b^2 c + 4 b c^2 + c^3) + a^3 (4 b^4 + 3 b^3 c - 10 b^2 c^2 + 3 b c^3 + 4 c^4)) | *** |
| 5563 | -(a (a + b - c) (a - b + c) (2 a - 3 (b + c))) | X(11011) |
| 5570 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + 2 b^2 c^2 + b c^3 + 2 c^4) - a^2 (b^5 - b^4 c + 4 b^3 c^2 + 4 b^2 c^3 - b c^4 + c^5)) | *** |
| 5584 | -(a (a + b - c) (a - b + c) (a^4 - 4 a^2 b c - 2 a^3 (b + c) + 2 a (b - c)^2 (b + c) - (b^2 - c^2)^2)) | X(1467) |
| 5597 | -((a + b - c) (a - b + c) (a^4 b - a^3 b (b - 3 c) + Sqrt[2] b (-b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^2 (b^3 + 6 b^2 c + 5 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b^4 + 3 b^3 c - 5 b^2 c^2 + b c^3 + 2 Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (a^4 c + a^3 (3 b - c) c + Sqrt[2] (b - c) c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^2 (5 b^2 c + 6 b c^2 + c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b^3 c - 5 b^2 c^2 + 3 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (-4 a^4 (b + c)^3 + 2 a^5 (b^2 + 3 b c + c^2) - Sqrt[2] (b^2 - c^2)^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a (b - c)^2 (b + c) (2 b^3 - 4 b^2 c - 4 b c^2 + 2 c^3 + 5 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (-20 b^3 c - 64 b^2 c^2 - 20 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (4 b^5 + 20 b^4 c - 24 b^3 c^2 + 4 c^5 + 5 Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + b^2 (-24 c^3 + 5 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + 2 b (10 c^4 + 9 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])))) | *** |
| 5598 | (a + b - c) (a - b + c) (a^4 b - a^3 b (b - 3 c) + Sqrt[2] b (b - c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^2 (-b^3 - 6 b^2 c - 5 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (-b^4 - 3 b^3 c + 5 b^2 c^2 - b c^3 + 2 Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (a^4 c + a^3 (3 b - c) c + Sqrt[2] c (-b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^2 (-5 b^2 c - 6 b c^2 - c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (-(b^3 c) + 5 b^2 c^2 - 3 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (-4 a^4 (b + c)^3 + 2 a^5 (b^2 + 3 b c + c^2) + Sqrt[2] (b^2 - c^2)^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a (b - c)^2 (b + c) (-2 b^3 + 4 b^2 c + 4 b c^2 - 2 c^3 + 5 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (20 b^3 c + 64 b^2 c^2 + 20 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (4 b^5 + 20 b^4 c - 24 b^3 c^2 - 24 b^2 c^3 + 20 b c^4 + 4 c^5 - 5 Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - 18 Sqrt[2] b c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - 5 Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) | *** |
| 5662 | a (a + b - c) (a - b + c) (-2 a^3 b (b - c)^2 c (b + c) + a^6 (b + c)^2 + a^4 b c (b + c)^2 - a^5 (b + c)^3 + b c (b^2 - c^2)^2 (b^2 + c^2) + a (b - c)^2 (b^5 - b^4 c - 2 b^3 c^2 - 2 b^2 c^3 - b c^4 + c^5) - a^2 (b^6 - 4 b^5 c + 3 b^4 c^2 + 3 b^2 c^4 - 4 b c^5 + c^6)) | *** |
| 5697 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 - 2 b^2 c - 2 b c^2 + c^3))) | *** |
| 5706 | a (a + b - c) (a - b + c) (a^4 b c (b + c) + b (b - c)^2 c (b + c)^3 + a^5 (b^2 + b c + c^2) + a (b^2 - c^2)^2 (b^2 + b c + c^2) - 2 a^2 b c (b^3 + b^2 c + b c^2 + c^3) - 2 a^3 (b^4 + b^3 c + b c^3 + c^4)) | *** |
| 5707 | a (a + b - c) (a - b + c) (a^4 b c (b + c) + b (b - c)^2 c (b + c)^3 + a^5 (b^2 + b c + c^2) + a (b^2 - c^2)^2 (b^2 + b c + c^2) - 2 a^2 b c (b^3 + b^2 c + b c^2 + c^3) - 2 a^3 (b^4 + b^3 c + b^2 c^2 + b c^3 + c^4)) | *** |
| 5708 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 - b c + c^2)) | *** |
| 5709 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^2 (b - c)^4 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^4 + c^4)) | *** |
| 5710 | a (a + b - c) (a - b + c) (b c (b + c)^2 + a^2 (b^2 + b c + c^2) + a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 5711 | a (a + b - c) (a - b + c) (b c (b + c)^2 + a^2 (b^2 + b c + c^2) + a (b^3 + 2 b^2 c + 2 b c^2 + c^3)) | *** |
| 5885 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - b c + 2 c^2) - a^4 (b^3 + c^3) + a^3 (4 b^4 + b^3 c + 4 b^2 c^2 + b c^3 + 4 c^4) - a^2 (b^5 - b^3 c^2 - b^2 c^3 + c^5)) | *** |
| 5902 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + 2 b^2 c + 2 b c^2 + c^3)) | *** |
| 5903 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + c^3)) | *** |
| 5908 | a (a + b - c) (a - b + c) (a^9 (b + c) + a (b - c)^6 (b + c)^3 + (b - c)^4 (b + c)^6 + a^8 (b^2 + 4 b c + c^2) - 4 a^3 (b + c) (b^3 - b^2 c + b c^2 - c^3)^2 - 4 a^7 (b^3 + b^2 c + b c^2 + c^3) - 2 a^2 (b^2 - c^2)^2 (2 b^4 - b^3 c + 2 b^2 c^2 - b c^3 + 2 c^4) - 2 a^6 (2 b^4 + b^3 c + 2 b^2 c^2 + b c^3 + 2 c^4) + 2 a^4 (b - c)^2 (3 b^4 + 3 b^3 c + 4 b^2 c^2 + 3 b c^3 + 3 c^4) + 2 a^5 (3 b^5 + b^4 c + 4 b^3 c^2 + 4 b^2 c^3 + b c^4 + 3 c^5)) | *** |
| 5919 | -(a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 - 7 b^2 c - 7 b c^2 + c^3))) | *** |
| 6244 | a (a + b - c) (a - b + c) (a^3 - 3 a (b - c)^2 + 2 (b - c)^2 (b + c)) | *** |
| 6282 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - 2 a^5 (b + c)^2 - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b - c)^2 (b^2 + 3 b c + c^2)) | *** |
| 6583 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 + b c + 2 c^2) - a^2 (b - c)^2 (b^3 + c^3) - a^4 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^3 (4 b^4 + 3 b^3 c + 4 b^2 c^2 + 3 b c^3 + 4 c^4))) | *** |
| 6766 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + 6 b c + c^2) - a^2 (b - c)^2 (b^3 - 13 b^2 c - 13 b c^2 + c^3) - a^4 (b^3 + 15 b^2 c + 15 b c^2 + c^3) + 4 a^3 (b^4 + 3 b^3 c + 3 b c^3 + c^4))) | *** |
| 6767 | a (a + b - c) (a - b + c) (a + 4 (b + c)) | *** |
| 6769 | -(a (a + b - c) (a - b + c) (a^6 (b + c) - a^2 (b - c)^4 (b + c) - 2 a^5 (b + c)^2 - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a (b - c)^2 (b + c)^4 + 4 a^3 (b^4 + 2 b^3 c - 2 b^2 c^2 + 2 b c^3 + c^4))) | *** |
| 7011 | -(a (a^5 - 2 a^2 (b - c)^2 (b + c) - a (b^2 - c^2)^2 + 2 (b^5 - b^4 c - b c^4 + c^5))) | *** |
| 7070 | a (a + b - c) (a - b + c) (a^4 (b - c)^2 + a^5 (b + c) - 2 a^3 (b - c)^2 (b + c) + a (b - c)^4 (b + c) + (b - c)^2 (b + c)^4 - 2 a^2 (b^2 - c^2)^2) | *** |
| 7146 | -(a (2 a^2 b c + a^3 (b + c) + a b c (b + c) - (b - c)^2 (b^2 + b c + c^2))) | *** |
| 7280 | -(a (4 a - b - c) (a + b - c) (a - b + c)) | *** |
| 7373 | a (a + b - c) (a - b + c) (a - 4 (b + c)) | *** |
| 7688 | -(a (a + b - c) (a - b + c) (2 a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 + 6 b c + c^2))) | *** |
| 7742 | -(a^2 (a + b - c) (a - b + c) (a^3 + b^3 + b^2 c + b c^2 + c^3 - a^2 (b + c) - a (b + c)^2)) | X(37579) |
| 7957 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^2 (b - c)^4 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - 2 a (b^2 - c^2)^2 (b^2 + b c + c^2) + 4 a^3 (b^4 + b^3 c - 2 b^2 c^2 + b c^3 + c^4)) | *** |
| 7962 | -(a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) + a (-3 b^3 + 7 b^2 c + 7 b c^2 - 3 c^3))) | *** |
| 7964 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 - 3 a^4 (b^2 + c^2) + 2 a^2 (b - c)^2 (b^2 + 3 b c + c^2) + 2 a^3 (b^3 - 2 b^2 c - 2 b c^2 + c^3) - 3 a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 7982 | -(a (a + b - c) (a - b + c) (3 a^3 (b + c) - 3 a (b - c)^2 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2))) | *** |
| 7987 | -(a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 10 b c + c^2))) | *** |
| 7991 | -(a (a + b - c) (a - b + c) (3 a^3 (b + c) - 3 a (b - c)^2 (b + c) + a^2 (-3 b^2 + 2 b c - 3 c^2) + 3 (b^2 - c^2)^2)) | *** |
| 7994 | a (a + b - c) (a - b + c) (a^5 (b + c) - 3 a^4 (b + c)^2 + (b - c)^4 (b + c)^2 - 3 a (b - c)^2 (b + c)^3 + 2 a^2 (b - c)^2 (b^2 + 6 b c + c^2) + 2 a^3 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 8069 | a^2 (a + b - c) (a - b + c) (a^3 + b^3 - a (b - c)^2 + b^2 c + b c^2 + c^3 - a^2 (b + c)) | X(1470) |
| 8071 | a^2 (a + b - c) (a - b + c) (a^3 + b^3 - a (b - c)^2 - 3 b^2 c - 3 b c^2 + c^3 - a^2 (b + c)) | X(26437) |
| 8148 | a (a + b - c) (a - b + c) (2 a^3 (b + c) - 2 a (b - c)^2 (b + c) + 2 (b^2 - c^2)^2 - a^2 (2 b^2 + b c + 2 c^2)) | *** |
| 8158 | a (a + b - c) (a - b + c) (a^4 - 5 a^3 (b + c) + 5 a (b - c)^2 (b + c) - 4 (b^2 - c^2)^2 + a^2 (3 b^2 + 2 b c + 3 c^2)) | *** |
| 8162 | a (a + b - c) (a - b + c) (a + 7 (b + c)) | *** |
| 8163 | a (a + b - c) (a - b + c) (a^4 - 8 a^3 (b + c) - 7 (b^2 - c^2)^2 + a^2 (6 b^2 + 8 b c + 6 c^2) + 8 a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 8171 | a^2 (a + b - c) (a - b + c) (3 a^2 + 3 b^2 + 10 b c + 3 c^2 - 6 a (b + c)) | *** |
| 8186 | -((a + b - c) (a - b + c) (2 a^4 b + a^3 b (-2 b + 3 c) + Sqrt[2] b (-b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^2 (2 b^3 + 6 b^2 c + 4 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (2 b^4 + 3 b^3 c - 4 b^2 c^2 - b c^3 + 2 Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (2 a^4 c + a^3 (3 b - 2 c) c + Sqrt[2] (b - c) c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^2 (4 b^2 c + 6 b c^2 + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (-(b^3 c) - 4 b^2 c^2 + 3 b c^3 + 2 c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (2 a^5 (b^2 + c^2) - 4 a^4 (b^3 + 6 b^2 c + 6 b c^2 + c^3) - 2 Sqrt[2] (b^2 - c^2)^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a (b - c)^2 (b + c) (2 b^3 - 10 b^2 c - 10 b c^2 + 2 c^3 + 7 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + 4 a^2 (b^5 + 8 b^4 c - 9 b^3 c^2 - 9 b^2 c^3 + 8 b c^4 + c^5 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 6 Sqrt[2] b c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (-20 b^3 c - 88 b^2 c^2 + 5 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 5 b (-4 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])))) | *** |
| 8187 | (a + b - c) (a - b + c) (2 a^4 b + a^3 b (-2 b + 3 c) + Sqrt[2] b (b - c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^2 (-2 b^3 - 6 b^2 c - 4 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (-2 b^4 - 3 b^3 c + 4 b^2 c^2 + b c^3 + 2 Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (2 a^4 c + a^3 (3 b - 2 c) c + Sqrt[2] c (-b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^2 (-4 b^2 c - 6 b c^2 - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (b^3 c + 4 b^2 c^2 - 3 b c^3 - 2 c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])) (2 a^5 (b^2 + c^2) - 4 a^4 (b^3 + 6 b^2 c + 6 b c^2 + c^3) + 2 Sqrt[2] (b^2 - c^2)^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a (b - c)^2 (b + c) (-2 b^3 + 10 b^2 c + 10 b c^2 - 2 c^3 + 7 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - 4 a^2 (-b^5 - 8 b^4 c + 9 b^3 c^2 + 9 b^2 c^3 - 8 b c^4 - c^5 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 6 Sqrt[2] b c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (20 b^3 c + 88 b^2 c^2 + 5 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + 5 b (4 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))) | *** |
| 8193 | a^2 (a + b - c) (a - b + c) (a^3 + a^2 (b + c) + (b - c)^2 (b + c) + a (b^2 + c^2)) | *** |
| 8251 | a (a + b - c) (a - b + c) (-(a^8 (b - c)^2) + a^9 (b + c) - 2 a^4 b c (b + c)^2 (b^2 + c^2) - a (b - c)^4 (b + c)^3 (b^2 + c^2) + (b^2 - c^2)^4 (b^2 + c^2) - 2 a^2 (b - c)^4 (b + c)^2 (b^2 + b c + c^2) - 2 a^7 (b^3 + c^3) - 2 a^5 b c (b^3 + b^2 c + b c^2 + c^3) + 2 a^6 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4) + 2 a^3 (b^7 - b^4 c^3 - b^3 c^4 + c^7)) | *** |
| 8270 | a (-b^5 + b^4 c + 2 a b (b - c)^2 c + b c^4 - c^5 + a^4 (b + c)) | *** |
| 8273 | a (a + b - c) (a - b + c) (a^4 + (b^2 - c^2)^2 - 2 a^2 (b^2 + 4 b c + c^2)) | *** |
| 8726 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - 2 a^5 (b + c)^2 - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^4 + b^3 c + 4 b^2 c^2 + b c^3 + c^4)) | *** |
| 8758 | a (a + b - c) (a - b + c) (a^2 - b^2 - c^2) (a^3 (b + c) + a (b - c)^2 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 + c^2)) | *** |
| 8924 | -(a (a + b - c) (a - b + c) (b^2 c^2 (b^2 - c^2)^2 - a^4 (b - c)^2 (b^2 + c^2) + a^5 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a b c (b^5 - b^3 c^2 - b^2 c^3 + c^5) - a^3 (b^5 + b^4 c + b^3 c^2 + b^2 c^3 + b c^4 + c^5) + a^2 (b^6 - 2 b^4 c^2 + 2 b^3 c^3 - 2 b^2 c^4 + c^6))) | *** |
| 9120 | a (a + b - c) (a - b + c) (8 a^9 b (b - c)^2 c + a^12 (b + c) + (b - c)^6 (b + c)^7 + 16 a^5 b^2 c^2 (b^2 - c^2)^2 - 8 a b c (b^2 - c^2)^4 (b^2 + c^2) - 16 a^7 b (b - c)^2 c (b^2 + b c + c^2) + 16 a^3 b (b - c)^4 c (b + c)^2 (b^2 + b c + c^2) + a^8 (b + c)^3 (15 b^2 - 14 b c + 15 c^2) - 2 a^10 (3 b^3 + 7 b^2 c + 7 b c^2 + 3 c^3) - 2 a^2 (b - c)^4 (b + c)^3 (3 b^4 + 2 b^3 c + 6 b^2 c^2 + 2 b c^3 + 3 c^4) - 4 a^6 (b + c)^3 (5 b^4 - 10 b^3 c + 14 b^2 c^2 - 10 b c^3 + 5 c^4) + a^4 (b - c)^2 (b + c)^3 (15 b^4 - 16 b^3 c + 34 b^2 c^2 - 16 b c^3 + 15 c^4)) | *** |
| 9364 | -(a (a (b - c)^4 + a^2 b c (b + c) + b (b - c)^2 c (b + c) - a^3 (b^2 + c^2))) | *** |
| 9371 | a (a + b - c) (a - b + c) (-4 a^2 b (b - c)^2 c + a^5 (b + c) - a (b - c)^4 (b + c) - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2)) | *** |
| 9441 | a (a + b - c) (a - b + c) (b (b - c)^2 c (b + c) + a^3 (b^2 + c^2) + a (b - c)^2 (b^2 + c^2) + a^2 (-2 b^3 + b^2 c + b c^2 - 2 c^3)) | *** |
| 9627 | a (a + b - c) (a - b + c) (2 a^3 b^2 c^2 + a^6 (b + c) + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) - a^2 (b^5 + b^4 c - 4 b^3 c^2 - 4 b^2 c^3 + b c^4 + c^5)) | *** |
| 9630 | a (a + b - c) (a - b + c) (2 a^3 b^2 c^2 + a^6 (b + c) + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) - a^2 (b^5 + b^4 c + b c^4 + c^5)) | *** |
| 9659 | a^2 (a + b - c) (a - b + c) (a^6 - 2 a b^2 c^2 (b + c) - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2) - a^2 (b^4 + c^4)) | *** |
| 9672 | a^2 (a + b - c) (a - b + c) (a^6 + 2 a b^2 c^2 (b + c) - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2) - a^2 (b^4 + c^4)) | *** |
| 9819 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + a^2 (-3 b^2 + 2 b c - 3 c^2) + 3 (b^2 - c^2)^2 + a (-3 b^3 + 11 b^2 c + 11 b c^2 - 3 c^3)) | *** |
| 9940 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + 6 b^2 c^2 + b c^3 + 2 c^4) - a^2 (b^5 - b^4 c - b c^4 + c^5))) | *** |
| 9957 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 - 5 b^2 c - 5 b c^2 + c^3)) | *** |
| 10202 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + 4 b^2 c^2 + b c^3 + 2 c^4) - a^2 (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 10222 | a (a + b - c) (a - b + c) (3 a^3 (b + c) - 3 a (b - c)^2 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 4 b c + 3 c^2)) | *** |
| 10225 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 - b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - 3 b c + 2 c^2) - a^2 (b - c)^2 (b^3 + c^3) - a^4 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^3 (4 b^4 - 5 b^3 c + 8 b^2 c^2 - 5 b c^3 + 4 c^4)) | *** |
| 10246 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 3 b c + c^2)) | *** |
| 10247 | a (a + b - c) (a - b + c) (2 a^3 (b + c) - 2 a (b - c)^2 (b + c) + 2 (b^2 - c^2)^2 - a^2 (2 b^2 + 3 b c + 2 c^2)) | *** |
| 10267 | a (a + b - c) (a - b + c) (a^4 + (b^2 - c^2)^2 - 2 a^2 (b^2 + b c + c^2)) | X(1454) |
| 10268 | a (a + b - c) (a - b + c) (-2 a^5 (b - c)^2 + a^6 (b + c) - a^2 (b - c)^4 (b + c) - 2 a (b - c)^4 (b + c)^2 - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 + 4 a^3 (b^4 - 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4)) | *** |
| 10269 | a (a + b - c) (a - b + c) (a^4 + 6 a^2 b c - 2 a^3 (b + c) + 2 a (b - c)^2 (b + c) - (b^2 - c^2)^2) | *** |
| 10270 | a (a + b - c) (a - b + c) (-2 a^5 (b - c)^2 + a^6 (b + c) - a^2 (b - c)^4 (b + c) - 2 a (b - c)^4 (b + c)^2 - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 + 4 a^3 (b^4 - 2 b^3 c + 6 b^2 c^2 - 2 b c^3 + c^4)) | *** |
| 10273 | a (a + b - c) (a - b + c) (3 a^6 (b + c) + 3 (b - c)^4 (b + c)^3 - 6 a^5 (b^2 + b c + c^2) - 2 a (b^2 - c^2)^2 (3 b^2 - 4 b c + 3 c^2) + a^4 (-3 b^3 + 5 b^2 c + 5 b c^2 - 3 c^3) - a^2 (b - c)^2 (3 b^3 + 11 b^2 c + 11 b c^2 + 3 c^3) + 2 a^3 (6 b^4 - b^3 c - b c^3 + 6 c^4)) | *** |
| 10284 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - 7 b c + 2 c^2) - a^4 (b^3 - 6 b^2 c - 6 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 8 b^2 c + 8 b c^2 + c^3) + a^3 (4 b^4 - 5 b^3 c - 8 b^2 c^2 - 5 b c^3 + 4 c^4)) | *** |
| 10306 | a (a + b - c) (a - b + c) (a^4 + a^3 (b + c) - a (b - c)^2 (b + c) + a^2 (-3 b^2 + 2 b c - 3 c^2) + 2 (b^2 - c^2)^2) | *** |
| 10310 | a (a + b - c) (a - b + c) (a^4 - 2 a^2 (b - c)^2 + (b^2 - c^2)^2) | *** |
| 10319 | a (a + b - c) (a - b + c) (-(a^4 (b - c)^2) + a^5 (b + c) + 2 a^3 b c (b + c) + 2 a^2 b c (b + c)^2 + (b^2 - c^2)^2 (b^2 + c^2) - a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 10383 | a (a + b - c) (a - b + c) (a^5 (b + c) - 3 a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 2 a^3 (b + c)^3 - a (b - c)^2 (3 b^3 + 5 b^2 c + 5 b c^2 + 3 c^3) + 2 a^2 (b^4 + 6 b^2 c^2 + c^4)) | *** |
| 10388 | a (a + b - c) (a - b + c) (a^5 (b + c) - 3 a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 2 a^3 (b + c)^3 - a (b - c)^2 (3 b^3 + 5 b^2 c + 5 b c^2 + 3 c^3) + 2 a^2 (b^4 - 10 b^2 c^2 + c^4)) | *** |
| 10389 | a (a + b - c) (a - b + c) (a^2 (b + c) + (b - c)^2 (b + c) - 2 a (b^2 + 4 b c + c^2)) | *** |
| 10434 | a (a + b - c) (a - b + c) (3 a^2 (b + c) - (b - c)^2 (b + c) + 2 a (b^2 + c^2)) | *** |
| 10439 | a (a + b - c) (a - b + c) (2 a^4 (b + c)^2 + 2 b c (b^2 - c^2)^2 - a^3 (2 b^3 + b^2 c + b c^2 + 2 c^3) + a (b - c)^2 (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3) - 2 a^2 (b^4 + c^4)) | *** |
| 10441 | a (a + b - c) (a - b + c) (2 a^4 b c (b + c) + a^5 (b + c)^2 + b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (b^2 + b c + c^2) - a^2 b c (b^3 + b^2 c + b c^2 + c^3) - a^3 (2 b^4 + b^3 c + b c^3 + 2 c^4)) | *** |
| 10470 | a (a + b - c) (a - b + c) (-4 a^4 b c (b + c) + a^5 (b + c)^2 + b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (b^2 + b c + c^2) - a^2 b c (b^3 + 7 b^2 c + 7 b c^2 + c^3) - a^3 (2 b^4 + 7 b^3 c + 6 b^2 c^2 + 7 b c^3 + 2 c^4)) | *** |
| 10473 | a (2 a^2 b c (b + c) - b (b - c)^2 c (b + c) + a^3 (b + c)^2 + a (-b^4 + b^3 c + 2 b^2 c^2 + b c^3 - c^4)) | *** |
| 10474 | -(a (-2 a^4 (b + c)^2 + 2 b c (b^2 - c^2)^2 - a^3 (2 b^3 + 7 b^2 c + 7 b c^2 + 2 c^3) + 2 a^2 (b^4 - 2 b^3 c - 5 b^2 c^2 - 2 b c^3 + c^4) + a (2 b^5 + b^4 c - 5 b^3 c^2 - 5 b^2 c^3 + b c^4 + 2 c^5))) | *** |
| 10475 | a (-b^3 + 3 b^2 c + 3 b c^2 - c^3 + 3 a^2 (b + c) + 2 a (b^2 + b c + c^2)) | *** |
| 10476 | a (a + b - c) (a - b + c) (5 a^4 b c (b + c) - 2 a^2 b (b - c)^2 c (b + c) + a^5 (b + c)^2 + b (b - c)^2 c (b + c)^3 + a (b - c)^2 (b + c)^4 - 2 a^3 (b^4 + c^4)) | *** |
| 10480 | a (a + b - c) (a - b + c) (2 a^4 b c (b + c) + a^5 (b + c)^2 + a^2 b c (b + c)^3 + b (b - c)^2 c (b + c)^3 + a^3 (-2 b^4 + b^3 c + 4 b^2 c^2 + b c^3 - 2 c^4) + a (b + c)^2 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4)) | *** |
| 10618 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^2 (b + c)^3 (b^2 + 6 b c + c^2) + 3 a (b^2 - c^2)^2 (2 b^2 + 3 b c + 2 c^2) + 2 a^5 (3 b^2 + 7 b c + 3 c^2) - a^4 (b^3 + c^3) - a^3 (12 b^4 + 23 b^3 c + 20 b^2 c^2 + 23 b c^3 + 12 c^4) - a^2 (b^5 + 8 b^4 c + 23 b^3 c^2 + 23 b^2 c^3 + 8 b c^4 + c^5)) | *** |
| 10679 | a (a + b - c) (a - b + c) (a^4 + a^3 (b + c) - a (b - c)^2 (b + c) + 2 (b^2 - c^2)^2 - 3 a^2 (b^2 + c^2)) | *** |
| 10680 | a (a + b - c) (a - b + c) (a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) - 2 (b^2 - c^2)^2 + a^2 (b^2 + 4 b c + c^2)) | *** |
| 10831 | a^2 (a^5 - b^5 + 2 a^3 b c + b^4 c + b c^4 - c^5 + a^4 (b + c) + 2 a^2 b c (b + c) - a (b^4 - 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4)) | *** |
| 10832 | a^2 (a + b - c) (a - b + c) (a^5 + b^5 + 2 a^3 b c - b^4 c - b c^4 + c^5 - a^4 (b + c) - 2 a^2 b c (b + c) - a (b^4 - 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4)) | *** |
| 10856 | a (a + b - c) (a - b + c) (a^5 (b + c) - 3 a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 2 a^3 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3) + 2 a^2 (b^4 - 4 b^3 c - 2 b^2 c^2 - 4 b c^3 + c^4)) | *** |
| 10857 | a (a + b - c) (a - b + c) (2 a^2 (b - c)^4 + a^5 (b + c) - 3 a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 2 a^3 (b^3 + 5 b^2 c + 5 b c^2 + c^3) - a (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3)) | *** |
| 10882 | a (a + b - c) (a - b + c) (5 a^3 (b + c) + (b^2 - c^2)^2 + a^2 (3 b^2 + 2 b c + 3 c^2) - a (b^3 - 5 b^2 c - 5 b c^2 + c^3)) | *** |
| 10902 | a (a + b - c) (a - b + c) (2 a^4 - a^3 (b + c) + a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2)) | *** |
| 10965 | a (a + b - c) (a - b + c) (a^4 + 2 a^3 (b + c) + 3 (b^2 - c^2)^2 - 2 a^2 (2 b^2 + b c + 2 c^2) - 2 a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 10966 | a (a + b - c) (a - b + c) (a^4 + 2 a^2 b c - 2 a^3 (b + c) - (b^2 - c^2)^2 + 2 a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 10980 | a (a + b - c) (a - b + c) (3 a^2 (b + c) + 3 (b - c)^2 (b + c) - 2 a (3 b^2 + 2 b c + 3 c^2)) | *** |
| 11009 | a (a + b - c) (a - b + c) (2 a^3 (b + c) + 2 (b^2 - c^2)^2 - 2 a^2 (b^2 + b c + c^2) + a (-2 b^3 + b^2 c + b c^2 - 2 c^3)) | *** |
| 11010 | a (a + b - c) (a - b + c) (-(a^2 (b - c)^2) + a^3 (b + c) + (b^2 - c^2)^2 - a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 11011 | a (2 a b c + 3 a^2 (b + c) - 3 (b - c)^2 (b + c)) | X(31794) |
| 11012 | a (a + b - c) (a - b + c) (2 a^4 - a^2 (b - c)^2 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) - (b^2 - c^2)^2) | *** |
| 11014 | a (a + b - c) (a - b + c) (a^6 (b + c) - 2 a^5 (b + c)^2 + (b - c)^4 (b + c)^3 - a (b^2 - c^2)^2 (2 b^2 - 5 b c + 2 c^2) + a^3 (b - c)^2 (4 b^2 + 7 b c + 4 c^2) - a^4 (b^3 - 6 b^2 c - 6 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 8 b^2 c + 8 b c^2 + c^3)) | *** |
| 11018 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (3 b^2 + 4 b c + 3 c^2) + 2 a^3 (b^3 + b^2 c + b c^2 + c^3) - a (b - c)^2 (3 b^3 + 5 b^2 c + 5 b c^2 + 3 c^3) + 2 a^2 (b^4 + b^3 c + 4 b^2 c^2 + b c^3 + c^4)) | *** |
| 11021 | a (a + b - c) (a - b + c) (2 a^4 (b + c)^2 + 2 b c (b^2 - c^2)^2 - a^3 (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3) - 2 a^2 (b^4 + 2 b^3 c + 4 b^2 c^2 + 2 b c^3 + c^4) + a (2 b^5 - 3 b^4 c - 7 b^3 c^2 - 7 b^2 c^3 - 3 b c^4 + 2 c^5)) | *** |
| 11224 | a (a + b - c) (a - b + c) (7 a^3 (b + c) - 7 a (b - c)^2 (b + c) + 7 (b^2 - c^2)^2 - a^2 (7 b^2 + 6 b c + 7 c^2)) | *** |
| 11227 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 + 2 a^3 (b + c)^3 + 2 a^2 (b - c)^2 (b^2 - b c + c^2) - a^4 (3 b^2 + 4 b c + 3 c^2) - a (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3)) | *** |
| 11248 | a (a + b - c) (a - b + c) (a^4 + (b^2 - c^2)^2 - 2 a^2 (b^2 - b c + c^2)) | *** |
| 11249 | a (a + b - c) (a - b + c) (a^4 + 2 a^2 b c - 2 a^3 (b + c) + 2 a (b - c)^2 (b + c) - (b^2 - c^2)^2) | *** |
| 11278 | a (a + b - c) (a - b + c) (5 a^3 (b + c) - 5 a (b - c)^2 (b + c) + 5 (b^2 - c^2)^2 - a^2 (5 b^2 + 4 b c + 5 c^2)) | *** |
| 11280 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) + a (-3 b^3 + 2 b^2 c + 2 b c^2 - 3 c^3)) | *** |
| 11407 | a (a + b - c) (a - b + c) (3 a^5 (b + c) + 3 (b - c)^4 (b + c)^2 + 2 a^2 (b - c)^2 (3 b^2 - 2 b c + 3 c^2) - a^4 (9 b^2 + 10 b c + 9 c^2) - 3 a (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3) + 2 a^3 (3 b^3 + 7 b^2 c + 7 b c^2 + 3 c^3)) | *** |
| 11507 | -(a (a + b - c) (a - b + c) (a^4 - 2 a b c (b + c) + (b^2 - c^2)^2 - 2 a^2 (b^2 + c^2))) | *** |
| 11508 | a (a + b - c) (a - b + c) (a^4 + 2 a b c (b + c) + (b^2 - c^2)^2 - 2 a^2 (b^2 + c^2)) | *** |
| 11509 | -(a (a^3 + a^2 (b + c) - (b - c)^2 (b + c) - a (b^2 - 4 b c + c^2))) | X(3338) |
| 11510 | a (a^3 + a^2 (b + c) - (b - c)^2 (b + c) - a (b^2 + c^2)) | X(46) |
| 11518 | a (a + b - c) (a - b + c) (3 a^3 (b + c) - 3 a (b + c)^3 + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2)) | *** |
| 11521 | a (a + b - c) (a - b + c) (2 a^4 b c (b + c) + 3 a^5 (b + c)^2 + 3 b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (3 b^2 + b c + 3 c^2) - a^2 b c (b^3 + 7 b^2 c + 7 b c^2 + c^3) - a^3 (6 b^4 + 3 b^3 c - 2 b^2 c^2 + 3 b c^3 + 6 c^4)) | *** |
| 11529 | -(a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) - a (3 b^3 + 5 b^2 c + 5 b c^2 + 3 c^3))) | *** |
| 11531 | -(a (a + b - c) (a - b + c) (5 a^3 (b + c) - 5 a (b - c)^2 (b + c) + 5 (b^2 - c^2)^2 - a^2 (5 b^2 + 2 b c + 5 c^2))) | *** |
| 11567 | a (a + b - c) (a - b + c) (2 a^6 (b + c) - 4 a^5 (b + c)^2 + 2 (b - c)^4 (b + c)^3 - a (b^2 - c^2)^2 (4 b^2 - 7 b c + 4 c^2) + a^4 (-2 b^3 + 9 b^2 c + 9 b c^2 - 2 c^3) - a^2 (b - c)^2 (2 b^3 + 13 b^2 c + 13 b c^2 + 2 c^3) + a^3 (8 b^4 + b^3 c - 16 b^2 c^2 + b c^3 + 8 c^4)) | *** |
| 11575 | a (a + b - c) (a - b + c) (a^5 (b + c) - 3 a (b - c)^4 (b + c) + (b - c)^4 (b + c)^2 - a^4 (3 b^2 + 4 b c + 3 c^2) + 2 a^3 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + 2 a^2 (b^4 - 7 b^3 c + 4 b^2 c^2 - 7 b c^3 + c^4)) | *** |
| 11849 | a (a + b - c) (a - b + c) (a^4 + a^2 (-2 b^2 + b c - 2 c^2) + (b^2 - c^2)^2) | *** |
| 12000 | a (a + b - c) (a - b + c) (a^4 + 3 a^3 (b + c) - 3 a (b - c)^2 (b + c) + 4 (b^2 - c^2)^2 - a^2 (5 b^2 + 4 b c + 5 c^2)) | *** |
| 12001 | a (a + b - c) (a - b + c) (a^4 - 5 a^3 (b + c) + 5 a (b - c)^2 (b + c) - 4 (b^2 - c^2)^2 + a^2 (3 b^2 + 8 b c + 3 c^2)) | *** |
| 12009 | a (a + b - c) (a - b + c) (3 a^6 (b + c) + 3 (b - c)^4 (b + c)^3 - 6 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (6 b^2 + b c + 6 c^2) - a^2 (b - c)^2 (3 b^3 + 2 b^2 c + 2 b c^2 + 3 c^3) - a^4 (3 b^3 + 4 b^2 c + 4 b c^2 + 3 c^3) + a^3 (12 b^4 + 7 b^3 c + 20 b^2 c^2 + 7 b c^3 + 12 c^4)) | *** |
| 12410 | a^2 (a + b - c) (a - b + c) (a^3 + b^3 - 3 b^2 c - 3 b c^2 + c^3 + a^2 (b + c) + a (b^2 + c^2)) | *** |
| 12435 | -(a (a + b - c) (a - b + c) (3 a^4 b c (b + c) + 2 a^5 (b + c)^2 - a^2 b c (b + c)^3 + 2 b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (2 b^2 + b c + 2 c^2) - a^3 (4 b^4 + b^3 c - 2 b^2 c^2 + b c^3 + 4 c^4))) | *** |
| 12555 | a (a + b - c) (a - b + c) (a^5 (b + c) + 5 a^4 (b + c)^2 + (b^2 - c^2)^2 (b^2 + 6 b c + c^2) + a^3 (-6 b^3 + 2 b^2 c + 2 b c^2 - 6 c^3) + a (b - c)^2 (5 b^3 + 7 b^2 c + 7 b c^2 + 5 c^3) - 2 a^2 (3 b^4 + 2 b^2 c^2 + 3 c^4)) | *** |
| 12702 | -(a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 - b c + c^2))) | *** |
| 12703 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 - 5 b c + c^2) - a^4 (b^3 - 7 b^2 c - 7 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 9 b^2 c + 9 b c^2 + c^3) + 2 a^3 (2 b^4 - 5 b^3 c - 2 b^2 c^2 - 5 b c^3 + 2 c^4))) | *** |
| 12704 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + b c + c^2) - a^2 (b - c)^2 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a^4 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + 2 b^2 c^2 + b c^3 + 2 c^4))) | *** |
| 12915 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 + 2 a^3 (b + c)^3 - a^4 (3 b^2 + 4 b c + 3 c^2) - a (b - c)^2 (3 b^3 + b^2 c + b c^2 + 3 c^3) + 2 a^2 (b^4 - 3 b^3 c - 4 b^2 c^2 - 3 b c^3 + c^4)) | *** |
| 13145 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - 3 b c + 2 c^2) - a^4 (b^3 - 2 b^2 c - 2 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 4 b^2 c + 4 b c^2 + c^3) + a^3 (4 b^4 - b^3 c + 4 b^2 c^2 - b c^3 + 4 c^4)) | *** |
| 13151 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + 3 b c + c^2) - a^4 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + a^3 (4 b^4 + 6 b^3 c + 8 b^2 c^2 + 6 b c^3 + 4 c^4)) | *** |
| 13370 | -(a (-2 a^3 + a^2 (b + c) - (b - c)^2 (b + c) + 2 a (b^2 - 6 b c + c^2))) | *** |
| 13373 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^2 (b - c)^4 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - 2 a (b^2 - c^2)^2 (b^2 + b c + c^2) + 4 a^3 (b^4 + b^3 c + 3 b^2 c^2 + b c^3 + c^4)) | *** |
| 13384 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 10 b c + 3 c^2) - a (3 b^3 + b^2 c + b c^2 + 3 c^3)) | *** |
| 13388 | a (a + b - c) (a - b + c) (a^3 - a^2 c - b^2 c + c^3 - a (b^2 + c^2) + b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) (a^3 - a^2 b + b^3 - b c^2 - a (b^2 + c^2) + c Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) (a^5 (b + c) + a^4 (b + c)^2 + a^2 (3 b^2 + 2 b c + 3 c^2) Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - a (b - c)^2 (b + c) (-3 b^2 - 2 b c - 3 c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) - (b^2 - c^2)^2 (b^2 - 2 b c + c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) - a^3 (b + c) (4 b^2 + 4 c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])) | *** |
| 13389 | -(a (a + b - c) (a - b + c) (-a^3 + a^2 c + b^2 c - c^3 + a (b^2 + c^2) + b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) (-a^3 + a^2 b - b^3 + b c^2 + a (b^2 + c^2) + c Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) (a^5 (b + c) + a^4 (b + c)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - (b^2 - c^2)^2 (b^2 - 2 b c + c^2 - Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) + a^3 (b + c) (-4 b^2 - 4 c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) + a (b - c)^2 (b + c) (3 b^2 + 2 b c + 3 c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]))) | *** |
| 13462 | -(a (8 a b c - a^2 (b + c) + (b - c)^2 (b + c))) | X(5919) |
| 13528 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 + 4 a^3 (b - c)^2 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 - 3 b c + c^2) - 2 a^5 (b^2 - b c + c^2)) | *** |
| 13600 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 6 b c + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 - 11 b^2 c - 11 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 13 b^2 c + 13 b c^2 + c^3) + 2 a^3 (2 b^4 - 5 b^3 c - 6 b^2 c^2 - 5 b c^3 + 2 c^4)) | *** |
| 13601 | -(a (-(a^5 (b + c)) + (b - c)^4 (b + c)^2 + a^4 (b^2 + c^2) - a (b - c)^2 (b^3 - 5 b^2 c - 5 b c^2 + c^3) + 2 a^3 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - 2 a^2 (b^4 - b^3 c + 4 b^2 c^2 - b c^3 + c^4))) | *** |
| 13624 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 8 b c + c^2)) | *** |
| 13750 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + 2 b^2 c^2 + b c^3 + 2 c^4) + a^2 (-b^5 + b^4 c + 4 b^3 c^2 + 4 b^2 c^3 + b c^4 - c^5)) | *** |
| 13751 | -(a (-(a^5 (b + c)) + (b - c)^4 (b + c)^2 + a^4 (b^2 + c^2) - a (b - c)^2 (b^3 + 4 b^2 c + 4 b c^2 + c^3) + a^3 (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3) - 2 a^2 (b^4 - b^3 c + b^2 c^2 - b c^3 + c^4))) | *** |
| 14000 | a (a + b - c) (a - b + c) (5 a^6 (b + c) + a^5 (-8 b^2 + 2 b c - 8 c^2) + (b - c)^2 (b + c)^3 (5 b^2 - 8 b c + 5 c^2) - a (b^2 - c^2)^2 (8 b^2 - 11 b c + 8 c^2) - a^4 (5 b^3 + 4 b^2 c + 4 b c^2 + 5 c^3) + a^3 (16 b^4 - 13 b^3 c + 32 b^2 c^2 - 13 b c^3 + 16 c^4) - a^2 (5 b^5 - 2 b^4 c + 5 b^3 c^2 + 5 b^2 c^3 - 2 b c^4 + 5 c^5)) | *** |
| 14110 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 + 4 a^3 (b^2 - c^2)^2 - 2 a (b^2 - c^2)^2 (b^2 - b c + c^2) - 2 a^5 (b^2 + b c + c^2)) | *** |
| 14115 | a (a + b - c) (a - b + c) (a^7 (b + c)^2 - 2 a^6 (b + c)^3 + b (b - c)^4 c (b + c)^3 + a (b - c)^4 (b + c)^2 (b^2 - 3 b c + c^2) - a^5 (b^4 - 9 b^3 c - 8 b^2 c^2 - 9 b c^3 + c^4) - 2 a^2 (b - c)^2 (b^5 - 3 b^4 c - 3 b c^4 + c^5) + a^4 (4 b^5 - 5 b^4 c - 7 b^3 c^2 - 7 b^2 c^3 - 5 b c^4 + 4 c^5) - a^3 (b^6 + 6 b^5 c - 13 b^4 c^2 + 8 b^3 c^3 - 13 b^2 c^4 + 6 b c^5 + c^6)) | *** |
| 14122 | a (a^4 (b + c) + 3 a^2 b c (b + c) - 3 a^3 (b^2 + c^2) - (b - c)^2 (b^3 - 2 b^2 c - 2 b c^2 + c^3) + a (3 b^4 - 12 b^3 c + 16 b^2 c^2 - 12 b c^3 + 3 c^4)) | *** |
| 14131 | a (a + b - c) (a - b + c) (2 a^4 b c (b + c) + a^5 (b + c)^2 + b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (b^2 + b c + c^2) - a^2 b c (b^3 + b^2 c + b c^2 + c^3) - a^3 (2 b^4 + b^3 c + 14 b^2 c^2 + b c^3 + 2 c^4)) | *** |
| 14132 | a (a + b - c) (a - b + c) (a^9 (b + c) + (b - c)^4 (b + c)^6 + a^8 (b^2 + 4 b c + c^2) - 2 a^2 (b - c)^2 (b + c)^4 (2 b^2 - b c + 2 c^2) - a^7 (4 b^3 + b^2 c + b c^2 + 4 c^3) + a (b - c)^2 (b + c)^3 (b^4 - b^3 c - 2 b^2 c^2 - b c^3 + c^4) - 2 a^6 (2 b^4 + 5 b^3 c + 3 b^2 c^2 + 5 b c^3 + 2 c^4) + a^5 (6 b^5 - b^4 c - b^3 c^2 - b^2 c^3 - b c^4 + 6 c^5) + 2 a^4 (3 b^6 + 5 b^5 c + 2 b^4 c^2 + 2 b^3 c^3 + 2 b^2 c^4 + 5 b c^5 + 3 c^6) + a^3 (-4 b^7 + b^6 c + 7 b^5 c^2 + 4 b^4 c^3 + 4 b^3 c^4 + 7 b^2 c^5 + b c^6 - 4 c^7)) | *** |
| 14792 | a^2 (a + b - c) (a - b + c) (2 a^3 + 2 b^3 - 2 a (b - c)^2 - 3 b^2 c - 3 b c^2 + 2 c^3 - 2 a^2 (b + c)) | *** |
| 14793 | a^2 (a + b - c) (a - b + c) (a^3 + b^3 - a (b - c)^2 - 2 b^2 c - 2 b c^2 + c^3 - a^2 (b + c)) | *** |
| 14794 | a^2 (a + b - c) (a - b + c) (2 a^3 + 2 b^3 - 3 b^2 c - 3 b c^2 + 2 c^3 - 2 a^2 (b + c) - 2 a (b^2 + c^2)) | *** |
| 14795 | a (a + b - c) (a - b + c) (2 a^4 - a^3 (b + c) + (b^2 - c^2)^2 - 3 a^2 (b^2 + c^2) + a (b^3 + c^3)) | *** |
| 14796 | -(a (a + b - c) (a - b + c) (a^4 + (1 + Sqrt[2]) a^3 b - a^2 c (b + Sqrt[2] b + 2 c) - (b^2 - c^2) (b^2 + (1 + Sqrt[2]) b c + c^2) - a b ((1 + Sqrt[2]) b^2 + (3 + 2 Sqrt[2]) b c + (1 + Sqrt[2]) c^2)) (a^4 + (1 + Sqrt[2]) a^3 c - a^2 b (2 b + c + Sqrt[2] c) + (b^2 - c^2) (b^2 + (1 + Sqrt[2]) b c + c^2) - a c ((1 + Sqrt[2]) b^2 + (3 + 2 Sqrt[2]) b c + (1 + Sqrt[2]) c^2)) (2 a^5 + 3 (1 + Sqrt[2]) a^4 (b + c) - (1 + Sqrt[2]) (b - c)^2 (b + c)^3 - (5 + 2 Sqrt[2]) a (b^2 - c^2)^2 + (3 + 2 Sqrt[2]) a^3 (b^2 + 4 b c + c^2) - a^2 (b + c) (2 (1 + Sqrt[2]) b^2 - (11 + 9 Sqrt[2]) b c + 2 (1 + Sqrt[2]) c^2))) | *** |
| 14797 | a (a + b - c) (a - b + c) (2 a^5 - 3 (-1 + Sqrt[2]) a^4 (b + c) + (-1 + Sqrt[2]) (b - c)^2 (b + c)^3 + (-5 + 2 Sqrt[2]) a (b^2 - c^2)^2 - (-3 + 2 Sqrt[2]) a^3 (b^2 + 4 b c + c^2) + a^2 (b + c) (2 (-1 + Sqrt[2]) b^2 + (11 - 9 Sqrt[2]) b c + 2 (-1 + Sqrt[2]) c^2)) (a^4 + a^3 (b - Sqrt[2] b) + a^2 ((-1 + Sqrt[2]) b - 2 c) c + a b ((-1 + Sqrt[2]) b^2 + (-3 + 2 Sqrt[2]) b c + (-1 + Sqrt[2]) c^2) - (b^2 - c^2) (b^2 + c^2 + b (c - Sqrt[2] c))) (a^4 + a^3 (c - Sqrt[2] c) - a^2 b (2 b + c - Sqrt[2] c) + a c ((-1 + Sqrt[2]) b^2 + (-3 + 2 Sqrt[2]) b c + (-1 + Sqrt[2]) c^2) + (b^2 - c^2) (b^2 + c^2 + b (c - Sqrt[2] c))) | *** |
| 14798 | a (a + b - c) (a - b + c) (2 a^4 - a^3 (b + c) + (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) + a (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 14799 | a (a + b - c) (a - b + c) (2 a^4 - a^3 (b + c) + (b^2 - c^2)^2 - a^2 (3 b^2 + 4 b c + 3 c^2) + a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 14800 | a (a + b - c) (a - b + c) (2 a^4 - 3 a^3 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 - 8 b c + c^2) + a (3 b^3 - 2 b^2 c - 2 b c^2 + 3 c^3)) | *** |
| 14801 | a (a + b - c) (a - b + c) (a^10 - a^9 ((3 + Sqrt[2]) b + 2 c) + a^8 ((1 + 2 Sqrt[2]) b^2 + (11 + Sqrt[2]) b c - 3 c^2) - (b - c)^5 (b + c)^3 (b^2 - (1 + Sqrt[2]) b c + c^2) + a^7 (2 (3 + Sqrt[2]) b^3 - (15 + 8 Sqrt[2]) b^2 c + 2 (-1 + Sqrt[2]) b c^2 + 8 c^3) + a^5 c (3 (7 + 4 Sqrt[2]) b^4 - (41 + 27 Sqrt[2]) b^3 c + (15 + 8 Sqrt[2]) b^2 c^2 + 24 b c^3 - 12 c^4) + a (b - c)^3 (b + c)^2 ((3 + Sqrt[2]) b^4 - 3 (4 + Sqrt[2]) b^3 c + (10 + 7 Sqrt[2]) b^2 c^2 - (9 + Sqrt[2]) b c^3 + 2 c^4) + a^6 (-2 (4 + 3 Sqrt[2]) b^4 + 8 Sqrt[2] b^3 c + (29 + 6 Sqrt[2]) b^2 c^2 - 2 (15 + Sqrt[2]) b c^3 + 2 c^4) - a^2 (b^2 - c^2) ((1 + 2 Sqrt[2]) b^6 - 8 (2 + Sqrt[2]) b^5 c + 2 (22 + 9 Sqrt[2]) b^4 c^2 - (43 + 25 Sqrt[2]) b^3 c^3 + 2 (13 + 3 Sqrt[2]) b^2 c^4 + 2 (-1 + Sqrt[2]) b c^5 - 3 c^6) + a^4 ((8 + 6 Sqrt[2]) b^6 - 6 (5 + 3 Sqrt[2]) b^5 c + 6 (3 + 2 Sqrt[2]) b^4 c^2 + (35 + 17 Sqrt[2]) b^3 c^3 - 4 (15 + 4 Sqrt[2]) b^2 c^4 + 24 b c^5 + 2 c^6) + a^3 (-2 (3 + Sqrt[2]) b^7 + 11 b^6 c + (27 + 17 Sqrt[2]) b^5 c^2 - 9 (7 + 4 Sqrt[2]) b^4 c^3 + (35 + 17 Sqrt[2]) b^3 c^4 + (15 + 8 Sqrt[2]) b^2 c^5 - 2 (15 + Sqrt[2]) b c^6 + 8 c^7)) (a^10 - a^9 (2 b + (3 + Sqrt[2]) c) + (b - c)^5 (b + c)^3 (b^2 - (1 + Sqrt[2]) b c + c^2) + a^8 (-3 b^2 + (11 + Sqrt[2]) b c + (1 + 2 Sqrt[2]) c^2) + a^7 (8 b^3 + 2 (-1 + Sqrt[2]) b^2 c - (15 + 8 Sqrt[2]) b c^2 + 2 (3 + Sqrt[2]) c^3) - a (b - c)^3 (b + c)^2 (2 b^4 - (9 + Sqrt[2]) b^3 c + (10 + 7 Sqrt[2]) b^2 c^2 - 3 (4 + Sqrt[2]) b c^3 + (3 + Sqrt[2]) c^4) + a^6 (2 b^4 - 2 (15 + Sqrt[2]) b^3 c + (29 + 6 Sqrt[2]) b^2 c^2 + 8 Sqrt[2] b c^3 - 2 (4 + 3 Sqrt[2]) c^4) + a^5 b (-12 b^4 + 24 b^3 c + (15 + 8 Sqrt[2]) b^2 c^2 - (41 + 27 Sqrt[2]) b c^3 + 3 (7 + 4 Sqrt[2]) c^4) - a^2 (b^2 - c^2) (3 b^6 - 2 (-1 + Sqrt[2]) b^5 c - 2 (13 + 3 Sqrt[2]) b^4 c^2 + (43 + 25 Sqrt[2]) b^3 c^3 - 2 (22 + 9 Sqrt[2]) b^2 c^4 + 8 (2 + Sqrt[2]) b c^5 - (1 + 2 Sqrt[2]) c^6) + a^4 (2 b^6 + 24 b^5 c - 4 (15 + 4 Sqrt[2]) b^4 c^2 + (35 + 17 Sqrt[2]) b^3 c^3 + 6 (3 + 2 Sqrt[2]) b^2 c^4 - 6 (5 + 3 Sqrt[2]) b c^5 + 2 (4 + 3 Sqrt[2]) c^6) + a^3 (8 b^7 - 2 (15 + Sqrt[2]) b^6 c + (15 + 8 Sqrt[2]) b^5 c^2 + (35 + 17 Sqrt[2]) b^4 c^3 - 9 (7 + 4 Sqrt[2]) b^3 c^4 + (27 + 17 Sqrt[2]) b^2 c^5 + 11 b c^6 - 2 (3 + Sqrt[2]) c^7)) (2 a^14 - 3 (3 + Sqrt[2]) a^13 (b + c) + (1 + Sqrt[2]) (b - c)^8 (b + c)^6 - a^11 (b + c) ((-9 + 4 Sqrt[2]) b^2 + 3 (42 + 19 Sqrt[2]) b c + (-9 + 4 Sqrt[2]) c^2) - a (b - c)^6 (b + c)^5 ((8 + 5 Sqrt[2]) b^2 - (13 + 10 Sqrt[2]) b c + (8 + 5 Sqrt[2]) c^2) + a^12 ((12 + 11 Sqrt[2]) b^2 + 20 (3 + Sqrt[2]) b c + (12 + 11 Sqrt[2]) c^2) + a^2 (b^2 - c^2)^4 ((17 + 8 Sqrt[2]) b^4 - 4 (21 + 10 Sqrt[2]) b^3 c + (131 + 67 Sqrt[2]) b^2 c^2 - 4 (21 + 10 Sqrt[2]) b c^3 + (17 + 8 Sqrt[2]) c^4) + a^9 (b + c) ((46 + 41 Sqrt[2]) b^4 + 3 (61 + 22 Sqrt[2]) b^3 c - (542 + 277 Sqrt[2]) b^2 c^2 + 3 (61 + 22 Sqrt[2]) b c^3 + (46 + 41 Sqrt[2]) c^4) + a^3 (b - c)^2 (b + c)^3 ((5 + 4 Sqrt[2]) b^6 + 9 (12 + 5 Sqrt[2]) b^5 c - 3 (154 + 67 Sqrt[2]) b^4 c^2 + (695 + 306 Sqrt[2]) b^3 c^3 - 3 (154 + 67 Sqrt[2]) b^2 c^4 + 9 (12 + 5 Sqrt[2]) b c^5 + (5 + 4 Sqrt[2]) c^6) + a^8 ((29 + 19 Sqrt[2]) b^6 - 4 (81 + 59 Sqrt[2]) b^5 c - (177 + 20 Sqrt[2]) b^4 c^2 + 4 (227 + 115 Sqrt[2]) b^3 c^3 - (177 + 20 Sqrt[2]) b^2 c^4 - 4 (81 + 59 Sqrt[2]) b c^5 + (29 + 19 Sqrt[2]) c^6) - a^4 (b^2 - c^2)^2 ((58 + 31 Sqrt[2]) b^6 - 6 (11 + 3 Sqrt[2]) b^5 c - 12 (29 + 17 Sqrt[2]) b^4 c^2 + 2 (359 + 193 Sqrt[2]) b^3 c^3 - 12 (29 + 17 Sqrt[2]) b^2 c^4 - 6 (11 + 3 Sqrt[2]) b c^5 + (58 + 31 Sqrt[2]) c^6) - a^7 (b + c) ((94 + 64 Sqrt[2]) b^6 - 2 (89 + 62 Sqrt[2]) b^5 c - (565 + 337 Sqrt[2]) b^4 c^2 + (1274 + 779 Sqrt[2]) b^3 c^3 - (565 + 337 Sqrt[2]) b^2 c^4 - 2 (89 + 62 Sqrt[2]) b c^5 + 2 (47 + 32 Sqrt[2]) c^6) + a^6 (4 (11 + 6 Sqrt[2]) b^8 + 2 (133 + 93 Sqrt[2]) b^7 c - (715 + 441 Sqrt[2]) b^6 c^2 - 4 (85 + 56 Sqrt[2]) b^5 c^3 + 4 (377 + 229 Sqrt[2]) b^4 c^4 - 4 (85 + 56 Sqrt[2]) b^3 c^5 - (715 + 441 Sqrt[2]) b^2 c^6 + 2 (133 + 93 Sqrt[2]) b c^7 + 4 (11 + 6 Sqrt[2]) c^8) + a^5 (b + c) ((51 + 31 Sqrt[2]) b^8 - 6 (62 + 33 Sqrt[2]) b^7 c + (450 + 163 Sqrt[2]) b^6 c^2 + (699 + 557 Sqrt[2]) b^5 c^3 - (1655 + 1106 Sqrt[2]) b^4 c^4 + (699 + 557 Sqrt[2]) b^3 c^5 + (450 + 163 Sqrt[2]) b^2 c^6 - 6 (62 + 33 Sqrt[2]) b c^7 + (51 + 31 Sqrt[2]) c^8) + a^10 (-((47 + 32 Sqrt[2]) b^4) + 2 (179 + 77 Sqrt[2]) b^2 c^2 + 18 (1 + 3 Sqrt[2]) b c^3 - (47 + 32 Sqrt[2]) c^4 + 18 b^3 (c + 3 Sqrt[2] c))) | *** |
| 14802 | a (a + b - c) (a - b + c) (a^10 + a^9 ((-3 + Sqrt[2]) b - 2 c) + a^8 ((1 - 2 Sqrt[2]) b^2 - (-11 + Sqrt[2]) b c - 3 c^2) - (b - c)^5 (b + c)^3 (b^2 + (-1 + Sqrt[2]) b c + c^2) + a^7 (-2 (-3 + Sqrt[2]) b^3 + (-15 + 8 Sqrt[2]) b^2 c - 2 (1 + Sqrt[2]) b c^2 + 8 c^3) + a^5 c (-3 (-7 + 4 Sqrt[2]) b^4 + (-41 + 27 Sqrt[2]) b^3 c + (15 - 8 Sqrt[2]) b^2 c^2 + 24 b c^3 - 12 c^4) - a (b - c)^3 (b + c)^2 ((-3 + Sqrt[2]) b^4 - 3 (-4 + Sqrt[2]) b^3 c + (-10 + 7 Sqrt[2]) b^2 c^2 - (-9 + Sqrt[2]) b c^3 - 2 c^4) + a^6 ((-8 + 6 Sqrt[2]) b^4 - 8 Sqrt[2] b^3 c + (29 - 6 Sqrt[2]) b^2 c^2 + 2 (-15 + Sqrt[2]) b c^3 + 2 c^4) + a^4 ((8 - 6 Sqrt[2]) b^6 + 6 (-5 + 3 Sqrt[2]) b^5 c - 6 (-3 + 2 Sqrt[2]) b^4 c^2 + (35 - 17 Sqrt[2]) b^3 c^3 + 4 (-15 + 4 Sqrt[2]) b^2 c^4 + 24 b c^5 + 2 c^6) + a^2 (b^2 - c^2) ((-1 + 2 Sqrt[2]) b^6 - 8 (-2 + Sqrt[2]) b^5 c + 2 (-22 + 9 Sqrt[2]) b^4 c^2 + (43 - 25 Sqrt[2]) b^3 c^3 + 2 (-13 + 3 Sqrt[2]) b^2 c^4 + 2 (1 + Sqrt[2]) b c^5 + 3 c^6) + a^3 (2 (-3 + Sqrt[2]) b^7 + 11 b^6 c + (27 - 17 Sqrt[2]) b^5 c^2 + 9 (-7 + 4 Sqrt[2]) b^4 c^3 + (35 - 17 Sqrt[2]) b^3 c^4 + (15 - 8 Sqrt[2]) b^2 c^5 + 2 (-15 + Sqrt[2]) b c^6 + 8 c^7)) (a^10 + a^9 (-2 b + (-3 + Sqrt[2]) c) + (b - c)^5 (b + c)^3 (b^2 + (-1 + Sqrt[2]) b c + c^2) + a^8 (-3 b^2 - (-11 + Sqrt[2]) b c + (1 - 2 Sqrt[2]) c^2) + a^7 (8 b^3 - 2 (1 + Sqrt[2]) b^2 c + (-15 + 8 Sqrt[2]) b c^2 - 2 (-3 + Sqrt[2]) c^3) + a^5 b (-12 b^4 + 24 b^3 c + (15 - 8 Sqrt[2]) b^2 c^2 + (-41 + 27 Sqrt[2]) b c^3 + 3 (7 - 4 Sqrt[2]) c^4) - a (b - c)^3 (b + c)^2 (2 b^4 + (-9 + Sqrt[2]) b^3 c + (10 - 7 Sqrt[2]) b^2 c^2 + 3 (-4 + Sqrt[2]) b c^3 - (-3 + Sqrt[2]) c^4) + a^6 (2 b^4 + 2 (-15 + Sqrt[2]) b^3 c + (29 - 6 Sqrt[2]) b^2 c^2 - 8 Sqrt[2] b c^3 + 2 (-4 + 3 Sqrt[2]) c^4) + a^4 (2 b^6 + 24 b^5 c + 4 (-15 + 4 Sqrt[2]) b^4 c^2 + (35 - 17 Sqrt[2]) b^3 c^3 - 6 (-3 + 2 Sqrt[2]) b^2 c^4 + 6 (-5 + 3 Sqrt[2]) b c^5 + 2 (4 - 3 Sqrt[2]) c^6) - a^2 (b^2 - c^2) (3 b^6 + 2 (1 + Sqrt[2]) b^5 c + 2 (-13 + 3 Sqrt[2]) b^4 c^2 + (43 - 25 Sqrt[2]) b^3 c^3 + 2 (-22 + 9 Sqrt[2]) b^2 c^4 - 8 (-2 + Sqrt[2]) b c^5 + (-1 + 2 Sqrt[2]) c^6) + a^3 (8 b^7 + 2 (-15 + Sqrt[2]) b^6 c + (15 - 8 Sqrt[2]) b^5 c^2 + (35 - 17 Sqrt[2]) b^4 c^3 + 9 (-7 + 4 Sqrt[2]) b^3 c^4 + (27 - 17 Sqrt[2]) b^2 c^5 + 11 b c^6 + 2 (-3 + Sqrt[2]) c^7)) (2 a^14 + 3 (-3 + Sqrt[2]) a^13 (b + c) - (-1 + Sqrt[2]) (b - c)^8 (b + c)^6 + a^12 ((12 - 11 Sqrt[2]) b^2 - 20 (-3 + Sqrt[2]) b c + (12 - 11 Sqrt[2]) c^2) + a^11 (b + c) ((9 + 4 Sqrt[2]) b^2 + 3 (-42 + 19 Sqrt[2]) b c + (9 + 4 Sqrt[2]) c^2) + a (b - c)^6 (b + c)^5 ((-8 + 5 Sqrt[2]) b^2 + (13 - 10 Sqrt[2]) b c + (-8 + 5 Sqrt[2]) c^2) - a^2 (b^2 - c^2)^4 ((-17 + 8 Sqrt[2]) b^4 + (84 - 40 Sqrt[2]) b^3 c + (-131 + 67 Sqrt[2]) b^2 c^2 + 4 (21 - 10 Sqrt[2]) b c^3 + (-17 + 8 Sqrt[2]) c^4) + a^10 ((-47 + 32 Sqrt[2]) b^4 + 18 (1 - 3 Sqrt[2]) b^3 c + 2 (179 - 77 Sqrt[2]) b^2 c^2 + 18 (1 - 3 Sqrt[2]) b c^3 + (-47 + 32 Sqrt[2]) c^4) - a^9 (b + c) ((-46 + 41 Sqrt[2]) b^4 + 3 (-61 + 22 Sqrt[2]) b^3 c + (542 - 277 Sqrt[2]) b^2 c^2 + 3 (-61 + 22 Sqrt[2]) b c^3 + (-46 + 41 Sqrt[2]) c^4) + a^8 ((29 - 19 Sqrt[2]) b^6 + 4 (-81 + 59 Sqrt[2]) b^5 c + (-177 + 20 Sqrt[2]) b^4 c^2 + 4 (227 - 115 Sqrt[2]) b^3 c^3 + (-177 + 20 Sqrt[2]) b^2 c^4 + 4 (-81 + 59 Sqrt[2]) b c^5 + (29 - 19 Sqrt[2]) c^6) - a^3 (b - c)^2 (b + c)^3 ((-5 + 4 Sqrt[2]) b^6 + 9 (-12 + 5 Sqrt[2]) b^5 c + 3 (154 - 67 Sqrt[2]) b^4 c^2 + (-695 + 306 Sqrt[2]) b^3 c^3 + 3 (154 - 67 Sqrt[2]) b^2 c^4 + 9 (-12 + 5 Sqrt[2]) b c^5 + (-5 + 4 Sqrt[2]) c^6) + a^4 (b^2 - c^2)^2 ((-58 + 31 Sqrt[2]) b^6 + 6 (11 - 3 Sqrt[2]) b^5 c + 12 (29 - 17 Sqrt[2]) b^4 c^2 + 2 (-359 + 193 Sqrt[2]) b^3 c^3 + 12 (29 - 17 Sqrt[2]) b^2 c^4 + 6 (11 - 3 Sqrt[2]) b c^5 + (-58 + 31 Sqrt[2]) c^6) + a^7 (b + c) ((-94 + 64 Sqrt[2]) b^6 - 2 (-89 + 62 Sqrt[2]) b^5 c + (565 - 337 Sqrt[2]) b^4 c^2 + (-1274 + 779 Sqrt[2]) b^3 c^3 + (565 - 337 Sqrt[2]) b^2 c^4 - 2 (-89 + 62 Sqrt[2]) b c^5 + 2 (-47 + 32 Sqrt[2]) c^6) + a^6 ((44 - 24 Sqrt[2]) b^8 + 2 (133 - 93 Sqrt[2]) b^7 c + (-715 + 441 Sqrt[2]) b^6 c^2 + 4 (-85 + 56 Sqrt[2]) b^5 c^3 + 4 (377 - 229 Sqrt[2]) b^4 c^4 + 4 (-85 + 56 Sqrt[2]) b^3 c^5 + (-715 + 441 Sqrt[2]) b^2 c^6 + 2 (133 - 93 Sqrt[2]) b c^7 + 4 (11 - 6 Sqrt[2]) c^8) - a^5 (b + c) ((-51 + 31 Sqrt[2]) b^8 - 6 (-62 + 33 Sqrt[2]) b^7 c + (-450 + 163 Sqrt[2]) b^6 c^2 + (-699 + 557 Sqrt[2]) b^5 c^3 + (1655 - 1106 Sqrt[2]) b^4 c^4 + (-699 + 557 Sqrt[2]) b^3 c^5 + (-450 + 163 Sqrt[2]) b^2 c^6 - 6 (-62 + 33 Sqrt[2]) b c^7 + (-51 + 31 Sqrt[2]) c^8)) | *** |
| 14803 | a (a + b - c) (a - b + c) (2 a^4 - 3 a^3 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 - 10 b c + c^2) + a (3 b^3 - b^2 c - b c^2 + 3 c^3)) | *** |
| 14804 | a (a + b - c) (a - b + c) (2 a^4 - 3 a^3 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 - 4 b c + c^2) + 3 a (b^3 + c^3)) | *** |
| 14882 | a (a^3 + a^2 (b + c) - (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2)) | X(3337) |
| 15016 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - b c + 2 c^2) - a^4 (b^3 + c^3) + a^3 (4 b^4 + b^3 c + 6 b^2 c^2 + b c^3 + 4 c^4) - a^2 (b^5 - b^3 c^2 - b^2 c^3 + c^5)) | *** |
| 15177 | a^2 (a + b - c) (a - b + c) (a^6 - a^3 b c (b + c) + a b (b - c)^2 c (b + c) - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 - b c + c^2) - a^2 (b - c)^2 (b^2 + b c + c^2)) | *** |
| 15178 | a (a + b - c) (a - b + c) (3 a^3 (b + c) - 3 a (b - c)^2 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 8 b c + 3 c^2)) | *** |
| 15803 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 - 6 b c + c^2)) | *** |
| 15804 | a^2 (a^4 - 2 a^3 (b + c) - (b - c)^2 (b^2 - 6 b c + c^2) + 2 a (b^3 - 3 b^2 c - 3 b c^2 + c^3)) | *** |
| 15931 | a (a + b - c) (a - b + c) (2 a^3 - 3 a^2 (b + c) + (b - c)^2 (b + c)) | *** |
| 15932 | -(a (a^4 (b - c)^2 - a^5 (b + c) + (b - c)^4 (b + c)^2 - a (b - c)^2 (b^3 + 4 b^2 c + 4 b c^2 + c^3) + a^3 (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3) - 2 a^2 (b^4 - 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4))) | *** |
| 15934 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 + b c + c^2)) | *** |
| 15941 | a (a + b - c) (a - b + c) (-(a^8 (b - c)^2) + a^9 (b + c) - a (b - c)^4 (b + c)^3 (b^2 + c^2) + (b^2 - c^2)^4 (b^2 + c^2) - 2 a^4 b c (b + c)^2 (b^2 - 4 b c + c^2) - 2 a^2 (b - c)^4 (b + c)^2 (b^2 + b c + c^2) - 2 a^7 (b^3 + c^3) - 2 a^5 b c (b^3 - 3 b^2 c - 3 b c^2 + c^3) + 2 a^6 (b^4 - b^3 c - 2 b^2 c^2 - b c^3 + c^4) + 2 a^3 (b^7 - 4 b^5 c^2 + 3 b^4 c^3 + 3 b^3 c^4 - 4 b^2 c^5 + c^7)) | *** |
| 16189 | a (a + b - c) (a - b + c) (9 a^3 (b + c) - 9 a (b - c)^2 (b + c) + 9 (b^2 - c^2)^2 - a^2 (9 b^2 + 10 b c + 9 c^2)) | *** |
| 16191 | a (a + b - c) (a - b + c) (17 a^3 (b + c) - 17 a (b - c)^2 (b + c) + 17 (b^2 - c^2)^2 - a^2 (17 b^2 + 18 b c + 17 c^2)) | *** |
| 16192 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 - 14 b c + c^2)) | *** |
| 16193 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b - c)^2 (b + c)^4 - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + 2 a^3 (2 b^4 + 3 b^3 c + 6 b^2 c^2 + 3 b c^3 + 2 c^4) - a^2 (b^5 - 5 b^4 c - 4 b^3 c^2 - 4 b^2 c^3 - 5 b c^4 + c^5)) | *** |
| 16200 | a (a + b - c) (a - b + c) (5 a^3 (b + c) - 5 a (b - c)^2 (b + c) + 5 (b^2 - c^2)^2 - a^2 (5 b^2 + 6 b c + 5 c^2)) | *** |
| 16201 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b - c)^2 (b + c)^4 - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + 2 a^3 (2 b^4 + 3 b^3 c + 6 b^2 c^2 + 3 b c^3 + 2 c^4) - a^2 (b^5 - 5 b^4 c - 28 b^3 c^2 - 28 b^2 c^3 - 5 b c^4 + c^5)) | *** |
| 16202 | a (a + b - c) (a - b + c) (a^4 + a^3 (b + c) - a (b - c)^2 (b + c) + 2 (b^2 - c^2)^2 - a^2 (3 b^2 + 4 b c + 3 c^2)) | *** |
| 16203 | a (a + b - c) (a - b + c) (a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) - 2 (b^2 - c^2)^2 + a^2 (b^2 + 8 b c + c^2)) | *** |
| 16204 | a (a + b - c) (a - b + c) (9 a^6 (b + c) + 9 (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (9 b^2 - 10 b c + 9 c^2) - 2 a^5 (9 b^2 + 14 b c + 9 c^2) - 3 a^4 (3 b^3 - 7 b^2 c - 7 b c^2 + 3 c^3) - 3 a^2 (b - c)^2 (3 b^3 + 13 b^2 c + 13 b c^2 + 3 c^3) + 4 a^3 (9 b^4 + 2 b^3 c - 10 b^2 c^2 + 2 b c^3 + 9 c^4)) | *** |
| 16205 | a (a + b - c) (a - b + c) (9 a^6 (b + c) + 9 (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (9 b^2 - 26 b c + 9 c^2) - 2 a^5 (9 b^2 + 14 b c + 9 c^2) + a^4 (-9 b^3 + 53 b^2 c + 53 b c^2 - 9 c^3) - a^2 (b - c)^2 (9 b^3 + 71 b^2 c + 71 b c^2 + 9 c^3) + 12 a^3 (3 b^4 - 2 b^3 c - 6 b^2 c^2 - 2 b c^3 + 3 c^4)) | *** |
| 16206 | a (a + b - c) (a - b + c) (9 a^6 (b + c) + 9 (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (9 b^2 - 11 b c + 9 c^2) - 2 a^5 (9 b^2 + 14 b c + 9 c^2) + a^4 (-9 b^3 + 23 b^2 c + 23 b c^2 - 9 c^3) - a^2 (b - c)^2 (9 b^3 + 41 b^2 c + 41 b c^2 + 9 c^3) + a^3 (36 b^4 + 6 b^3 c - 44 b^2 c^2 + 6 b c^3 + 36 c^4)) | *** |
| 16207 | a (a + b - c) (a - b + c) (9 a^6 (b + c) + 9 (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (9 b^2 - 25 b c + 9 c^2) - 2 a^5 (9 b^2 + 14 b c + 9 c^2) + a^4 (-9 b^3 + 51 b^2 c + 51 b c^2 - 9 c^3) - 3 a^2 (b - c)^2 (3 b^3 + 23 b^2 c + 23 b c^2 + 3 c^3) + a^3 (36 b^4 - 22 b^3 c - 68 b^2 c^2 - 22 b c^3 + 36 c^4)) | *** |
| 16208 | a (a + b - c) (a - b + c) (-2 a^5 (b - c)^2 + a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 3 b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 - 5 b^3 c - 6 b^2 c^2 - 5 b c^3 + 2 c^4) - a^2 (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 16209 | a (a + b - c) (a - b + c) (-2 a^5 (b - c)^2 + a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - b c + c^2) - a^2 (b - c)^2 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a^4 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + a^3 (4 b^4 - 6 b^3 c + 28 b^2 c^2 - 6 b c^3 + 4 c^4)) | *** |
| 16215 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b - c)^2 (b + c)^4 - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + 2 a^3 (2 b^4 + 3 b^3 c + 6 b^2 c^2 + 3 b c^3 + 2 c^4) - a^2 (b^5 - 5 b^4 c + 20 b^3 c^2 + 20 b^2 c^3 - 5 b c^4 + c^5)) | *** |
| 16216 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - a^2 (b + c)^3 (b^2 - 10 b c + c^2) - 2 a^5 (b^2 + b c + c^2) + 4 a^3 (b^2 + b c + c^2)^2 - 2 a (b^2 - c^2)^2 (b^2 + 3 b c + c^2) - a^4 (b^3 + 7 b^2 c + 7 b c^2 + c^3)) | *** |
| 16217 | a (a + b - c) (a - b + c) (a^9 (b + c) - 2 a^7 b c (b + c) + (b - c)^6 (b + c)^4 - a^8 (3 b^2 + 4 b c + 3 c^2) - a (b - c)^4 (b + c)^3 (3 b^2 + 4 b c + 3 c^2) + 2 a^2 b c (b^2 - c^2)^2 (5 b^2 + 6 b c + 5 c^2) + 2 a^6 (4 b^4 + 7 b^3 c + 12 b^2 c^2 + 7 b c^3 + 4 c^4) + a^5 (-6 b^5 + 2 b^3 c^2 + 2 b^2 c^3 - 6 c^5) - 2 a^4 (3 b^6 + 9 b^5 c + 15 b^4 c^2 + 10 b^3 c^3 + 15 b^2 c^4 + 9 b c^5 + 3 c^6) + 2 a^3 (4 b^7 + b^6 c - 5 b^5 c^2 + 16 b^4 c^3 + 16 b^3 c^4 - 5 b^2 c^5 + b c^6 + 4 c^7)) | *** |
| 16218 | a (a + b - c) (a - b + c) (a^9 (b + c) + 2 a^7 b c (b + c) + 2 a^2 b (b - c)^4 c (b + c)^2 + (b - c)^6 (b + c)^4 - 3 a (b - c)^4 (b + c)^3 (b^2 + c^2) - a^8 (3 b^2 + 4 b c + 3 c^2) - 2 a^4 (b - c)^2 (3 b^4 + 7 b^3 c + 14 b^2 c^2 + 7 b c^3 + 3 c^4) + 2 a^6 (4 b^4 + 3 b^3 c + 8 b^2 c^2 + 3 b c^3 + 4 c^4) - 2 a^5 (3 b^5 + 2 b^4 c + 9 b^3 c^2 + 9 b^2 c^3 + 2 b c^4 + 3 c^5) + 2 a^3 (4 b^7 - b^6 c + 5 b^5 c^2 - 24 b^4 c^3 - 24 b^3 c^4 + 5 b^2 c^5 - b c^6 + 4 c^7)) | *** |
| 16541 | a^2 (a + b - c) (a - b + c) (a^5 + b^5 + 2 a^3 b c - b^4 c - b c^4 + c^5 - a^4 (b + c) - 2 a^2 b c (b + c) - a (b + c)^2 (b^2 - 4 b c + c^2)) | *** |
| 16678 | a^3 (a + b - c) (a - b + c) (b + c) | X(1402) |
| 16687 | -(a (a + b - c) (a - b + c) (b + c) (b^2 + c^2)) | *** |
| 16763 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^2 + c^2)^2 + a^2 (-b^5 + 3 b^4 c + b^3 c^2 + b^2 c^3 + 3 b c^4 - c^5)) | *** |
| 16778 | a (a + b - c) (a - b + c) (b + c) (3 a^2 - b^2 - c^2) | *** |
| 16877 | a (a + b - c) (a - b + c) (b + c) (a^2 - b c) (a^2 + b c) | *** |
| 16878 | a (b + c) (3 a + b + c) | X(37593) |
| 17102 | a (a + b - c) (a - b + c) (2 a^5 b c - 2 a^3 b (b - c)^2 c + a^6 (b + c) - a^4 (b + c)^3 + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^2 (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 17437 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^2 + c^2)^2 - a^2 (b^5 - 3 b^4 c + 6 b^3 c^2 + 6 b^2 c^3 - 3 b c^4 + c^5)) | *** |
| 17502 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b - c)^2 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 12 b c + c^2)) | *** |
| 17591 | a (a + b - c) (a - b + c) (2 b^3 - a (b - c)^2 + b^2 c + b c^2 + 2 c^3 + 2 a^2 (b + c)) | *** |
| 17592 | a (a + b - c) (a - b + c) (b^3 + 2 b^2 c + 2 b c^2 + c^3 + a^2 (b + c) + a (b^2 + 4 b c + c^2)) | *** |
| 17593 | a (a + b - c) (a - b + c) (2 b^3 + b^2 c + b c^2 + 2 c^3 + 2 a^2 (b + c) - a (b^2 - 4 b c + c^2)) | *** |
| 17594 | a (a + b - c) (a - b + c) (b^3 + 4 a b c + b^2 c + b c^2 + c^3 + a^2 (b + c)) | *** |
| 17595 | a (a + b - c) (a - b + c) (b^3 + c^3 + a^2 (b + c) - a (b^2 - b c + c^2)) | *** |
| 17596 | a (a + b - c) (a - b + c) (b^3 - a (b - c)^2 + c^3 + a^2 (b + c)) | *** |
| 17597 | a (a + b - c) (a - b + c) (b^3 + c^3 + a^2 (b + c) - a (b^2 + b c + c^2)) | *** |
| 17598 | a (a + b - c) (a - b + c) (2 b^3 + b^2 c + b c^2 + 2 c^3 + 2 a^2 (b + c) - a (b^2 + c^2)) | *** |
| 17599 | a (a + b - c) (a - b + c) (b^3 + a b c + b^2 c + b c^2 + c^3 + a^2 (b + c)) | *** |
| 17600 | a (a + b - c) (a - b + c) (2 b^3 + 3 b^2 c + 3 b c^2 + 2 c^3 + 2 a^2 (b + c) + a (b^2 + 4 b c + c^2)) | *** |
| 17601 | a (a + b - c) (a - b + c) (b^3 + c^3 + a^2 (b + c) - a (b^2 - 4 b c + c^2)) | *** |
| 17603 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (3 b^2 + 4 b c + 3 c^2) + 2 a^3 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + 2 a^2 (b^4 - b^3 c + 4 b^2 c^2 - b c^3 + c^4) - 3 a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 17609 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + 9 b^2 c + 9 b c^2 + c^3)) | *** |
| 17642 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 + 2 a^2 (b + c)^2 (b^2 - 3 b c + c^2) - a^4 (3 b^2 + 4 b c + 3 c^2) + 2 a^3 (b^3 + 2 b^2 c + 2 b c^2 + c^3) - 3 a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 17699 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^2 + c^2)^2 - a^2 (b^5 - 3 b^4 c - 10 b^3 c^2 - 10 b^2 c^3 - 3 b c^4 + c^5)) | *** |
| 17700 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^2 + c^2)^2 - a^2 (b^5 - 3 b^4 c - 2 b^3 c^2 - 2 b^2 c^3 - 3 b c^4 + c^5)) | *** |
| 17715 | a (a + b - c) (a - b + c) (b^3 + c^3 + a^2 (b + c) - a (b^2 + 4 b c + c^2)) | *** |
| 17716 | a (a + b - c) (a - b + c) (b^3 + 2 b^2 c + 2 b c^2 + c^3 + a^2 (b + c) + a (b^2 + c^2)) | *** |
| 17798 | a (a + b - c) (a - b + c) (a^2 - b c) | X(1429) |
| 18115 | a (a + b - c) (a - b + c) (a^9 (b + c) - a^8 (b^2 + c^2) - 3 a^4 b^2 c^2 (b^2 + c^2) - a (b - c)^4 (b + c)^3 (b^2 + c^2) + (b^2 - c^2)^4 (b^2 + c^2) + 2 a^6 (b^2 + c^2)^2 - 2 a^7 (b^3 + b^2 c + b c^2 + c^3) + a^5 b c (2 b^3 + b^2 c + b c^2 + 2 c^3) - a^2 (b^2 - c^2)^2 (2 b^4 + b^2 c^2 + 2 c^4) + a^3 (b - c)^2 (2 b^5 + 2 b^4 c + b^3 c^2 + b^2 c^3 + 2 b c^4 + 2 c^5)) | *** |
| 18193 | a (a + b - c) (a - b + c) (3 b^3 - b^2 c - b c^2 + 3 c^3 + 3 a^2 (b + c) - 4 a (b^2 + c^2)) | *** |
| 18201 | a (a + b - c) (a - b + c) (2 b^3 - b^2 c - b c^2 + 2 c^3 + 2 a^2 (b + c) - 3 a (b^2 + c^2)) | *** |
| 18208 | a (a + b - c) (a - b + c) (b^5 + c^5 + a^4 (b + c) - a^3 (b^2 + c^2) - a (b^2 + c^2)^2 + a^2 (b^3 + c^3)) | *** |
| 18280 | a (a + b - c) (a - b + c) (2 a^10 + a^9 (b + c) + a (b - c)^4 (b + c)^5 - (b - c)^4 (b + c)^6 - a^8 (9 b^2 + 2 b c + 9 c^2) - 4 a^7 (b^3 + b^2 c + b c^2 + c^3) + a^2 (b^2 - c^2)^2 (6 b^4 + 8 b^3 c + b^2 c^2 + 8 b c^3 + 6 c^4) + 2 a^6 (8 b^4 + 4 b^3 c + 7 b^2 c^2 + 4 b c^3 + 8 c^4) - a^4 (b + c)^2 (14 b^4 - 16 b^3 c + 15 b^2 c^2 - 16 b c^3 + 14 c^4) + 3 a^5 (2 b^5 + 2 b^4 c + b^3 c^2 + b^2 c^3 + 2 b c^4 + 2 c^5) - a^3 (b - c)^2 (4 b^5 + 12 b^4 c + 15 b^3 c^2 + 15 b^2 c^3 + 12 b c^4 + 4 c^5)) | *** |
| 18330 | a (a + b - c) (a - b + c) (a^8 (b + c)^2 + b c (b^2 - c^2)^4 + a (b - c)^4 (b + c)^3 (b^2 - b c + c^2) - a^7 (b^3 + 2 b^2 c + 2 b c^2 + c^3) - a^2 (b^2 - c^2)^2 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4) - a^6 (3 b^4 + b^3 c + b c^3 + 3 c^4) + a^5 (3 b^5 + 2 b^4 c + b^3 c^2 + b^2 c^3 + 2 b c^4 + 3 c^5) - a^3 (b - c)^2 (3 b^5 + 4 b^4 c + 3 b^3 c^2 + 3 b^2 c^3 + 4 b c^4 + 3 c^5) + a^4 (3 b^6 - 3 b^5 c - b^4 c^2 - b^2 c^4 - 3 b c^5 + 3 c^6)) | *** |
| 18398 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + c^2) - a (b^3 + 4 b^2 c + 4 b c^2 + c^3)) | *** |
| 18421 | a (8 a b c + 5 a^2 (b + c) - 5 (b - c)^2 (b + c)) | *** |
| 18443 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - 2 a^5 (b + c)^2 - a^2 (b - c)^2 (b + c)^3 + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) + 4 a^3 (b^4 + b^3 c + 2 b^2 c^2 + b c^3 + c^4)) | *** |
| 18447 | a (a + b - c) (a - b + c) (-2 a^3 b^2 c^2 + a^6 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 18453 | a (a + b - c) (a - b + c) (-(a^8 (b - c)^2) + a^9 (b + c) - a (b - c)^4 (b + c)^3 (b^2 + c^2) + (b^2 - c^2)^4 (b^2 + c^2) - 2 a^2 (b - c)^4 (b + c)^2 (b^2 + b c + c^2) - 2 a^7 (b^3 + c^3) - 2 a^5 b c (b^3 + c^3) + 2 a^6 (b^4 - b^3 c + b^2 c^2 - b c^3 + c^4) - 2 a^4 b c (b^4 + b^3 c + b c^3 + c^4) + 2 a^3 (b^7 - b^5 c^2 - b^2 c^5 + c^7)) | *** |
| 18455 | a (a + b - c) (a - b + c) (2 a^3 b^2 c^2 + a^6 (b + c) - a^2 (b - c)^2 (b + c)^3 + (b - c)^2 (b + c)^3 (b^2 + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 18758 | a (a + b - c) (a - b + c) (a^2 (b - c)^2 - b c (b^2 + c^2) - a (b^3 + c^3)) | *** |
| 18788 | a (a + b - c) (a - b + c) (b^5 - a^3 (b - c)^2 - b^3 c^2 - b^2 c^3 + c^5 + a^4 (b + c) - a^2 b c (b + c) - a (b - c)^2 (b^2 + c^2)) | *** |
| 18838 | -(a (-(a^5 (b + c)) + (b - c)^4 (b + c)^2 + a^4 (b^2 + c^2) + 2 a^3 (b^3 + c^3) - 2 a^2 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4) - a (b^5 - b^4 c - b c^4 + c^5))) | X(5570) |
| 18839 | a (a + b - c) (a - b + c) (a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (3 b^2 + 4 b c + 3 c^2) + 2 a^3 (b^3 + 2 b^2 c + 2 b c^2 + c^3) + 2 a^2 (b^4 - b^3 c - 2 b^2 c^2 - b c^3 + c^4) - 3 a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 18856 | a (a + b - c) (a - b + c) (a^9 (b + c) + 6 a^7 b c (b + c) + (b - c)^6 (b + c)^4 - a (b - c)^4 (b + c)^3 (3 b^2 - 4 b c + 3 c^2) - 2 a^2 b c (b^2 - c^2)^2 (3 b^2 - 4 b c + 3 c^2) - a^8 (3 b^2 + 4 b c + 3 c^2) + a^6 (8 b^4 - 2 b^3 c + 8 b^2 c^2 - 2 b c^3 + 8 c^4) - 2 a^5 (3 b^5 + 4 b^4 c + 5 b^3 c^2 + 5 b^2 c^3 + 4 b c^4 + 3 c^5) + 2 a^3 (b - c)^2 (4 b^5 + 5 b^4 c + 7 b^3 c^2 + 7 b^2 c^3 + 5 b c^4 + 4 c^5) - 2 a^4 (3 b^6 - 7 b^5 c + 5 b^4 c^2 - 14 b^3 c^3 + 5 b^2 c^4 - 7 b c^5 + 3 c^6)) | *** |
| 18857 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 3 b c + c^2) - 2 a^5 (b^2 + 5 b c + c^2) - a^4 (b^3 - 13 b^2 c - 13 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 15 b^2 c + 15 b c^2 + c^3) + 4 a^3 (b^4 + b^3 c - 7 b^2 c^2 + b c^3 + c^4)) | *** |
| 18967 | a (a^3 - 3 a^2 (b + c) + 3 (b - c)^2 (b + c) - a (b^2 + c^2)) | *** |
| 19758 | a (a + b - c) (a - b + c) (a^2 (b + c)^4 + b c (b + c)^2 (b^2 + c^2) + a (b + c)^3 (b^2 + c^2) + a^4 (b^2 + 3 b c + c^2) + a^3 (b^3 + 5 b^2 c + 5 b c^2 + c^3)) | *** |
| 19761 | a (a + b - c) (a - b + c) (a^2 (b + c)^2 (b^2 + c^2) + b c (b + c)^2 (b^2 + c^2) + a (b + c)^3 (b^2 + c^2) + a^4 (b^2 + b c + c^2) + a^3 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 19765 | a (a + b - c) (a - b + c) (b c (b + c)^2 + a (b + c)^3 + a^2 (b^2 + 3 b c + c^2)) | *** |
| 19782 | a (a + b - c) (a - b + c) (a^4 b c (b + c) - 2 a^2 b^2 c^2 (b + c) + b (b - c)^2 c (b + c)^3 + a (b^2 - c^2)^2 (b^2 + b c + c^2) + a^5 (b^2 + 3 b c + c^2) - 2 a^3 (b^4 + b^3 c + b^2 c^2 + b c^3 + c^4)) | *** |
| 20182 | a (a + b - c) (a - b + c) (b^3 + 2 b^2 c + 2 b c^2 + c^3 + a^2 (b + c) + a (b^2 + 3 b c + c^2)) | *** |
| 20254 | a (a + b - c) (a - b + c) (2 a^2 b^2 c^2 + a^5 (b + c) - a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2) - a (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 20323 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2) - a (b^3 - 7 b^2 c - 7 b c^2 + c^3)) | X(13601) |
| 20358 | a (a + b - c) (a - b + c) (b (b - c)^2 c (b + c) + a^3 (b + c)^2 - a^2 (2 b^3 + b^2 c + b c^2 + 2 c^3) + a (b^4 + c^4)) | *** |
| 20359 | a (a + b - c) (a - b + c) (a^4 (b + c)^2 + b c (b^2 - c^2)^2 - a^3 (b^3 + c^3) - a^2 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4) + a (b^5 + b^3 c^2 + b^2 c^3 + c^5)) | *** |
| 20367 | a (a + b - c) (a - b + c) (b (b - c)^2 c (b + c) + a^3 (b + c)^2 + a (b - c)^2 (b^2 + b c + c^2) - 2 a^2 (b^3 + c^3)) | *** |
| 20368 | a (a + b - c) (a - b + c) (a^4 (b + c)^2 + b c (b^2 - c^2)^2 - a^2 (b - c)^2 (b^2 - b c + c^2) - a^3 (b^3 + c^3) + a (b - c)^2 (b^3 + c^3)) | *** |
| 20764 | -(a (a + b - c) (a - b + c) (a^5 b c + a^4 (b - c)^2 (b + c) - a b c (b^2 - c^2)^2 + (b - c)^2 (b + c)^3 (b^2 + c^2) - 2 a^2 (b^5 - b^3 c^2 - b^2 c^3 + c^5))) | *** |
| 20788 | a (a + b - c) (a - b + c) (2 a^5 b c (b + c)^2 + a^6 (b + c)^3 + b^2 (b - c)^2 c^2 (b + c)^3 + 2 a b c (b^2 - c^2)^2 (b^2 + b c + c^2) - 2 a^3 b c (b^4 + 2 b^3 c + b^2 c^2 + 2 b c^3 + c^4) - 2 a^4 (b^5 + b^4 c + b c^4 + c^5) + a^2 (b^7 + b^6 c - 4 b^4 c^3 - 4 b^3 c^4 + b c^6 + c^7)) | *** |
| 20789 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 6 b c + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 - 11 b^2 c - 11 b c^2 + c^3) + 2 a^3 (2 b^4 - 5 b^3 c - 10 b^2 c^2 - 5 b c^3 + 2 c^4) - a^2 (b^5 + 11 b^4 c - 28 b^3 c^2 - 28 b^2 c^3 + 11 b c^4 + c^5)) | *** |
| 20790 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - 2 a (b^2 - c^2)^2 (b^2 + 6 b c + c^2) - a^4 (b^3 + 13 b^2 c + 13 b c^2 + c^3) + 2 a^3 (2 b^4 + 7 b^3 c + 14 b^2 c^2 + 7 b c^3 + 2 c^4) - a^2 (b^5 - 13 b^4 c - 52 b^3 c^2 - 52 b^2 c^3 - 13 b c^4 + c^5)) | *** |
| 20878 | a^3 (a + b - c) (a - b + c) (-(b c (b + c)) + a (b^2 + c^2)) | *** |
| 21010 | -(a (a + b - c) (a - b + c) (b^2 + b c + c^2)) | X(7146) |
| 21164 | a (a + b - c) (a - b + c) (-2 a^5 (b - c)^2 + a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - a^2 (b - c)^2 (b^3 - 5 b^2 c - 5 b c^2 + c^3) - a^4 (b^3 + 7 b^2 c + 7 b c^2 + c^3) + 4 a^3 (b^4 - b^3 c + 8 b^2 c^2 - b c^3 + c^4)) | *** |
| 21334 | a (a + b - c) (a - b + c) (a^4 (b + c)^2 + b c (b^2 - c^2)^2 - a^3 (b^3 + c^3) + a^2 (-b^4 + b^3 c + 2 b^2 c^2 + b c^3 - c^4) + a (b^5 + b^3 c^2 + b^2 c^3 + c^5)) | *** |
| 21842 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2) - a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 22341 | a (a^5 (b + c) - 2 a^3 (b - c)^2 (b + c) + a (b - c)^4 (b + c) - 2 a^2 (b^2 - c^2)^2 + a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2)) | *** |
| 22765 | a (a + b - c) (a - b + c) (a^4 + 3 a^2 b c - 2 a^3 (b + c) + 2 a (b - c)^2 (b + c) - (b^2 - c^2)^2) | *** |
| 22766 | a (a + b - c) (a - b + c) (a^4 + 4 a^2 b c - 2 a^3 (b + c) - (b^2 - c^2)^2 + 2 a (b^3 + c^3)) | *** |
| 22767 | a (a + b - c) (a - b + c) (a^4 + 4 a^2 b c - 2 a^3 (b + c) - (b^2 - c^2)^2 + 2 a (b^3 - 2 b^2 c - 2 b c^2 + c^3)) | *** |
| 22768 | a (a + b - c) (a - b + c) (a^4 + 6 a^2 b c - 2 a^3 (b + c) - (b^2 - c^2)^2 + 2 a (b^3 + c^3)) | *** |
| 22770 | a (a + b - c) (a - b + c) (a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) + a^2 (b + c)^2 - 2 (b^2 - c^2)^2) | *** |
| 23171 | -(a (a + b - c) (a - b + c) (b + c) (b^5 - b^4 c - b c^4 + c^5 - a^2 (b - c)^2 (b + c) + a^3 (b^2 - b c + c^2) - a (b - c)^2 (b^2 + b c + c^2))) | *** |
| 23207 | a (a + b - c) (a - b + c) (a^5 (b + c) + a (b - c)^2 (b + c)^3 + 2 a^2 (b^2 - c^2)^2 - a^4 (b^2 + c^2) - (b^2 - c^2)^2 (b^2 + c^2) - 2 a^3 (b^3 + b^2 c + b c^2 + c^3)) | *** |
| 23340 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 4 b c + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 - 7 b^2 c - 7 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 9 b^2 c + 9 b c^2 + c^3) + a^3 (4 b^4 - 6 b^3 c - 8 b^2 c^2 - 6 b c^3 + 4 c^4)) | *** |
| 23703 | -(a (b - c)^2 (a^3 - b c (b + c) - a (b^2 - 3 b c + c^2))) | *** |
| 23832 | a (2 a - b - c) (b - c)^2 (a + b - c) (a - b + c) | *** |
| 23853 | a^2 (a + b - c) (a - b + c) (-(b c) + a (b + c)) | X(1403) |
| 23890 | -(a (b - c)^2 (a^4 - b (b - c)^2 c - 3 a^3 (b + c) - a (b + c)^3 + a^2 (3 b^2 + 7 b c + 3 c^2))) | *** |
| 23960 | a (a + b - c) (a - b + c) (4 a^6 (b + c) + 4 (b - c)^4 (b + c)^3 - 4 a^5 (2 b^2 + 3 b c + 2 c^2) - a (b^2 - c^2)^2 (8 b^2 - 19 b c + 8 c^2) + a^4 (-4 b^3 + 19 b^2 c + 19 b c^2 - 4 c^3) - a^2 (b - c)^2 (4 b^3 + 27 b^2 c + 27 b c^2 + 4 c^3) + a^3 (16 b^4 - 7 b^3 c - 28 b^2 c^2 - 7 b c^3 + 16 c^4)) | *** |
| 23961 | -(a (a + b - c) (a - b + c) (4 a^4 - 5 a^3 (b + c) + 5 a (b - c)^2 (b + c) - (b^2 - c^2)^2 - 3 a^2 (b^2 - 4 b c + c^2))) | *** |
| 23981 | a (a - b - c) (b - c)^2 (a^2 - b^2 + b c - c^2) | *** |
| 24299 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + 3 b c + c^2) - a^4 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + a^3 (4 b^4 + 6 b^3 c + 6 b c^3 + 4 c^4)) | *** |
| 24301 | -(a (a + b - c) (a - b + c) (a^9 (b + c) - 2 a^5 b (b - c)^2 c (b + c) - a (b - c)^4 (b + c)^3 (b^2 + c^2) + (b^2 - c^2)^4 (b^2 + c^2) + 2 a^3 (b - c)^2 (b + c)^3 (b^2 - b c + c^2) - a^8 (b^2 + 4 b c + c^2) - 2 a^7 (b^3 + c^3) + 4 a^4 b c (b^4 + c^4) + 2 a^6 (b^4 + 2 b^3 c + 2 b c^3 + c^4) - 2 a^2 (b^2 - c^2)^2 (b^4 + 2 b^3 c + 2 b c^3 + c^4))) | *** |
| 24310 | a (a + b - c) (a - b + c) (b + c) (a^4 (b + c) + b (b - c)^2 c (b + c) - a^3 (b^2 - 3 b c + c^2) + a (b - c)^2 (b^2 + b c + c^2) - a^2 (b^3 + c^3)) | *** |
| 24464 | a (a + b - c) (a - b + c) (2 a^2 b^2 c^2 + 2 a^3 b c (b + c) + a^4 (b + c)^2 + b c (b^4 + b^3 c + b c^3 + c^4) + a (b^5 + b^4 c + b c^4 + c^5)) | *** |
| 24468 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) - a (b^2 - c^2)^2 (2 b^2 + b c + 2 c^2) - a^2 (b - c)^2 (b^3 - 2 b^2 c - 2 b c^2 + c^3) - a^4 (b^3 + 4 b^2 c + 4 b c^2 + c^3) + a^3 (4 b^4 + b^3 c - 2 b^2 c^2 + b c^3 + 4 c^4)) | *** |
| 24474 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 + c^2) - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 + b^2 c + b c^2 + c^3) + 2 a^3 (2 b^4 + b^3 c + b c^3 + 2 c^4) - a^2 (b^5 - b^4 c - b c^4 + c^5)) | *** |
| 24806 | -(a (-(a^4 (b + c)^2) + b c (b^2 - c^2)^2 + a^2 (b - c)^2 (b^2 + b c + c^2) - a^3 (b^3 + c^3) + a (b - c)^2 (b^3 + c^3))) | *** |
| 24926 | a (a + b - c) (a - b + c) (2 a^3 (b + c) + 2 (b^2 - c^2)^2 - 2 a^2 (b^2 + 3 b c + c^2) + a (-2 b^3 + b^2 c + b c^2 - 2 c^3)) | *** |
| 24927 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a (b^2 - c^2)^2 (b^2 - 4 b c + c^2) - 2 a^5 (b^2 + 3 b c + c^2) - a^4 (b^3 - 11 b^2 c - 11 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 13 b^2 c + 13 b c^2 + c^3) + a^3 (4 b^4 - 2 b^3 c - 24 b^2 c^2 - 2 b c^3 + 4 c^4)) | *** |
| 24928 | a (a + b - c) (a - b + c) (a^3 (b + c) + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2) - a (b^3 - 5 b^2 c - 5 b c^2 + c^3)) | *** |
| 24929 | a (a + b - c) (a - b + c) (a^3 (b + c) - a (b + c)^3 + (b^2 - c^2)^2 - a^2 (b^2 + 4 b c + c^2)) | *** |
| 25405 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 8 b c + 3 c^2) + a (-3 b^3 + 7 b^2 c + 7 b c^2 - 3 c^3)) | *** |
| 25413 | a (a + b - c) (a - b + c) (a^6 (b + c) - 2 a (b - c)^4 (b + c)^2 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a^4 (b^3 - 3 b^2 c - 3 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 5 b^2 c + 5 b c^2 + c^3) + a^3 (4 b^4 - 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + 4 c^4)) | *** |
| 25414 | -(a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - 5 b c + 2 c^2) - a^4 (b^3 - 4 b^2 c - 4 b c^2 + c^3) + a^3 (4 b^4 - 3 b^3 c - 4 b^2 c^2 - 3 b c^3 + 4 c^4) - a^2 (b^5 + 4 b^4 c - 7 b^3 c^2 - 7 b^2 c^3 + 4 b c^4 + c^5))) | *** |
| 25415 | a (a + b - c) (a - b + c) (3 a^3 (b + c) + 3 (b^2 - c^2)^2 - a^2 (3 b^2 + 2 b c + 3 c^2) + a (-3 b^3 + b^2 c + b c^2 - 3 c^3)) | *** |
| 26086 | a (a + b - c) (a - b + c) (4 a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) + a^2 (-5 b^2 + 8 b c - 5 c^2) + (b^2 - c^2)^2) | *** |
| 26087 | a (a + b - c) (a - b + c) (2 a^6 (b + c) - 4 a^5 (b + c)^2 + 2 (b - c)^4 (b + c)^3 - a (b^2 - c^2)^2 (4 b^2 - 9 b c + 4 c^2) + a^4 (-2 b^3 + 11 b^2 c + 11 b c^2 - 2 c^3) - a^2 (b - c)^2 (2 b^3 + 15 b^2 c + 15 b c^2 + 2 c^3) + a^3 (8 b^4 - b^3 c - 16 b^2 c^2 - b c^3 + 8 c^4)) | *** |
| 26285 | a (a + b - c) (a - b + c) (2 a^4 - a^3 (b + c) + a (b - c)^2 (b + c) + a^2 (-3 b^2 + 4 b c - 3 c^2) + (b^2 - c^2)^2) | *** |
| 26286 | a (a + b - c) (a - b + c) (2 a^4 - 3 a^3 (b + c) + 3 a (b - c)^2 (b + c) - (b^2 - c^2)^2 - a^2 (b^2 - 4 b c + c^2)) | *** |
| 26287 | a (a + b - c) (a - b + c) (a^6 (b + c) + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + 3 b c + c^2) - a (b^2 - c^2)^2 (2 b^2 - 3 b c + 2 c^2) - a^4 (b^3 - 6 b^2 c - 6 b c^2 + c^3) - a^2 (b - c)^2 (b^3 + 8 b^2 c + 8 b c^2 + c^3) + a^3 (4 b^4 + 3 b^3 c - 12 b^2 c^2 + 3 b c^3 + 4 c^4)) | *** |
| 26357 | a^2 (a + b - c) (a - b + c) (a^3 + b^3 - 3 b^2 c - 3 b c^2 + c^3 - a^2 (b + c) - a (b^2 + c^2)) | *** |
| 26358 | a (a + b - c) (a - b + c) (a^4 + a^3 (b + c) + 2 (b^2 - c^2)^2 - 3 a^2 (b^2 + c^2) - a (b^3 - 3 b^2 c - 3 b c^2 + c^3)) | *** |
| 26437 | a (a^3 - 2 a^2 (b + c) + 2 (b - c)^2 (b + c) - a (b^2 + c^2)) | *** |
| 26903 | a (a^11 (b + c) - a (b - c)^6 (b + c)^5 + a^2 (b - c)^4 (b + c)^6 + a^10 (-3 b^2 + 2 b c - 3 c^2) - (b^2 - c^2)^4 (b^2 + c^2)^2 + a^3 (b - c)^4 (b + c)^3 (5 b^2 + 2 b c + 5 c^2) - a^9 (5 b^3 + 3 b^2 c + 3 b c^2 + 5 c^3) + 2 a^4 (b^2 - c^2)^2 (3 b^4 - 4 b^3 c + 6 b^2 c^2 - 4 b c^3 + 3 c^4) - 2 a^6 (b - c)^2 (7 b^4 + 8 b^3 c + 10 b^2 c^2 + 8 b c^3 + 7 c^4) + a^8 (11 b^4 - 8 b^3 c + 6 b^2 c^2 - 8 b c^3 + 11 c^4) + 2 a^7 (5 b^5 + b^4 c + 2 b^3 c^2 + 2 b^2 c^3 + b c^4 + 5 c^5) - 2 a^5 (b - c)^2 (5 b^5 + 9 b^4 c + 10 b^3 c^2 + 10 b^2 c^3 + 9 b c^4 + 5 c^5)) | *** |
| 26904 | a (a + b - c) (a - b + c) (a^11 (b + c) - a (b - c)^6 (b + c)^5 - a^2 (b - c)^4 (b + c)^6 + (b^2 - c^2)^4 (b^2 + c^2)^2 + a^10 (3 b^2 - 2 b c + 3 c^2) + a^3 (b - c)^4 (b + c)^3 (5 b^2 + 2 b c + 5 c^2) - a^9 (5 b^3 + 3 b^2 c + 3 b c^2 + 5 c^3) + a^8 (-11 b^4 + 8 b^3 c - 6 b^2 c^2 + 8 b c^3 - 11 c^4) - 2 a^4 (b^2 - c^2)^2 (3 b^4 - 4 b^3 c + 6 b^2 c^2 - 4 b c^3 + 3 c^4) + 2 a^6 (b - c)^2 (7 b^4 + 8 b^3 c + 10 b^2 c^2 + 8 b c^3 + 7 c^4) + 2 a^7 (5 b^5 + b^4 c + 2 b^3 c^2 + 2 b^2 c^3 + b c^4 + 5 c^5) - 2 a^5 (b - c)^2 (5 b^5 + 9 b^4 c + 10 b^3 c^2 + 10 b^2 c^3 + 9 b c^4 + 5 c^5)) | *** |
| 26908 | a (a + b - c) (a - b + c) (a^11 (b + c) - a^2 (b - c)^6 (b + c)^4 - a (b - c)^6 (b + c)^5 + (b^2 - c^2)^4 (b^2 + c^2)^2 + a^10 (3 b^2 + 2 b c + 3 c^2) + a^3 (b - c)^4 (b + c)^3 (5 b^2 + 2 b c + 5 c^2) - a^9 (5 b^3 + 3 b^2 c + 3 b c^2 + 5 c^3) - 2 a^4 (b^2 - c^2)^2 (3 b^4 + 4 b^3 c + 6 b^2 c^2 + 4 b c^3 + 3 c^4) + 2 a^6 (b + c)^2 (7 b^4 - 8 b^3 c + 10 b^2 c^2 - 8 b c^3 + 7 c^4) - a^8 (11 b^4 + 8 b^3 c + 6 b^2 c^2 + 8 b c^3 + 11 c^4) + 2 a^7 (5 b^5 + b^4 c + 2 b^3 c^2 + 2 b^2 c^3 + b c^4 + 5 c^5) - 2 a^5 (b - c)^2 (5 b^5 + 9 b^4 c + 10 b^3 c^2 + 10 b^2 c^3 + 9 b c^4 + 5 c^5)) | *** |
| 27247 | a (a + b - c) (a - b + c) (a^6 (b + c) - a^4 (b - c)^2 (b + c) - 2 a (b - c)^4 (b + c)^2 + (b - c)^4 (b + c)^3 - 2 a^5 (b^2 + c^2) + 4 a^3 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 + c^4) - a^2 (b^5 + b^4 c + b^3 c^2 + b^2 c^3 + b c^4 + c^5)) | *** |
El 11 de abril de 2020 falleció de forma repentina, a los 82 años, victima de la covic-19, John Horton Conway (la fiebre comenzó tan solo tres días antes). Fue un prolífico matemático activo en la teoría de conjuntos (teoría de conjuntos finitos), teoría de nudos, teoría de números, teoría de juegos y teoría de códigos. Entre los matemáticos aficionados, quizás es más conocido por su teoría de juegos combinatorios, en particular por ser el creador en 1970 del juego de la vida. También es uno de los inventores del juego del drago, así como del Phutball y ha realizado análisis detallados de muchos otros juegos y problemas, como el cubo Soma. Inventó un nuevo sistema numérico, los números surreales, los cuales se encuentran estrechamente relacionados a ciertos juegos y han sido objeto de una novela matemática por Donald Knuth.
A' = ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 + 2 (b^2 - c^2)^2 - 3 a^2 (b^2 + c^2)) : 2 b^2 (-a^2 + b^2 - c^2) ((b^2 - c^2)^2 - a^2 (b^2 + c^2)) : 2 c^2 (-a^2 - b^2 + c^2) ((b^2 - c^2)^2 - a^2 (b^2 + c^2))).
La matriz ℳ asociada de la transformación afín σ, que aplica ABC en A'B'C', tiene las entradas (las demás se deducen cíclicamente):
ℳ[1,1] = b^2 c^2 (-a^2+b^2-c^2) (a^2+b^2-c^2) (-a^8-a^4 (b^2-c^2)^2+2 (b^2-c^2)^4+3 a^6 (b^2+c^2)-3 a^2 (b^2-c^2)^2 (b^2+c^2)),
ℳ[1,2] = 2 a^4 c^2 (-a^2-b^2+c^2) (-a^2+b^2+c^2)^2 (a^4-b^2 c^2+c^4-a^2 (b^2+2 c^2)),
ℳ[1,3] = 2 a^4 b^2 (-a^2+b^2-c^2) (-a^2+b^2+c^2)^2 (a^4+b^4-b^2 c^2-a^2 (2 b^2+c^2)).
λ = -a^2 b^2 (a-b-c) (a+b-c) c^2 (a-b+c) (a+b+c) (a^2-b^2-c^2) (a^2+b^2-c^2) (a^2-b^2+c^2),
esX19210 = (a^4 (-a^2+b^2+c^2)^2 (-a^4-b^4+b^2 c^2+a^2 (2 b^2+c^2)) (a^4-b^2 c^2+c^4-a^2 (b^2+2 c^2)) : ... : ...).
X19210 es el de O respecto al y al punto X79 = , donde K es el .El 9 de abril de 1977 (sábado santo) en España y en plena transición a la democracia tras la dictadura de Franco, por decisión personal del presidente del Gobierno Adolfo Suárez, el Partido Comunista de España vuelve a ser legal. “La legalización del Partido Comunista es un verdadero golpe de Estado", dijo Manuel Fraga Iribarne al legalizarse el PCE después de la Matanza de Atocha y poco antes de las primeras elecciones democráticas. Y fundó un partido de derecha pura y dura llamado Alianza Popular (AP), aglutinando una federación de siete organizaciones políticas, que fue inscrito en el Registro de Partidos Políticos del Ministerio del Interior el 4 de mayo de 1977.
| Xn en IO |
Par bicéntrico (baricéntricas) |
|---|---|
| 3 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + c)): : |
| 35 | a (a^3 - 2 a b^2 + b^2 (b - c) - a^2 c): : |
| 36 | a (a - b) (a^2 + a (b - c) + b (-b + c)): : |
| 40 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + c^2)) : : P(44) = 1st Laemmel Point |
| 46 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 2 b c + c^2)): : |
| 55 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + c)): : |
| 56 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + 3 c)): : |
| 57 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 4 b c + c^2)): : |
| 65 | a (a^2 b + (b - c) c^2 + a (-b^2 + b c + c^2)): : |
| 165 | a (3 a^3 + 3 b^3 + a^2 (b - 3 c) - 3 b^2 c + b c^2 - c^3 + a (-7 b^2 + 2 b c + c^2)): : |
| 171 | a (a^3 + a^2 b + b (b^2 + c^2) + a (-b^2 + 2 b c + c^2)): : |
| 241 | a (a^4 (b + 2 c) + a^3 (b^2 - b c - 3 c^2) + (b - c)^2 c (2 b^2 + b c + c^2) + a^2 (-5 b^3 + 2 b^2 c + 2 b c^2 + c^3) + a (3 b^4 - 5 b^3 c + 4 b^2 c^2 - b c^3 - c^4)): : |
| 354 | a (a^2 b + (b - c) c^2 + a (-b^2 + 5 b c + c^2)): : |
| 484 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + b c + c^2)): : |
| 517 | a (a^2 b + (b - c) c^2 - a (b^2 + b c - c^2)): : |
| 559 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + b Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] + c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] + a (-3 b^2 + 4 b c + c^2 + Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)])): : |
| 940 | a (a^3 + a^2 (2 b + c) + a c (5 b + 2 c) + b (b^2 + b c + 2 c^2)): : |
| 942 | a (a^2 b + (b - c) c^2 + a (-b^2 + 3 b c + c^2)): : |
| 980 | a (b c^2 (2 b^2 + b c + c^2) + a^3 (b^2 + 2 b c + 2 c^2) + a c (4 b^3 + 2 b^2 c + 2 b c^2 + c^3) + a^2 (3 b^3 + 3 b^2 c + 2 b c^2 + c^3)): : |
| 982 | a (2 a b (b - c) + a^2 c + c (b^2 + c^2)): : |
| 986 | a (2 a b^2 + a^2 c + b^2 c + c^3): : |
| 988 | a (a^3 + b^3 - 3 b^2 c - b c^2 - c^3 - a^2 (b + 3 c) - a (5 b^2 - 2 b c + c^2)): : |
| 999 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + 5 c)): : |
| 1038 | a (a^6 + 4 a b^3 (b - c) c - 4 a^3 b c^2 + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 - 4 b c + c^2) - a^2 (b^4 + 8 b^3 c - 6 b^2 c^2 + c^4)): : |
| 1040 | a (a^6 + 4 a^3 b c^2 + 4 a b^3 c (-b + c) + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 + 4 b c + c^2) - a^2 (b^4 - 8 b^3 c + 2 b^2 c^2 + c^4)): : |
| 1060 | a (a^6 - a^4 (b - c)^2 + 2 a b^3 (b - c) c - 2 a^3 b c^2 + (b^2 - c^2)^2 (b^2 + c^2) - a^2 (b^4 + 4 b^3 c - 4 b^2 c^2 + c^4)): : |
| 1062 | a (a^6 + 2 a^3 b c^2 + 2 a b^3 c (-b + c) - a^4 (b + c)^2 + (b^2 - c^2)^2 (b^2 + c^2) - a^2 (b^4 - 4 b^3 c + c^4)): : |
| 1082 | -(a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 - b Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] - c Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)] + a (-3 b^2 + 4 b c + c^2 - Sqrt[-3 a^4 - 3 (b^2 - c^2)^2 + 6 a^2 (b^2 + c^2)]))): : |
| 1155 | a (2 a^3 + 2 b^3 + a^2 (b - 2 c) - 2 b^2 c + b c^2 - c^3 + a (-5 b^2 + 3 b c + c^2)): : |
| 1159 | a (a^3 + b^3 - b^2 c - 4 b c^2 + 4 c^3 - a^2 (4 b + c) + a (2 b^2 - 3 b c - 4 c^2)): : |
| 1214 | a (-2 a^2 b^3 (b + c) + a^5 (b + 2 c) + a^4 (2 b^2 - c^2) - 2 a^3 (2 b^3 + c^3) + a b (3 b^4 - 2 b^3 c - 2 b^2 c^2 + 2 b c^3 - c^4) + c (2 b^5 - b^4 c - 2 b^3 c^2 + c^5)): : |
| 1319 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - 5 b c + c^2)): : |
| 1385 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - 3 b c + c^2)): : |
| 1388 | a (3 a^3 + 3 b^3 - 3 b^2 c - 2 b c^2 + 2 c^3 - a^2 (2 b + 3 c) + a (-4 b^2 + 7 b c - 2 c^2)): : |
| 1402 | a (a^5 (b + c) + a^4 b (b + c) + b^3 c (b^2 - c^2) - a^3 (2 b^3 - 2 b c^2 + c^3) + a^2 b (-b^3 + b c^2 + c^3) + a b (b^4 - b^3 c + b c^3 + c^4)): : |
| 1403 | a (a^4 b^2 + a^5 (b + c) + b^3 c (b^2 - c^2) - a^2 b^2 (b^2 - 3 b c + 3 c^2) - a^3 (2 b^3 + b^2 c - 3 b c^2 + c^3) + a (b^5 - 2 b^4 c + b^3 c^2 + 2 b c^4)): : |
| 1420 | a (3 a^3 + 3 b^3 - 3 b^2 c - b c^2 + c^3 - a^2 (b + 3 c) - a (5 b^2 - 8 b c + c^2)): : |
| 1429 | a (a^5 + a^4 b - 2 a^3 b (b - c) - 2 a^2 c (b^2 + c^2) + b (b^4 - 2 b c^3 + c^4) + a (-b^4 + 2 b^3 c - 2 b^2 c^2 + 2 b c^3 + c^4)): : |
| 1454 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 4 b c + c^2) + a^3 (4 b^3 - 6 b c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 8 b^3 c + 4 b^2 c^2 - c^4) - 2 a (2 b^5 - 4 b^4 c + b^3 c^2 + 2 b^2 c^3 - c^5)): : |
| 1460 | a (a^6 + a^5 b + b^6 - a^4 b (b - 4 c) - b^2 c^4 + 2 a^3 b c (b + c) - a^2 (b^4 + 4 b^3 c - 4 b^2 c^2 - 4 b c^3 + c^4) + a b (-b^4 + 2 b^3 c + 2 b c^3 + c^4)): : |
| 1466 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 12 b^3 c + 14 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 8 b^3 c + 4 b^2 c^2 + c^4)): : |
| 1467 | a (a^6 - 2 a^5 (b + c) - a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 4 a^3 (b^3 - b^2 c + b c^2 + c^3) - a^2 (b^4 - 12 b^3 c + 14 b^2 c^2 + 4 b c^3 + c^4) - 2 a (b^5 + b^4 c - 2 b^3 c^2 + 2 b^2 c^3 - 3 b c^4 + c^5)): : |
| 1470 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - 3 b c^2 + c^3) + a^2 (b^4 - 10 b^3 c + 12 b^2 c^2 - c^4) + a b (-3 b^4 + 8 b^3 c - 4 b^2 c^2 - 2 b c^3 + c^4)): : |
| 1482 | a (a^3 + b^3 - b^2 c + a (3 b - 2 c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c)): : |
| 1617 | a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + c^3) + a^2 (b^4 + 2 b^3 c - 6 b^2 c^2 - c^4) + a b (-3 b^4 + 2 b^3 c + 2 b^2 c^2 - 2 b c^3 + c^4)): : |
| 1622 | a (a^9 + b^2 (b - c)^3 (b + c)^4 + a^8 (2 b + c) - 3 a^7 (b^2 + b c + c^2) - a^6 (7 b^3 + 2 b^2 c - 4 b c^2 + 3 c^3) - a b (b - c)^2 c (7 b^4 + 8 b^3 c + 2 b^2 c^2 - c^4) + a^5 (3 b^4 + 7 b^3 c + 8 b^2 c^2 - b c^3 + 3 c^4) - a^2 (b - c)^2 (5 b^5 + 4 b^4 c - 3 b^3 c^2 - b^2 c^3 + 2 b c^4 + c^5) + a^4 (9 b^5 - 6 b^4 c - 7 b^3 c^2 - b^2 c^3 - 6 b c^4 + 3 c^5) - a^3 (b^6 - 3 b^5 c + 11 b^4 c^2 - 10 b^3 c^3 + 3 b^2 c^4 - 3 b c^5 + c^6)): : |
| 1697 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 - 4 b c + c^2)): : |
| 1715 | a (a^8 (b + c) + a^7 (b^2 - 2 b c - c^2) + b (b - c)^3 c (b + c)^2 (b^2 + c^2) - a^6 (5 b^3 + 2 b^2 c - 4 b c^2 + c^3) + a^5 (-b^4 + 6 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4) - a^2 (b - c)^3 (3 b^4 + 3 b^3 c + 2 b^2 c^2 + 3 b c^3 + c^4) + a^4 (7 b^5 - 6 b^4 c - b^3 c^2 + 5 b^2 c^3 - 4 b c^4 - c^5) + a (b - c)^2 (b^6 - 4 b^5 c - 5 b^4 c^2 + b^2 c^4 - c^6) + a^3 (-b^6 + 2 b^5 c - b^4 c^2 - 4 b^3 c^3 + b^2 c^4 + 2 b c^5 + c^6)): : |
| 1735 | a (a^5 c - a^3 b (2 b^2 + b c - 3 c^2) + a^4 (2 b^2 - 2 b c - c^2) + a (b - c)^3 (2 b^2 + 2 b c + c^2) - a^2 b (2 b^3 - 5 b^2 c + 2 b c^2 + c^3) + c (b^5 - b^4 c - b c^4 + c^5)): : |
| 1754 | a (a^6 - 3 a^4 b^2 - a^5 c + a^3 b (2 b^2 - b c - c^2) + a^2 (b^4 + b^3 c - b c^3 - c^4) + b (b^5 - b^4 c - b c^4 + c^5) + a (-2 b^5 + 2 b^4 c + b^3 c^2 - 3 b^2 c^3 + b c^4 + c^5)): : |
| 1758 | a (a^6 - a^5 (b + 3 c) + a^4 (-5 b^2 + 3 b c + c^2) + 2 a^3 (3 b^3 - 2 b c^2 + c^3) + a^2 (3 b^4 - 4 b^3 c + 2 b^2 c^2 - c^4) + (b - c)^2 (b^4 - b^3 c - 2 b^2 c^2 - b c^3 - c^4) + a (-5 b^5 + 7 b^4 c - 4 b^2 c^3 + b c^4 + c^5)): : |
| 1764 | a (2 a^4 b^2 + a^5 (b + c) - a^3 b (2 b^2 + b c - 3 c^2) - a^2 b (2 b^3 + b^2 c + 4 b c^2 - c^3) + b c (b^4 - c^4) + a (b^5 - 4 b^4 c - b^3 c^2 + b^2 c^3 - c^5)): : |
| 1771 | a (a^6 - a^5 c + a^4 b (-3 b + 2 c) + a^3 b (2 b^2 + b c - 3 c^2) - a (b - c)^3 (2 b^2 + 2 b c + c^2) + a^2 (b^4 - 5 b^3 c + 4 b^2 c^2 + b c^3 - c^4) + b (b^5 - b^4 c - b c^4 + c^5)): : |
| 1936 | a (a^6 - a^5 c + a^4 b (-3 b + c) + 2 a^3 (b^3 - b c^2) + a^2 (b^4 - 2 b^3 c + 4 b^2 c^2 - c^4) + a (-2 b^5 + 3 b^4 c - 2 b^2 c^3 + c^5) + b (b^5 - b^4 c - b c^4 + c^5)): : |
| 2077 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 5 c) - a b^2 (3 b^3 - 7 b^2 c + 3 b c^2 + c^3) + a^3 (4 b^3 + b^2 c - 5 b c^2 + 2 c^3) + a^2 (b^4 - 9 b^3 c + 6 b^2 c^2 + b c^3 - c^4)): : |
| 2078 | a (a^6 + a^4 b (-3 b + c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a b^2 (-3 b^3 + 3 b^2 c + b c^2 - c^3) + a^3 (4 b^3 + b^2 c - b c^2 + 2 c^3) + a^2 (b^4 - b^3 c - 2 b^2 c^2 + b c^3 - c^4)): : |
| 2093 | a (a^3 + b^3 + a^2 (3 b - c) - b^2 c + 3 b c^2 - 3 c^3 + a (-5 b^2 + 2 b c + 3 c^2)): : |
| 2095 | a (a^6 + a^5 (b - 2 c) + a^4 (-7 b^2 + 4 b c + 2 c^2) + a^3 (4 b^3 - 8 b c^2 - 2 c^3) + (b - c)^3 (b^3 + b^2 c + 2 b c^2 + 2 c^3) + a^2 (5 b^4 - 10 b^3 c + 10 b^2 c^2 - c^4) - a (5 b^5 - 10 b^4 c + 2 b^3 c^2 + 6 b^2 c^3 + b c^4 - 4 c^5)): : |
| 2098 | a (a^3 + b^3 - b^2 c + a (5 b - 2 c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c)): : |
| 2099 | a (a^3 + b^3 - b^2 c + a (b - 2 c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c)): : |
| 2223 | a (a^3 (b - c) c + b^3 (b - c) c + a^4 (b + c) - a^2 b^2 (2 b + c) + a b (b^3 - b^2 c + c^3)): : |
| 2283 | -(a (a^7 (b + c) + b^3 (b - c)^3 c (b + c) - a^6 (b^2 + b c + 2 c^2) - 3 a^5 (b^3 - b c^2) + a^4 (4 b^4 + 2 b^3 c + b^2 c^2 - 5 b c^3 + 2 c^4) + a b (b - c)^2 (b^4 - b^3 c + 2 b^2 c^2 + 2 b c^3 + 2 c^4) + a^3 (b^5 - 6 b^4 c + 2 b^2 c^3 + 2 b c^4 - c^5) + a^2 (-3 b^6 + 6 b^5 c - 5 b^4 c^2 + 4 b^3 c^3 - 2 b c^5))): : |
| 2352 | a (a^5 (b + c) + a^4 b (b + 2 c) + b^3 c (b^2 - c^2) - a^3 (2 b^3 - b c^2 + c^3) - a^2 (b^4 + 2 b^3 c - b c^3) + a b (b^4 - b^2 c^2 + b c^3 + c^4)): : |
| 2446 | -(a (a^2 b + b c^2 - c^3 - a (b^2 + b c - c^2) - 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))])): : |
| 2447 | a (a^2 b + b c^2 - c^3 - a (b^2 + b c - c^2) + 2 Sqrt[a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2))]): : |
| 2564 | a (a^3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + b^2 (b - c) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] - a^2 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + a b (-2 c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 2 b Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])): : |
| 2565 | a (a^3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + b^2 (b - c) Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] - a^2 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + a b (2 c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 2 b Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])): : |
| 2572 | a (a^7 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + a^5 (5 c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + b^2 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 12 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^4 (b c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 5 c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b^3 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - b^2 c (5 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^2 (5 b^5 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b c^4 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b^3 c^2 (2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - c^5 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - b^4 c (5 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + 2 b^2 c^3 (-4 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + (b - c) (5 b^4 c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b^2 c^4 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^6 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^6 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^6 (b (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - c (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^3 (4 b^3 c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 b c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b^2 c^2 (-2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^4 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^4 (-7 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 10 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a (4 b^3 c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b^5 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + 2 b c^5 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + c^6 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - 3 b^2 c^4 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^4 c^2 (-7 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 8 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - b^6 (3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 10 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]))): : |
| 2573 | -(a (a^7 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + a^6 (-(b Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)]) + c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] - 4 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - a^2 (5 b^5 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b c^4 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b^4 c (-5 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^5 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + 2 b^3 c^2 (2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) - 2 b^2 c^3 (4 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 3 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + (b - c) (-5 b^4 c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b^2 c^4 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^6 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^6 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a (-4 b^3 c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b^5 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + 2 b c^5 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + b^6 (3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 10 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + 3 b^2 c^4 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 4 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^6 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^4 c^2 (7 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 8 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^3 (-4 b^3 c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 4 b c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 b^2 c^2 (2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + c^4 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^4 (7 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 10 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) - a^5 (5 c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 2 b c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)] + b^2 (Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 12 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])) + a^4 (-(b c^2 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)]) + 5 c^3 Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + b^3 (-Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] + 2 Sqrt[b^2 c^2 + a^2 (b^2 + c^2)]) + b^2 (5 c Sqrt[a^4 + b^4 - b^2 c^2 + c^4 - a^2 (b^2 + c^2)] - 2 c Sqrt[b^2 c^2 + a^2 (b^2 + c^2)])))): : |
| 2646 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - b c + c^2)): : |
| 2662 | a (-(a^9 b c (b + 3 c)) + b^2 c^2 (b^2 - c^2)^4 - 4 a^3 b (b - c)^2 c (b + c)^3 (b^2 - b c + c^2) + a^10 (b^2 + 3 b c + c^2) + 4 a^7 b c (b^3 + c^3) + a b (b - c)^3 c (b + c)^2 (3 b^4 + 2 b^2 c^2 - c^4) - 4 a^4 (b^2 - c^2)^2 (b^4 - 2 b^3 c + 3 b^2 c^2 - b c^3 + c^4) - a^8 (4 b^4 + 8 b^3 c - 3 b^2 c^2 + 4 b c^3 + 4 c^4) + a^2 (b - c)^3 (b + c)^2 (b^5 - 4 b^4 c + b^3 c^2 - 5 b^2 c^3 - c^5) + 2 a^5 b c (-b^5 + 3 b^4 c - 2 b^3 c^2 - 2 b^2 c^3 + b c^4 + c^5) + 2 a^6 (3 b^6 + b^5 c - 2 b^4 c^2 + 6 b^3 c^3 - 2 b^2 c^4 - b c^5 + 3 c^6)): : |
| 3057 | -(a (a^2 b + (b - c) c^2 + a (-b^2 - 3 b c + c^2))): : |
| 3072 | a (a^6 - a^5 c + a^4 b (-3 b + c) + 2 a^3 (b^3 - b c^2) + a^2 (b^4 - 2 b^3 c - c^4) + a (-2 b^5 + 3 b^4 c - 2 b^2 c^3 + c^5) + b (b^5 - b^4 c - b c^4 + c^5)): : |
| 3075 | a (a^6 - 3 a^4 b (b - c) - a^5 c + 2 a^3 (b^3 - 2 b c^2) + a^2 (b^4 - 6 b^3 c + 6 b^2 c^2 - c^4) + a (-2 b^5 + 5 b^4 c - 2 b^3 c^2 - 2 b^2 c^3 + c^5) + b (b^5 - b^4 c - b c^4 + c^5)): : |
| 3245 | a (a^3 + b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 - 2 c^3 + a (-4 b^2 + 2 c^2)): : |
| 3256 | a (a^6 - 3 a^4 b (b - c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 + 3 b^2 c - 3 b c^2 + 2 c^3) + a b (-3 b^4 + 5 b^3 c - b^2 c^2 + b c^3 - 2 c^4) + a^2 (b^4 - 7 b^3 c + 6 b^2 c^2 + 3 b c^3 - c^4)): : |
| 3295 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + 3 c)): : |
| 3303 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + 5 c)): : |
| 3304 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + 7 c)): : |
| 3333 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 8 b c + c^2)): : |
| 3336 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 3 b c + c^2)): : |
| 3337 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 5 b c + c^2)): : |
| 3338 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 + 6 b c + c^2)): : |
| 3339 | -(a (a^3 + b^3 + a^2 (3 b - c) - b^2 c + 3 b c^2 - 3 c^3 + a (-5 b^2 + 6 b c + 3 c^2))): : |
| 3340 | -(a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 - 3 c^2))): : |
| 3359 | a (a^6 - 2 a^5 c + 4 a^3 b (b^2 + b c - 2 c^2) + a^4 (-5 b^2 + 6 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 16 b^3 c + 6 b^2 c^2 + 4 b c^3 - c^4) - 2 a (2 b^5 - 5 b^4 c + 2 b^3 c^2 + 2 b c^4 - c^5)): : |
| 3361 | a (3 a^3 + 3 b^3 + a^2 (b - 3 c) - 3 b^2 c + b c^2 - c^3 + a (-7 b^2 + 10 b c + c^2)): : |
| 3428 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - b^2 c - b c^2 + c^3) + a^2 (b^4 + 6 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 4 b^3 c - 4 b c^3 + 3 c^4)): : |
| 3503 | a (a^5 (b^2 + b c + c^2) + a^4 (b^3 - b^2 c + b c^2 - c^3) + b^2 c^2 (b^3 - b^2 c + b c^2 - c^3) + a b c (b^4 - 3 b^3 c + 2 b^2 c^2 + b c^3 + c^4) + a^3 (-3 b^4 + 2 b^3 c - b^2 c^2 + 2 b c^3 + c^4) + a^2 (b^5 - b^4 c + 3 b^3 c^2 - 3 b^2 c^3 + b c^4 - c^5)): : |
| 3513 | a (a^4 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - a^3 Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + a (3 b^2 - 4 b c - c^2) Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - a^2 (2 b^2 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + c (2 c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])) - (b - c) (-(b^3 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)]) + b c^2 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + b^2 (-(c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)]) + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) + c^2 (c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]))): : |
| 3514 | -(a (a^4 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + a^3 Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + a (-3 b^2 + 4 b c + c^2) Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + (b - c) (b^3 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] - b c^2 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + c^2 (-(c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)]) + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) + b^2 (c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])) + a^2 (-2 b^2 Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - c (2 c Sqrt[-a^2 - (b - c)^2 + 2 a (b + c)] + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])))): : |
| 3550 | a (2 a^3 + a^2 (b - c) + b (2 b^2 - b c + c^2) + a (-3 b^2 + b c + c^2)): : |
| 3576 | a (3 a^3 + 3 b^3 - 3 b^2 c - b c^2 + c^3 - a^2 (b + 3 c) - a (5 b^2 - 4 b c + c^2)): : |
| 3579 | a (2 a^3 + 2 b^3 + a^2 (b - 2 c) - 2 b^2 c + b c^2 - c^3 + a (-5 b^2 + b c + c^2)): : |
| 3587 | a (a^6 - 2 a^5 c + 4 a^3 b (b^2 + c^2) + a^4 (-5 b^2 - 6 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 + 12 b^3 c - 2 b^2 c^2 - c^4) - 2 a (2 b^5 + b^4 c - 4 b^3 c^2 + 2 b^2 c^3 - c^5)): : |
| 3601 | -(a (3 a^3 + 3 b^3 - 3 b^2 c - b c^2 + c^3 - a^2 (b + 3 c) - a (5 b^2 + c^2))): : |
| 3612 | -(a (3 a^3 + 3 b^3 - 3 b^2 c - b c^2 + c^3 - a^2 (b + 3 c) - a (5 b^2 - 2 b c + c^2))): : |
| 3660 | -(a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (4 b + c) + a^4 (-2 b^2 + 6 b c + c^2) + 2 a^2 b^2 (b^2 - 7 b c + 8 c^2) - a (b^5 - 8 b^4 c + 6 b^3 c^2 + 2 b^2 c^3 + b c^4 - 2 c^5))): : |
| 3666 | a (a^2 (b + 2 c) + c (2 b^2 + b c + c^2) + a (3 b^2 + b c + c^2)): : |
| 3670 | a (a b (2 b - c) + a^2 c + c (b^2 + c^2)): : |
| 3675 | a (a^4 c + a^3 (b^2 - 2 b c - 2 c^2) + a^2 (-3 b^3 + 3 b^2 c + 2 b c^2 + c^3) + a (2 b^4 - 4 b^3 c + 4 b^2 c^2 - 2 b c^3 - c^4) + c (b^4 - 2 b^3 c + b^2 c^2 - b c^3 + c^4)): : |
| 3677 | a (a^3 + b^3 + 3 b^2 c + b c^2 + 3 c^3 + a^2 (b + 3 c) + a (5 b^2 - 4 b c + c^2)): : |
| 3744 | a (2 a^3 + a^2 b + 2 b^3 + b c^2 + c^3 - a (b^2 + b c - c^2)): : |
| 3745 | a (2 a^3 + 2 b^3 + 2 b^2 c + 3 b c^2 + c^3 + a^2 (3 b + 2 c) + a (b^2 + 5 b c + 3 c^2)): : |
| 3746 | a (a^3 + b^2 (b - c) - a^2 c - 2 a b (b + c)): : |
| 3748 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 + 7 b c + c^2)): : |
| 3749 | a (3 a^3 + 3 b^3 + a^2 (b - c) - b^2 c + b c^2 + c^3 + a (-3 b^2 - 2 b c + c^2)): : |
| 3750 | a (a^3 - a^2 (b + 2 c) + b (b^2 - 2 b c - c^2) - a (3 b^2 + 4 b c + c^2)): : |
| 3931 | a (a^2 (b + 2 c) + c (2 b^2 + b c + c^2) + a (3 b^2 + 3 b c + c^2)): : |
| 3953 | a (a b (2 b - 3 c) + a^2 c + c (b^2 + c^2)): : |
| 3976 | a (2 a b (b - 2 c) + a^2 c + c (b^2 + c^2)): : |
| 3999 | -(a (a^2 (b - 2 c) + c (-2 b^2 + b c - 3 c^2) + a (-5 b^2 + 9 b c + c^2))): : |
| 4003 | a (a^2 (b + 4 c) + a (7 b^2 - 3 b c + c^2) + c (4 b^2 + b c + 3 c^2)): : |
| 4038 | a (a^3 + a^2 (3 b + 2 c) + b (b^2 + 2 b c + 3 c^2) + a (b^2 + 8 b c + 3 c^2)): : |
| 4424 | a (a^2 c + a b (2 b + c) + c (b^2 + c^2)): : |
| 4689 | a (-2 a^3 - 2 b^3 + 4 b^2 c + b c^2 + c^3 + a^2 (b + 4 c) + a (7 b^2 + 3 b c + c^2)): : |
| 4694 | a (a b (2 b - 5 c) + a^2 c + c (b^2 + c^2)): : |
| 4860 | -(a (a^3 + b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 - 2 c^3 + a (-4 b^2 + 9 b c + 2 c^2))): : |
| 4883 | -(a (a^2 (3 b + 2 c) + c (2 b^2 + 3 b c - c^2) + a (b^2 + 11 b c + 3 c^2))): : |
| 5010 | a (2 a^3 + 2 b^2 (b - c) - 2 a^2 c + a b (-4 b + c)): : |
| 5045 | -(a (a^2 b + (b - c) c^2 + a (-b^2 + 7 b c + c^2))): : |
| 5048 | a (2 a^3 + 2 b^3 - 2 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 2 c) - a (b^2 - 7 b c + 3 c^2)): : |
| 5049 | a (a^2 b + (b - c) c^2 + a (-b^2 + 11 b c + c^2)): : |
| 5061 | a (a^6 + a^5 b - 2 a^4 b (b - 2 c) - a^3 c^2 (2 b + c) + a^2 c (-6 b^3 + 3 b^2 c + b c^2 - c^3) + b (b^5 - b^2 c^3 - b c^4 + c^5) + a (-b^5 + 4 b^4 c - 2 b^3 c^2 - b^2 c^3 + b c^4 + c^5)): : |
| 5078 | a (a^6 + a^5 b + b^6 - a^4 b (b - 3 c) + a^3 b c^2 - b^2 c^4 - a^2 (b^4 + 4 b^3 c + b^2 c^2 - 2 b c^3 + c^4) + a (-b^5 + b^4 c - b^3 c^2 + b c^4)): : |
| 5091 | a (a^5 - a^4 c + a^3 (-2 b^2 + b c + c^2) + a^2 (2 b^3 - b^2 c - 2 c^3) + b (b^4 - b^3 c + b^2 c^2 - 2 b c^3 + c^4) + a (-2 b^4 + 3 b^3 c - 2 b^2 c^2 + b c^3 + c^4)): : |
| 5119 | -(a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 - 2 b c + c^2))): : |
| 5122 | -(a (4 a^3 + 4 b^3 + a^2 (b - 4 c) - 4 b^2 c + b c^2 - c^3 + a (-9 b^2 + 7 b c + c^2))): : |
| 5126 | a (4 a^3 + 4 b^3 - 4 b^2 c - b c^2 + c^3 - a^2 (b + 4 c) - a (7 b^2 - 9 b c + c^2)): : |
| 5128 | -(a (3 a^3 + 3 a^2 (b - c) + a (-9 b^2 + 4 b c + 3 c^2) + 3 (b^3 - b^2 c + b c^2 - c^3))): : |
| 5131 | -(a (3 a^3 + 3 b^3 + a^2 (b - 3 c) - 3 b^2 c + b c^2 - c^3 + a (-7 b^2 + 5 b c + c^2))): : |
| 5137 | a (a^6 + a^5 b - 2 a^4 b (b - c) - a^3 c (b^2 + c^2) - a^2 c (b^3 + c^3) + b (b^5 - b^2 c^3 - b c^4 + c^5) + a (-b^5 + 2 b^4 c - 2 b^2 c^3 + 2 b c^4 + c^5)): : |
| 5143 | a (a^4 b^2 + a^5 (b + c) + b^3 c (b^2 - c^2) - a^2 b^2 (b^2 - b c + c^2) - a^3 (2 b^3 + b^2 c - 2 b c^2 + c^3) + a b (b^4 - 2 b^3 c + c^4)): : |
| 5172 | a (a^6 - 3 a^4 b (b - c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - 3 b c^2 + 2 c^3) + a^2 (b^4 - 4 b^3 c + 3 b^2 c^2 - c^4) + a b (-3 b^4 + 5 b^3 c - b^2 c^2 - 2 b c^3 + c^4)): : |
| 5173 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + 2 b c + c^2) - 2 a^3 c (2 b^2 + 2 b c + c^2) + 2 a^2 (b^4 - b^3 c - 2 b c^3) - a (b^5 - 4 b^4 c + 2 b^3 c^2 + 6 b^2 c^3 - 3 b c^4 - 2 c^5)): : |
| 5183 | -(a (2 a^3 + 2 b^3 + a^2 (3 b - 2 c) - 2 b^2 c + 3 b c^2 - 3 c^3 + a (-7 b^2 + b c + 3 c^2))): : |
| 5193 | a (a^6 - 3 a^4 b (b - 3 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - 3 b^2 c - 9 b c^2 + 2 c^3) + a^2 (b^4 - 13 b^3 c + 18 b^2 c^2 - 3 b c^3 - c^4) + a b (-3 b^4 + 11 b^3 c - 7 b^2 c^2 - 5 b c^3 + 4 c^4)): : |
| 5204 | -(a (3 a^3 + 3 b^2 (b - c) - 3 a^2 c + a b (-6 b + 5 c))): : |
| 5217 | -(a (3 a^3 + 3 b^2 (b - c) - 3 a^2 c + a b (-6 b + c))): : |
| 5221 | -(a (a^3 + b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 - 2 c^3 + a (-4 b^2 + 5 b c + 2 c^2))): : |
| 5228 | -(a (a^5 - a^4 c + a^3 (-3 b^2 + b c + c^2) + b (b - c)^2 (b^2 + b c + 2 c^2) + a^2 (3 b^3 - 4 b^2 c - 4 b c^2 - 3 c^3) + a (-2 b^4 + 5 b^3 c - 6 b^2 c^2 + b c^3 + 2 c^4))): : |
| 5255 | a (a^3 + a^2 b - a b^2 + b^3 + a c^2 + b c^2): : |
| 5264 | a (a^3 + a^2 b + b (b^2 + c^2) + a (-b^2 + b c + c^2)): : |
| 5266 | a (2 a^3 + a^2 b + 2 b^3 + b c^2 + c^3 + a (-b^2 + b c + c^2)): : |
| 5269 | a (3 a^3 + 3 b^3 + b^2 c + 3 b c^2 + c^3 + a^2 (3 b + c) + a (-b^2 + 4 b c + 3 c^2)): : |
| 5285 | -(a (a^6 + a^5 b + b^6 - b^2 c^4 + a^4 b (-b + c) + a^3 b c (-b + c) - a b^2 (b^3 + b^2 c + b c^2 + c^3) - a^2 (b^4 + 3 b^3 c - b c^3 + c^4))): : |
| 5329 | -(a (a^2 - b^2 + c^2) (a^4 + a^3 b + a^2 (2 b - c) c + a b (b^2 + c^2) - b^2 (b^2 + c^2))): : |
| 5337 | a (a^5 - a^2 b (b - 2 c) c + a^4 (2 b + c) + a^3 c (3 b + c) + a c (b^3 + 3 b c^2 + c^3) + b (b^4 + b^3 c + b^2 c^2 + c^4)): : |
| 5347 | -(a (a^6 + a^5 b + b^6 + 3 a^3 b c^2 - b^2 c^4 + a^4 b (-b + c) - a^2 (b^4 - b^2 c^2 - 2 b c^3 + c^4) + a (-b^5 - b^4 c + b^3 c^2 + b c^4))): : |
| 5348 | -(a (a^6 - a^5 c + a^4 b (-3 b + 2 c) + a^3 (2 b^3 - 3 b c^2) + a^2 (b^4 - 4 b^3 c + 3 b^2 c^2 - c^4) + a (-2 b^5 + 4 b^4 c - b^3 c^2 - 2 b^2 c^3 + c^5) + b (b^5 - b^4 c - b c^4 + c^5))): : |
| 5363 | -(a (a^6 + a^5 b + b^6 - a^4 b (b - 3 c) - b^2 c^4 + a^3 b c (b + 2 c) - a^2 (b^4 + 3 b^3 c - 2 b^2 c^2 - 3 b c^3 + c^4) + a b (-b^4 + b^3 c + b c^3 + c^4))): : |
| 5425 | a (a^3 + b^3 - b^2 c - 2 b c^2 + 2 c^3 - 2 a c (b + c) - a^2 (2 b + c)): : |
| 5482 | a (a^4 b (b - 3 c) + a^3 c^2 (5 b + c) + b c^3 (b^2 - c^2) + a^2 b (-b^3 + 6 b^2 c - 4 b c^2 + c^3) + a c (-5 b^4 + 3 b^3 c + b^2 c^2 - c^4)): : |
| 5535 | a (a^6 - 2 a^5 c + a^3 b (4 b^2 + b c - 5 c^2) + a^4 (-5 b^2 + 3 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 7 b^3 c + 6 b^2 c^2 + b c^3 - c^4) - a (4 b^5 - 7 b^4 c + b^3 c^2 + 3 b^2 c^3 + b c^4 - 2 c^5)): : |
| 5536 | a (a^6 - 2 a^5 c + a^3 b (4 b^2 - b c - 5 c^2) + a^4 (-5 b^2 + 3 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 5 b^3 c + 8 b^2 c^2 - b c^3 - c^4) + a (-4 b^5 + 7 b^4 c - b^3 c^2 - 5 b^2 c^3 + b c^4 + 2 c^5)): : |
| 5537 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 5 c) + a^3 (4 b^3 + 3 b^2 c - 5 b c^2 + 2 c^3) + a b (-3 b^4 + 7 b^3 c - 3 b^2 c^2 + b c^3 - 2 c^4) + a^2 (b^4 - 11 b^3 c + 4 b^2 c^2 + 3 b c^3 - c^4)): : |
| 5538 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 - 7 b c + c^2) + a^3 (4 b^3 - b^2 c - 5 b c^2 + 4 c^3) - a^2 (b^4 + 9 b^3 c - 8 b^2 c^2 + b c^3 + c^4) - a (2 b^5 - 7 b^4 c + 5 b^3 c^2 + b^2 c^3 - 3 b c^4 + 2 c^5)): : |
| 5563 | -(a (a^3 - 2 a b (b - 2 c) + b^2 (b - c) - a^2 c)): : |
| 5570 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (2 b + c) + a^4 (-2 b^2 + 2 b c + c^2) + 2 a^2 b^2 (b^2 - 3 b c + 4 c^2) - a (b - c)^2 (b^3 - 2 b^2 c - 3 b c^2 - 2 c^3)): : |
| 5584 | -(a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a^4 b (3 b + 2 c) + 2 a^3 (2 b^3 - b^2 c + b c^2 + c^3) + a^2 (b^4 + 8 b^3 c + 2 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 4 b^2 c^2 - 4 b c^3 + 3 c^4))): : |
| 5597 | a (a^3 - 2 a b^2 + b^3 - a^2 c - a b c - b^2 c + Sqrt[2] Sqrt[-(a b c (a + b + c) (a^2 + (b - c)^2 - 2 a (b + c)))]): : |
| 5598 | a (a^3 - 2 a b^2 + b^3 - a^2 c - a b c - b^2 c - Sqrt[2] Sqrt[-(a b c (a + b + c) (a^2 + (b - c)^2 - 2 a (b + c)))]): : |
| 5662 | a (a^6 (b^2 + b c + 2 c^2) + a^5 (2 b^3 - 2 b^2 c - 5 b c^2 - c^3) + a^4 (-4 b^4 - b^3 c + b^2 c^2 + 6 b c^3 - 2 c^4) + a (b - c)^2 c (3 b^4 - b^3 c - b^2 c^2 + c^4) - a^3 b (2 b^4 - 7 b^3 c + 2 b c^3 + c^4) + a^2 b^2 (3 b^4 - 8 b^3 c + 7 b^2 c^2 - 4 b c^3 + 2 c^4) + b c^2 (2 b^5 - b^4 c - 2 b^3 c^2 + c^5)): : |
| 5697 | -(a (a^2 b + (b - c) c^2 + a (-b^2 - 2 b c + c^2))): : |
| 5706 | a (a^6 + a^5 b - 3 a^4 b^2 - 2 a^3 c (b^2 + b c + c^2) + a^2 (b^4 - 2 b^2 c^2 - 2 b c^3 - c^4) + b (b^5 - 2 b^2 c^3 - b c^4 + 2 c^5) + a (-b^5 + 2 b^4 c - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 5707 | a (a^6 + a^5 b - 2 a^3 c (b + c)^2 + a^4 b (-3 b + 2 c) + a^2 (b^4 - 4 b^3 c - 2 b c^3 - c^4) + b (b^5 - 2 b^2 c^3 - b c^4 + 2 c^5) + a (-b^5 + 4 b^4 c - 2 b^3 c^2 - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 5708 | a (a^3 + b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 - 2 c^3 + a (-4 b^2 + 7 b c + 2 c^2)): : |
| 5709 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 2 b c + c^2) + 4 a^3 (b^3 - b c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 4 b^3 c + 6 b^2 c^2 - c^4) + a (-4 b^5 + 6 b^4 c - 4 b^2 c^3 + 2 c^5)): : |
| 5710 | a (a^3 + a^2 (2 b + c) + a c (b + 2 c) + b (b^2 + b c + 2 c^2)): : |
| 5711 | a (a^3 + a^2 (2 b + c) + a c (3 b + 2 c) + b (b^2 + b c + 2 c^2)): : |
| 5885 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^3 c (b^2 - 4 b c - 2 c^2) + a^4 (-2 b^2 + 2 b c + c^2) + a^2 b (2 b^3 - 7 b^2 c + 3 b c^2 + c^3) - a (b^5 - 4 b^4 c + 2 b^3 c^2 + b^2 c^3 + 2 b c^4 - 2 c^5)): : |
| 5902 | a (a^2 b + (b - c) c^2 + a (-b^2 + 2 b c + c^2)): : |
| 5903 | a (a^2 b + (b - c) c^2 + a (-b^2 + c^2)): : |
| 5908 | a (a^8 b + (b - c)^3 c^2 (b + c)^4 + a^7 (b^2 - 3 b c + c^2) + a^6 (-3 b^3 - 2 b^2 c + 8 b c^2 + c^3) - a^5 (3 b^4 - 15 b^3 c + 12 b^2 c^2 + 5 b c^3 + 3 c^4) + a^3 (b - c)^2 (3 b^4 + b^3 c + 16 b^2 c^2 + 9 b c^3 + 3 c^4) + a^4 (3 b^5 - 12 b^4 c - 3 b^3 c^2 + 19 b^2 c^3 - 4 b c^4 - 3 c^5) - a^2 (b - c)^2 (b^5 - 12 b^4 c - 3 b^3 c^2 + 3 b^2 c^3 - 2 b c^4 - 3 c^5) - a (b - c)^2 (b^6 + 9 b^5 c + 7 b^4 c^2 + 2 b^3 c^3 - b^2 c^4 - 3 b c^5 + c^6)): : |
| 5919 | -(a (a^2 b + (b - c) c^2 + a (-b^2 - 7 b c + c^2))): : |
| 6244 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 8 c) + 2 a^3 (2 b^3 + 2 b^2 c - 4 b c^2 + c^3) + a b (-3 b^4 + 10 b^3 c - 6 b^2 c^2 + 2 b c^3 - 3 c^4) + a^2 (b^4 - 18 b^3 c + 6 b^2 c^2 + 4 b c^3 - c^4)): : |
| 6282 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 - 10 b c + c^2) + 4 a^3 (b^3 - 2 b c^2 + c^3) - a^2 (b^4 + 16 b^3 c - 10 b^2 c^2 + c^4) - 2 a (b^5 - 5 b^4 c + 4 b^3 c^2 - b c^4 + c^5)): : |
| 6583 | -(a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + 2 b c + c^2) - a^3 c (b^2 + 4 b c + 2 c^2) + a^2 b (2 b^3 - 5 b^2 c + 5 b c^2 - c^3) - a (b^5 - 4 b^4 c + 2 b^3 c^2 + 3 b^2 c^3 - 2 c^5))): : |
| 6766 | -(a (a^6 - 2 a^5 c + 4 a^3 b (b^2 - 3 b c - c^2) + a^4 (-5 b^2 + 2 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 + 8 b^3 c + 18 b^2 c^2 - 12 b c^3 - c^4) + 2 a (-2 b^5 + 3 b^4 c - 8 b^2 c^3 + 6 b c^4 + c^5))): : |
| 6767 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + 7 c)): : |
| 6769 | a (-a^6 + 2 a^5 (b + c) - (b - c)^4 (b + c)^2 + a^4 (b^2 - 6 b c + c^2) - 4 a^3 (b^3 + b^2 c - b c^2 + c^3) + a^2 (b^4 + 12 b^3 c - 2 b^2 c^2 - 4 b c^3 + c^4) + 2 a (b^5 - 3 b^4 c + 2 b^3 c^2 - 2 b^2 c^3 + b c^4 + c^5)): : |
| 7011 | -(a (a^9 + b^2 (b - c)^3 (b + c)^4 + a^8 (2 b + c) + a^7 (-3 b^2 + b c - 3 c^2) - a^6 (7 b^3 + 2 b^2 c - 4 b c^2 + 3 c^3) - a b (b - c)^2 c (3 b^4 - 6 b^2 c^2 - 8 b c^3 - 5 c^4) + a^5 (3 b^4 + 3 b^3 c - 5 b c^3 + 3 c^4) - a^2 (b - c)^2 (5 b^5 + 4 b^4 c + 5 b^3 c^2 + 7 b^2 c^3 + 2 b c^4 + c^5) + a^4 (9 b^5 - 6 b^4 c + b^3 c^2 + 7 b^2 c^3 - 6 b c^4 + 3 c^5) - a^3 (b^6 + b^5 c + 3 b^4 c^2 - 2 b^3 c^3 - 5 b^2 c^4 + b c^5 + c^6))): : |
| 7070 | a (3 a^6 + 4 a^3 b^3 - 2 a^5 c - a^4 (7 b^2 + 2 b c + c^2) + a^2 (b^4 + 4 b^3 c + 6 b^2 c^2 - 3 c^4) + (b - c)^2 (3 b^4 + 4 b^3 c + 4 b^2 c^2 + 4 b c^3 + c^4) + 2 a (-2 b^5 + b^4 c + 2 b^3 c^2 - 2 b^2 c^3 + c^5)): : |
| 7146 | a (a^4 c - 2 a^3 c (b + c) - 2 a^2 b (b^2 + c^2) + 2 a (b^4 - b^3 c - b c^3) + c (b^4 - 2 b^3 c + c^4)): : |
| 7280 | -(a (2 a^3 + 2 b^2 (b - c) - 2 a^2 c + a b (-4 b + 3 c))): : |
| 7373 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + 9 c)): : |
| 7688 | -(a (a^6 + b^2 (b - c)^3 (b + c) - a^4 b (3 b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - b^2 c + b c^2 + 2 c^3) + a^2 (b^4 + 5 b^3 c + 2 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + b^3 c + 3 b^2 c^2 - 3 b c^3 + 2 c^4))): : |
| 7742 | -(a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + c^3) + a^2 (b^4 + 2 b^3 c - 2 b^2 c^2 - c^4) + a b (-3 b^4 + 2 b^3 c + 2 b^2 c^2 - 2 b c^3 + c^4))): : |
| 7957 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - 4 b c + c^2) - 2 a^3 c (b^2 - b c + c^2) + 2 a^2 (b^4 + 4 b^3 c - b c^3) + a (-b^5 - 2 b^4 c + 4 b^3 c^2 - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 7962 | -(a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 + 8 b c - 3 c^2))): : |
| 7964 | a (2 a^6 - a^5 (b + 4 c) + a^4 (-8 b^2 - 4 b c + c^2) + 2 a^3 (4 b^3 - b^2 c + b c^2 + c^3) + (b - c)^3 (2 b^3 + 2 b^2 c + b c^2 + c^3) + 2 a^2 (2 b^4 + 6 b^3 c + 2 b^2 c^2 - b c^3 - c^4) + a (-7 b^5 + 2 b^4 c + 8 b^3 c^2 - 8 b^2 c^3 + 3 b c^4 + 2 c^5)): : |
| 7982 | -(a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 + 4 b c - 3 c^2))): : |
| 7987 | -(a (5 a^3 + 5 b^3 - 5 b^2 c - b c^2 + c^3 - a (-3 b + c)^2 - a^2 (b + 5 c))): : |
| 7991 | -(a (a^3 + b^3 + a^2 (3 b - c) - b^2 c + 3 b c^2 - 3 c^3 + a (-5 b^2 - 2 b c + 3 c^2))): : |
| 7994 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 - 10 b c + c^2) + 4 a^3 (b^3 + 2 b^2 c - 2 b c^2 + c^3) - a^2 (b^4 + 24 b^3 c - 2 b^2 c^2 - 8 b c^3 + c^4) - 2 a (b^5 - 5 b^4 c + 4 b^3 c^2 - 4 b^2 c^3 + 3 b c^4 + c^5)): : |
| 8069 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) - a b (b - c)^2 (3 b^2 - c^2) + 2 a^3 (2 b^3 - 2 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 2 b^2 c^2 - c^4)): : |
| 8071 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) - a b (b - c)^2 (3 b^2 - c^2) + 2 a^3 (2 b^3 - 2 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 10 b^2 c^2 - c^4)): : |
| 8148 | a (a^3 + b^3 - b^2 c - 4 b c^2 + 4 c^3 - a^2 (4 b + c) + a (2 b^2 + 5 b c - 4 c^2)): : |
| 8158 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 - 4 b^2 c - 2 b c^2 + c^3) + a^2 (b^4 + 2 b^3 c + 14 b^2 c^2 - 8 b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 10 b c^3 + 9 c^4)): : |
| 8162 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + 13 c)): : |
| 8163 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 10 c) + 2 a^3 (2 b^3 - 7 b^2 c - 5 b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 42 b^2 c^2 - 14 b c^3 - c^4) + a b (-3 b^4 + 12 b^3 c - 8 b^2 c^2 - 16 b c^3 + 15 c^4)): : |
| 8171 | a (3 a^6 + 3 b^2 (b - c)^3 (b + c) - 3 a^5 (b + 2 c) + a^4 b (-9 b + 4 c) + 2 a^3 (6 b^3 - 2 b c^2 + 3 c^3) + a^2 (3 b^4 - 2 b^3 c - 22 b^2 c^2 - 3 c^4) + a b (-9 b^4 + 10 b^3 c + 2 b^2 c^2 - 6 b c^3 + 3 c^4)): : |
| 8186 | a (2 a^3 - 4 a b^2 + 2 b^3 - 2 a^2 c - 2 a b c - 2 b^2 c + Sqrt[2] Sqrt[-(a b c (a + b + c) (a^2 + (b - c)^2 - 2 a (b + c)))]): : |
| 8187 | a (2 a^3 - 4 a b^2 + 2 b^3 - 2 a^2 c - 2 a b c - 2 b^2 c - Sqrt[2] Sqrt[-(a b c (a + b + c) (a^2 + (b - c)^2 - 2 a (b + c)))]): : |
| 8193 | a (a^6 + a^5 b - a^4 b^2 + b^6 - b^2 c^4 + 2 a^3 b c (-b + c) - a b (b^4 + 2 b^3 c + 2 b c^3 - c^4) - a^2 (b^4 + c^4)): : |
| 8251 | a (a^9 + a^8 (b - c) + 2 a^7 b (-2 b + c) - 2 a^6 b c (b + 2 c) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3)^2 + 2 a^5 (b^4 - 3 b^3 c + 2 b^2 c^2 - c^4) + 2 a^2 b^2 c (-3 b^4 + 2 b^3 c + 2 b^2 c^2 - 2 b c^3 + c^4) + 2 a^3 b (2 b^5 + b^4 c - 2 b^3 c^2 + 2 b^2 c^3 + 2 b c^4 - c^5) + 2 a^4 (-b^5 + 5 b^4 c + b c^4 + c^5) + a (-3 b^8 + 2 b^7 c + 6 b^4 c^4 - 2 b^3 c^5 - 4 b^2 c^6 + c^8)): : |
| 8270 | a (a^6 - a^4 (b - c)^2 + 2 a^3 b (b - c) c + (b^2 - c^2)^2 (b^2 + c^2) + 2 a b c (b^3 - b^2 c + b c^2 - c^3) - a^2 (b^4 + 6 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4)): : |
| 8273 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - 3 a^4 b (b + 2 c) + 2 a^3 (2 b^3 + b^2 c + 3 b c^2 + c^3) + a^2 (b^4 + 12 b^3 c - 6 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 + 4 b^3 c - 8 b^2 c^2 + c^4)): : |
| 8726 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 + 6 b c + c^2) + 4 a^3 (b^3 + 2 b c^2 + c^3) - a^2 (b^4 - 16 b^3 c + 6 b^2 c^2 + c^4) - 2 a (b^5 + 3 b^4 c - 4 b^3 c^2 - b c^4 + c^5)): : |
| 8758 | a (a^5 (b + 2 c) + a^4 (2 b^2 - 2 b c - c^2) + 2 a^2 b^2 (-b^2 + b c + c^2) - 2 a^3 (2 b^3 - b c^2 + c^3) + a b (3 b^4 - 4 b^3 c + 2 b c^3 - c^4) + c (2 b^5 - b^4 c - 2 b^3 c^2 + c^5)): : |
| 8924 | -(a (a^5 (b^2 - b c + c^2) + a^4 (b^3 - b^2 c + b c^2 - c^3) + b^2 c^2 (b^3 - b^2 c + b c^2 - c^3) - a b c (b^4 + 3 b^3 c - 2 b^2 c^2 - b c^3 + c^4) + a^3 (-3 b^4 + 2 b^3 c - b^2 c^2 + 2 b c^3 + c^4) + a^2 (b^5 - b^4 c + 3 b^3 c^2 - 3 b^2 c^3 + b c^4 - c^5))): : |
| 9120 | a (a^12 + 8 a^9 b (b - c) c + a^10 (-6 b^2 + 8 b c - 6 c^2) + (b^2 - c^2)^6 + 8 a b (b - c)^3 c (b^3 + b^2 c + b c^2 + c^3)^2 + a^8 (15 b^4 - 32 b^3 c + 18 b^2 c^2 + 15 c^4) + a^4 (b^2 - c^2)^2 (15 b^4 + 32 b^3 c + 18 b^2 c^2 + 15 c^4) - 16 a^5 b c (b^5 - b^4 c + b c^4 - c^5) - 2 a^2 (b^2 - c^2)^2 (3 b^6 + 12 b^5 c - 3 b^4 c^2 + 8 b^3 c^3 - 3 b^2 c^4 - 4 b c^5 + 3 c^6) - 4 a^6 (5 b^6 - 4 b^5 c + 3 b^4 c^2 - 8 b^3 c^3 + 3 b^2 c^4 + 4 b c^5 + 5 c^6)): : |
| 9364 | a (a^6 - a^5 c + a^4 b (-3 b + 5 c) + 2 a^3 b (b^2 + b c - 3 c^2) + a^2 (b^4 - 12 b^3 c + 10 b^2 c^2 + 2 b c^3 - c^4) + a (-2 b^5 + 7 b^4 c - 4 b^3 c^2 - 2 b c^4 + c^5) + b (b^5 - b^4 c - b c^4 + c^5)): : |
| 9371 | a (a^5 (b + 2 c) + a^4 (2 b^2 - 6 b c - c^2) - 2 a^3 (2 b^3 + b^2 c - 3 b c^2 + c^3) - 2 a^2 b (b^3 - 6 b^2 c + 2 b c^2 + c^3) + a b (3 b^4 - 8 b^3 c + 4 b^2 c^2 + c^4) + c (2 b^5 - b^4 c - 2 b^3 c^2 + c^5)): : |
| 9441 | a (a^5 - a^4 (b + 2 c) - 2 a^3 (b^2 - c^2) + b (b - c)^2 (b^2 + c^2) + a^2 (4 b^3 - 2 c^3) + a (-3 b^4 + 4 b^3 c - 2 b^2 c^2 + c^4)): : |
| 9627 | a (a^6 + a^3 b c^2 + a b^3 c (-b + c) + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 + b c + c^2) - a^2 (b^4 - 2 b^3 c - 3 b^2 c^2 + c^4)): : |
| 9630 | a (a^6 + a^3 b c^2 + a b^3 c (-b + c) + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 + b c + c^2) - a^2 (b^4 - 2 b^3 c + b^2 c^2 + c^4)): : |
| 9659 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 - c^4) + a^4 (-b^5 + 2 b^4 c - b^3 c^2 + b^2 c^3 + c^5) + a^3 (3 b^6 - b^5 c - b^4 c^2 + 4 b^3 c^3 + b^2 c^4 - b c^5 + c^6) - a^2 (b^7 - b^4 c^3 + b^3 c^4 - 2 b^2 c^5 + c^7)): : |
| 9672 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 - c^4) + a^4 (-b^5 + 2 b^4 c - b^3 c^2 + b^2 c^3 + c^5) + a^3 (3 b^6 - b^5 c - b^4 c^2 - 4 b^3 c^3 + b^2 c^4 - b c^5 + c^6) - a^2 (b^7 - b^4 c^3 + b^3 c^4 - 2 b^2 c^5 + c^7)): : |
| 9819 | a (a^3 + b^3 + a^2 (3 b - c) - b^2 c + 3 b c^2 - 3 c^3 + a (-5 b^2 - 10 b c + 3 c^2)): : |
| 9940 | -(a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (4 b + c) + a^4 (-2 b^2 + 6 b c + c^2) + 2 a^2 b^2 (b^2 - 7 b c + 4 c^2) - a (b^5 - 8 b^4 c + 6 b^3 c^2 + 2 b^2 c^3 + b c^4 - 2 c^5))): : |
| 9957 | a (a^2 b + (b - c) c^2 + a (-b^2 - 5 b c + c^2)): : |
| 10202 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (3 b + c) + a^4 (-2 b^2 + 4 b c + c^2) + 2 a^2 b^2 (b^2 - 5 b c + 3 c^2) - a (b^5 - 6 b^4 c + 4 b^3 c^2 + 2 b^2 c^3 + b c^4 - 2 c^5)): : |
| 10222 | a (2 a^3 + 2 b^3 - 2 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 2 c) - a (b^2 - 5 b c + 3 c^2)): : |
| 10225 | a (2 a^6 - a^5 (b + 4 c) + a^4 (-8 b^2 + 8 b c + c^2) + (b - c)^3 (2 b^3 + 2 b^2 c + b c^2 + c^3) + a^3 (8 b^3 + 3 b^2 c - 10 b c^2 + 2 c^3) + a^2 (4 b^4 - 17 b^3 c + 11 b^2 c^2 + 3 b c^3 - 2 c^4) - a (7 b^5 - 14 b^4 c + 4 b^3 c^2 + 3 b^2 c^3 + 2 b c^4 - 2 c^5)): : |
| 10246 | a (3 a^3 + 3 b^3 - 3 b^2 c - 2 b c^2 + 2 c^3 - a^2 (2 b + 3 c) + a (-4 b^2 + 5 b c - 2 c^2)): : |
| 10247 | a (3 a^3 + 3 b^3 - 3 b^2 c - 4 b c^2 + 4 c^3 - a^2 (4 b + 3 c) + a (-2 b^2 + 7 b c - 4 c^2)): : |
| 10267 | a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c + c^3) + a^2 (b^4 + 2 b c^3 - c^4) + a (-3 b^5 + 2 b^4 c + 2 b^3 c^2 - b c^4)): : |
| 10268 | a (3 a^6 - 2 a^5 (b + 3 c) + a^4 (-11 b^2 + 2 b c + c^2) + 4 a^3 (3 b^3 + b^2 c - b c^2 + c^3) + (b - c)^3 (3 b^3 + 3 b^2 c + b c^2 + c^3) + a^2 (5 b^4 - 4 b^3 c + 6 b^2 c^2 + 4 b c^3 - 3 c^4) - 2 a (5 b^5 - 5 b^4 c - 2 b^3 c^2 + 2 b^2 c^3 + b c^4 - c^5)): : |
| 10269 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 8 c) + 2 a^3 (2 b^3 - b^2 c - 4 b c^2 + c^3) + a^2 (b^4 - 12 b^3 c + 12 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 10 b^3 c - 6 b^2 c^2 - 4 b c^3 + 3 c^4)): : |
| 10270 | a (3 a^6 - 2 a^5 (b + 3 c) + a^4 (-11 b^2 + 18 b c + c^2) + 4 a^3 (3 b^3 + b^2 c - 5 b c^2 + c^3) + (b - c)^3 (3 b^3 + 3 b^2 c + b c^2 + c^3) + a^2 (5 b^4 - 36 b^3 c + 22 b^2 c^2 + 4 b c^3 - 3 c^4) - 2 a (5 b^5 - 13 b^4 c + 6 b^3 c^2 + 2 b^2 c^3 + b c^4 - c^5)): : |
| 10273 | a (3 a^5 b + 3 (b - c)^3 c^2 (b + c) + a^4 (-6 b^2 + 3 c^2) - 2 a^3 c (-4 b^2 + 3 b c + 3 c^2) + 2 a^2 b (3 b^3 - 7 b^2 c - b c^2 + 4 c^3) + a (-3 b^5 + 6 b^4 c + 2 b^2 c^3 - 11 b c^4 + 6 c^5)): : |
| 10284 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^3 c (7 b^2 + 2 b c - 2 c^2) + a^4 (-2 b^2 - 4 b c + c^2) + a^2 b (2 b^3 - b^2 c - 9 b c^2 + 7 c^3) - a (b^5 + 2 b^4 c - 4 b^3 c^2 - 5 b^2 c^3 + 8 b c^4 - 2 c^5)): : |
| 10306 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 + 2 b^2 c - 2 b c^2 + c^3) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 + 2 b c^3 - 3 c^4) + a^2 (b^4 - 10 b^3 c + 2 b^2 c^2 + 4 b c^3 - c^4)): : |
| 10310 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 12 b^3 c + 6 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 8 b^3 c + 4 b^2 c^2 + c^4)): : |
| 10319 | a (a^6 + 2 a^5 b - 4 a^3 b^2 c + (b^2 - c^2) (b^2 + c^2)^2 + a^4 (-b^2 + 4 b c + c^2) - 2 a b (b^4 + 2 b^2 c^2 + 2 b c^3 - c^4) - a^2 (b^4 + 8 b^3 c + 6 b^2 c^2 + c^4)): : |
| 10383 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 + 10 b c + c^2) + 4 a^3 (b^3 + b^2 c + 3 b c^2 + c^3) - a^2 (b^4 - 20 b^3 c - 2 b^2 c^2 - 4 b c^3 + c^4) - 2 a (b^5 + 5 b^4 c - 6 b^3 c^2 - 2 b^2 c^3 + b c^4 + c^5)): : |
| 10388 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 - 6 b c + c^2) + 4 a^3 (b^3 + b^2 c - b c^2 + c^3) - a^2 (b^4 + 12 b^3 c + 14 b^2 c^2 - 4 b c^3 + c^4) - 2 a (b^5 - 3 b^4 c + 2 b^3 c^2 - 2 b^2 c^3 + b c^4 + c^5)): : |
| 10389 | a (3 a^3 + 3 b^3 - 3 b^2 c - b c^2 + c^3 - a^2 (b + 3 c) - a (5 b^2 + 8 b c + c^2)): : |
| 10434 | a (2 a^5 (b + c) + a^4 b (2 b + c) + 2 b^3 c (b^2 - c^2) + a^3 (-4 b^3 - 3 b^2 c + b c^2 - 2 c^3) - a^2 b (2 b^3 + 3 b^2 c + 4 b c^2 + c^3) + a b (2 b^4 - 3 b^3 c - 3 b^2 c^2 - b c^3 + c^4)): : |
| 10439 | a (a^4 b (2 b - c) + 2 b c^3 (b^2 - c^2) + a^3 c (b^2 + 5 b c + 2 c^2) + a^2 b (-2 b^3 + b^2 c - 4 b c^2 + 3 c^3) + a c (-5 b^4 + b^3 c + 3 b^2 c^2 - b c^3 - 2 c^4)): : |
| 10441 | a (a^4 b^2 + a^3 c^2 (2 b + c) + b c^3 (b^2 - c^2) - a^2 b (b^3 + b c^2 - c^3) - a (2 b^4 c - b^2 c^3 + c^5)): : |
| 10470 | a (2 a^4 b^2 + 3 a^5 (b + c) + a^3 (-6 b^3 - 3 b^2 c + b c^2 - 4 c^3) - a^2 b (2 b^3 + 3 b^2 c + 8 b c^2 + c^3) + b c (3 b^4 - 4 b^2 c^2 + c^4) + a (3 b^5 - 4 b^4 c - 3 b^3 c^2 - b^2 c^3 + c^5)): : |
| 10473 | a (a^4 b^2 + b c^3 (b^2 - c^2) + a^3 c (2 b^2 + 4 b c + c^2) + a^2 b (-b^3 + 2 b^2 c + b c^2 + 3 c^3) - a c (2 b^4 - 2 b^3 c - 3 b^2 c^2 + c^4)): : |
| 10474 | a (a^5 (b + c) - a^4 b (b + c) + a^2 b (b^3 - 2 b^2 c - 5 b c^2 - 3 c^3) - a^3 (2 b^3 + 2 b^2 c + 4 b c^2 + 3 c^3) + b c (b^4 - 3 b^2 c^2 + 2 c^4) + a (b^5 + b^4 c - 2 b^3 c^2 - 3 b^2 c^3 - b c^4 + 2 c^5)): : |
| 10475 | a (a^4 b (b - c) + a^5 (b + c) + b^3 c (b^2 - c^2) - a^2 b (b^3 - 2 b^2 c + 3 b c^2 - 3 c^3) - a^3 (2 b^3 - 2 b^2 c - 4 b c^2 + c^3) + a b (b^4 - 3 b^3 c + 2 b^2 c^2 + 3 b c^3 - c^4)): : |
| 10476 | a (a^4 b (2 b - c) + a^5 (b + c) - 2 a^3 (b^3 - 2 b c^2) - 2 a^2 b (b^3 + 3 b c^2 - c^3) + b c (b^4 - c^4) + a (b^5 - 5 b^4 c + 2 b^2 c^3 - b c^4 - c^5)): : |
| 10480 | a (a^4 b^2 + b c^3 (b^2 - c^2) + a^3 (-2 b^2 c + c^3) - a^2 b (b^3 + 2 b^2 c + 3 b c^2 + c^3) - a c (2 b^4 + 2 b^3 c + b^2 c^2 + c^4)): : |
| 10508 | -(a (-(a Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)]) - b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - c Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + (a^2 b + (b - c) c^2 + a (-b^2 - 7 b c + c^2)) Cos[A/2] + (a^2 b + (b - c) c^2 + a (-b^2 - 7 b c + c^2)) Cos[B/2] + a^2 b Cos[C/2] - a b^2 Cos[C/2] - 7 a b c Cos[C/2] + a c^2 Cos[C/2] + b c^2 Cos[C/2] - c^3 Cos[C/2])): : |
| 10618 | a (a^5 (7 b + 8 c) + a^4 (2 b^2 + 2 b c - c^2) + (b - c)^2 c (8 b^3 + 15 b^2 c + 8 b c^2 + c^3) - a^2 b (2 b^3 + 9 b^2 c + 15 b c^2 + 9 c^3) - a^3 (16 b^3 + 9 b^2 c + 8 b c^2 + 14 c^3) + a (9 b^5 - 10 b^3 c^2 - 7 b^2 c^3 + 2 b c^4 + 6 c^5)): : |
| 10679 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + 2 b^2 c - b c^2 + c^3) + a b (-3 b^4 + 4 b^3 c + 2 b c^3 - 3 c^4) + a^2 (b^4 - 6 b^3 c + 4 b c^3 - c^4)): : |
| 10680 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - 2 b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 12 b^2 c^2 - 4 b c^3 - c^4) + a b (-3 b^4 + 8 b^3 c - 4 b^2 c^2 - 6 b c^3 + 5 c^4)): : |
| 10831 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c - b c^3 - c^4) + a^4 (-b^5 + 2 b^4 c - b^3 c^2 + 3 b^2 c^3 + c^5) + a^3 (3 b^6 - b^5 c + 3 b^4 c^2 + 6 b^3 c^3 + b^2 c^4 - b c^5 + c^6) - a^2 (b^7 + 2 b^5 c^2 - 3 b^4 c^3 + b^3 c^4 - 2 b^2 c^5 + c^7)): : |
| 10832 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c - b c^3 - c^4) + a^4 (-b^5 + 2 b^4 c - b^3 c^2 + 3 b^2 c^3 + c^5) + a^3 (3 b^6 - b^5 c + 3 b^4 c^2 - 10 b^3 c^3 + b^2 c^4 - b c^5 + c^6) - a^2 (b^7 + 2 b^5 c^2 - 3 b^4 c^3 + b^3 c^4 - 2 b^2 c^5 + c^7)): : |
| 10856 | a (a^6 + b^6 + 6 b^5 c - b^4 c^2 - 4 b^3 c^3 - b^2 c^4 - 2 b c^5 + c^6 + 6 a^5 (b + c) + a^4 (7 b^2 + 2 b c - c^2) - 4 a^3 (3 b^3 + 2 b^2 c - 2 b c^2 + c^3) - a^2 (9 b^4 + 8 b^3 c + 22 b^2 c^2 + c^4) + 2 a (3 b^5 - 7 b^4 c - 4 b^3 c^2 + b c^4 - c^5)): : |
| 10857 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 + 14 b c + c^2) + 4 a^3 (b^3 + 4 b c^2 + c^3) - a^2 (b^4 - 32 b^3 c + 14 b^2 c^2 + c^4) - 2 a (b^5 + 7 b^4 c - 8 b^3 c^2 - b c^4 + c^5)): : |
| 10882 | a (a^4 b (2 b - c) + 2 a^5 (b + c) + 2 b^3 c (b^2 - c^2) - a^2 b (2 b^3 + b^2 c + 8 b c^2 - c^3) - a^3 (4 b^3 + b^2 c - 3 b c^2 + 2 c^3) + a b (2 b^4 - 5 b^3 c - b^2 c^2 + b c^3 - c^4)): : |
| 10902 | a (a^6 + a^4 b (-3 b + c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a b^2 (-3 b^3 + 3 b^2 c + b c^2 - c^3) + a^3 (4 b^3 + b^2 c - b c^2 + 2 c^3) + a^2 (b^4 - b^3 c + 2 b^2 c^2 + b c^3 - c^4)): : |
| 10965 | a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + 3 b^2 c + c^3) + a b (-3 b^4 + 2 b^3 c + 2 b^2 c^2 + 4 b c^3 - 5 c^4) + a^2 (b^4 - 4 b^3 c - 8 b^2 c^2 + 6 b c^3 - c^4)): : |
| 10966 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 - b^2 c - 2 b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 12 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 4 b c^3 + 3 c^4)): : |
| 10980 | a (a^3 + b^3 + a^2 (3 b - c) - b^2 c + 3 b c^2 - 3 c^3 + a (-5 b^2 + 14 b c + 3 c^2)): : |
| 11009 | a (a^3 + b^3 - b^2 c + 2 a (b - c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c)): : |
| 11010 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 - b c + c^2)): : |
| 11011 | a (2 a^3 + 2 b^3 - 2 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 2 c) - a (b^2 - 3 b c + 3 c^2)): : |
| 11012 | a (a^6 - 3 a^4 b (b - c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - b^2 c - 3 b c^2 + 2 c^3) - a b (3 b^4 - 5 b^3 c + b^2 c^2 + 3 b c^3 - 2 c^4) + a^2 (b^4 - 3 b^3 c + 6 b^2 c^2 - b c^3 - c^4)): : |
| 11014 | a (a^6 - 2 a^5 (b + c) + (b - c)^4 (b + c)^2 - a^4 (b^2 - 5 b c + c^2) + a^3 (4 b^3 - 5 b^2 c - 3 b c^2 + 4 c^3) - a^2 (b^4 + b^3 c - 10 b^2 c^2 + 5 b c^3 + c^4) - a (2 b^5 - 5 b^4 c + 3 b^3 c^2 + 5 b^2 c^3 - 7 b c^4 + 2 c^5)): : |
| 11018 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (2 b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) - a (b - c)^2 (b^3 - 6 b^2 c - 7 b c^2 - 2 c^3) + 2 a^2 b (b^3 - 5 b^2 c - 2 b c^2 - 2 c^3)): : |
| 11021 | a (a^4 b (2 b + c) + 2 b c^3 (b^2 - c^2) + a^3 c (7 b^2 + 11 b c + 2 c^2) + a^2 b (-2 b^3 + 7 b^2 c + 8 b c^2 + 9 c^3) + a c (-3 b^4 + 7 b^3 c + 9 b^2 c^2 + b c^3 - 2 c^4)): : |
| 11224 | a (3 a^3 + 3 b^3 - 3 b^2 c - 7 b c^2 + 7 c^3 - a^2 (7 b + 3 c) + a (b^2 + 10 b c - 7 c^2)): : |
| 11227 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (6 b + c) + a^4 (-2 b^2 + 10 b c + c^2) + 2 a^2 b^2 (b^2 - 11 b c + 6 c^2) - a (b^5 - 12 b^4 c + 10 b^3 c^2 + 2 b^2 c^3 + b c^4 - 2 c^5)): : |
| 11248 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 + b^2 c - 2 b c^2 + c^3) + a^2 (b^4 - 8 b^3 c + 4 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 6 b^3 c + 2 b^2 c^2 + c^4)): : |
| 11249 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 - b^2 c - 2 b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 8 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 4 b c^3 + 3 c^4)): : |
| 11278 | a (2 a^3 + 2 b^3 - 2 b^2 c - 5 b c^2 + 5 c^3 - a^2 (5 b + 2 c) + a (b^2 + 7 b c - 5 c^2)): : |
| 11280 | a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 + 3 b c - 3 c^2)): : |
| 11366 | -(a (a^3 + b^3 - a^2 c - b^2 c - a b (2 b + c) + 2 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11367 | -(a (a^3 + b^3 - a^2 c - b^2 c - a b (2 b + c) - 2 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11407 | a (a^6 + 2 a^5 (b - c) + a^4 (-9 b^2 + 26 b c + 3 c^2) + 4 a^3 (b^3 - 8 b c^2 - c^3) + (b - c)^3 (b^3 + b^2 c + 3 b c^2 + 3 c^3) + a^2 (7 b^4 - 56 b^3 c + 34 b^2 c^2 - c^4) - 2 a (3 b^5 - 17 b^4 c + 12 b^3 c^2 + 4 b^2 c^3 + b c^4 - 3 c^5)): : |
| 11507 | -(a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 6 b^2 c^2 + 2 b c^3 - c^4) - a (3 b^5 - 4 b^4 c + b c^4))): : |
| 11508 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - b c^2 + c^3) + a^2 (b^4 - 4 b^3 c - 2 b^2 c^2 + 2 b c^3 - c^4) - a (3 b^5 - 4 b^4 c + b c^4)): : |
| 11509 | -(a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 + b^2 c - 2 b c^2 + c^3) + a^2 (b^4 - 8 b^3 c + 8 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 6 b^3 c + 2 b^2 c^2 + c^4))): : |
| 11510 | a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c + c^3) + a^2 (b^4 - 4 b^2 c^2 + 2 b c^3 - c^4) + a (-3 b^5 + 2 b^4 c + 2 b^3 c^2 - b c^4)): : |
| 11518 | a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 - 8 b c - 3 c^2)): : |
| 11521 | a (a^5 (b + c) - 2 a^4 b (b + c) + a^3 (-2 b^3 + b^2 c - 3 b c^2 - 4 c^3) + a^2 b (2 b^3 + b^2 c - 4 b c^2 - c^3) + b c (b^4 - 4 b^2 c^2 + 3 c^4) + a (b^5 + 2 b^4 c + b^3 c^2 - b^2 c^3 - 2 b c^4 + 3 c^5)): : |
| 11529 | -(a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 - 4 b c - 3 c^2))): : |
| 11531 | -(a (a^3 + b^3 - b^2 c - 5 b c^2 + 5 c^3 - a^2 (5 b + c) + a (3 b^2 + 6 b c - 5 c^2))): : |
| 11567 | a (2 a^6 - 4 a^5 (b + c) + 2 (b - c)^4 (b + c)^2 - 2 a^4 (b^2 - 6 b c + c^2) + a^3 (8 b^3 - 7 b^2 c - 8 b c^2 + 8 c^3) - a^2 (2 b^4 + 9 b^3 c - 19 b^2 c^2 + 7 b c^3 + 2 c^4) - a (4 b^5 - 12 b^4 c + 8 b^3 c^2 + 7 b^2 c^3 - 11 b c^4 + 4 c^5)): : |
| 11575 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (-2 b^2 + 8 b c + c^2) + a^4 (-2 b^2 + 14 b c + c^2) + 2 a^2 b (b^3 - 17 b^2 c + 14 b c^2 + 2 c^3) - a (b^5 - 16 b^4 c + 14 b^3 c^2 - 2 b^2 c^3 + 5 b c^4 - 2 c^5)): : |
| 11849 | a (a^6 - 3 a^4 b (b - c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 + 2 b^2 c - 3 b c^2 + 2 c^3) + a^2 (b^4 - 6 b^3 c + 3 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 5 b^3 c + b^2 c^2 + c^4)): : |
| 11877 | -(a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (4 b^3 + 2 b^2 c - 2 b c^2 + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-b^4 + 4 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (3 b^5 - 4 b^4 c + b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))): : |
| 11878 | a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-4 b^3 - 2 b^2 c + 2 b c^2 - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (b^4 - 4 b^3 c + 2 b^2 c^2 + 2 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (-3 b^5 + 4 b^4 c - b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11879 | -(a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (4 b^3 + 2 b^2 c - 2 b c^2 + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-b^4 + 4 b^3 c - 2 b^2 c^2 - 2 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (3 b^5 - 4 b^4 c + b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - 4 Sqrt[2] b c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))): : |
| 11880 | a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-4 b^3 - 2 b^2 c + 2 b c^2 - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (b^4 - 4 b^3 c + 2 b^2 c^2 + 2 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (-3 b^5 + 4 b^4 c + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - b (c^4 + 4 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))): : |
| 11881 | a (a^6 - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + (b - c)^2 (b + c) (b^3 - b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (4 b^3 + 2 b^2 c - 4 b c^2 + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-b^4 + 8 b^3 c - 2 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (3 b^5 - 6 b^4 c + 2 b^3 c^2 + b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11882 | a (a^6 - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + (b - c)^2 (b + c) (b^3 - b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-4 b^3 - 2 b^2 c + 4 b c^2 - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (b^4 - 8 b^3 c + 2 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (-3 b^5 + 6 b^4 c - 2 b^3 c^2 - b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11883 | a (a^6 - 3 a^4 b^2 - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (4 b^3 + 2 b^2 c + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-b^4 - 4 b^2 c^2 - 2 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (3 b^5 - 2 b^4 c - 2 b^3 c^2 + b c^4 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - 4 Sqrt[2] b c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 11884 | a (a^6 - 3 a^4 b^2 - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-4 b^3 - 2 b^2 c - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (b^4 + 4 b^2 c^2 + 2 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (-3 b^5 + 2 b^4 c + 2 b^3 c^2 + Sqrt[2] b^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c^2 Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - b (c^4 + 4 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))): : |
| 12000 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a^4 b (3 b + 2 c) + 2 a^3 (2 b^3 + 4 b^2 c + b c^2 + c^3) + a b (-3 b^4 + 4 b^2 c^2 + 6 b c^3 - 7 c^4) + a^2 (b^4 - 2 b^3 c - 8 b^2 c^2 + 8 b c^3 - c^4)): : |
| 12001 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 10 c) + 2 a^3 (2 b^3 - 4 b^2 c - 5 b c^2 + c^3) + a^2 (b^4 - 10 b^3 c + 20 b^2 c^2 - 8 b c^3 - c^4) + a b (-3 b^4 + 12 b^3 c - 8 b^2 c^2 - 10 b c^3 + 9 c^4)): : |
| 12009 | a (3 a^5 b + 3 (b - c)^3 c^2 (b + c) + a^4 (-6 b^2 + 10 b c + 3 c^2) - a^3 c (b^2 + 16 b c + 6 c^2) + a^2 b (6 b^3 - 25 b^2 c + 17 b c^2 - c^3) - a (3 b^5 - 16 b^4 c + 10 b^3 c^2 + 7 b^2 c^3 + 2 b c^4 - 6 c^5)): : |
| 12410 | a (a^6 + a^5 b - a^4 b^2 + b^6 - b^2 c^4 + 2 a^3 b c (-b + c) - a b (b^4 + 2 b^3 c + 2 b c^3 - c^4) - a^2 (b^4 - 4 b^2 c^2 + c^4)): : |
| 12435 | -(a (a^4 b (2 b + c) + 2 b c^3 (b^2 - c^2) + a^3 c (-b^2 + 3 b c + 2 c^2) + a^2 (-2 b^4 - b^3 c + b c^3) + a c (-3 b^4 - b^3 c + b^2 c^2 + b c^3 - 2 c^4))): : |
| 12555 | a (a^6 + b^6 - 2 b^5 c - b^4 c^2 - 4 b^3 c^3 - b^2 c^4 + 6 b c^5 + c^6 - 2 a^5 (b + c) - a^4 (9 b^2 - 2 b c + c^2) + 4 a^3 (b^3 - 4 b c^2 - c^3) + a^2 (7 b^4 + 10 b^2 c^2 - 8 b c^3 - c^4) - 2 a (b^5 - 9 b^4 c + 4 b^2 c^3 - b c^4 - 3 c^5)): : |
| 12702 | -(a (a^3 + b^3 + a^2 (2 b - c) - b^2 c + 2 b c^2 - 2 c^3 - a (4 b^2 + b c - 2 c^2))): : |
| 12703 | -(a (a^6 - 2 a^5 c + 2 a^3 b (2 b^2 + 5 b c - c^2) + a^4 (-5 b^2 + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 10 b^3 c - 6 b^2 c^2 + 10 b c^3 - c^4) + 2 a (-2 b^5 + 2 b^4 c + b^3 c^2 + 3 b^2 c^3 - 5 b c^4 + c^5))): : |
| 12704 | -(a (a^6 - 2 a^5 c + 2 a^3 b (2 b^2 - b c - 3 c^2) + a^4 (-5 b^2 + 4 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 6 b^3 c + 10 b^2 c^2 - 2 b c^3 - c^4) + 2 a (-2 b^5 + 4 b^4 c - b^3 c^2 - 3 b^2 c^3 + b c^4 + c^5))): : |
| 12915 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (2 b + c) + a^4 (-2 b^2 + 2 b c + c^2) + 2 a^2 b^2 (b^2 - 3 b c + 10 c^2) - a (b - c)^2 (b^3 - 2 b^2 c - 3 b c^2 - 2 c^3)): : |
| 13145 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^3 c (3 b^2 - 4 b c - 2 c^2) + a^4 (-2 b^2 + 2 b c + c^2) + a^2 b (2 b^3 - 9 b^2 c + b c^2 + 3 c^3) + a (-b^5 + 4 b^4 c - 2 b^3 c^2 + b^2 c^3 - 4 b c^4 + 2 c^5)): : |
| 13151 | a (2 a^6 - a^5 (3 b + 4 c) - a^4 (4 b^2 + c^2) + 2 a^2 c (3 b^3 + b^2 c - c^3) + (b - c)^3 (2 b^3 + 2 b^2 c - b c^2 - c^3) + 2 a^3 (4 b^3 + b c^2 + 3 c^3) + a (-5 b^5 + 2 b^4 c + 4 b^3 c^2 - 2 b^2 c^3 + 3 b c^4 - 2 c^5)): : |
| 13370 | a (a^6 - 3 a^4 b (b - 3 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - b^2 c - 9 b c^2 + 2 c^3) + a^2 (b^4 - 15 b^3 c + 20 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + 11 b^3 c - 7 b^2 c^2 - 3 b c^3 + 2 c^4)): : |
| 13373 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) + 2 a^2 b (b^3 - 6 b^2 c + 5 b c^2 - c^3) + a (-b^5 + 8 b^4 c - 6 b^3 c^2 - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 13384 | a (5 a^3 + 5 b^3 - 5 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 5 c) + a (-7 b^2 + 4 b c - 3 c^2)): : |
| 13388 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 - b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] - c Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + a (-3 b^2 + 4 b c + c^2 - Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])): : |
| 13389 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + b Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + c Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)] + a (-3 b^2 + 4 b c + c^2 + Sqrt[-a^4 - (b^2 - c^2)^2 + 2 a^2 (b^2 + c^2)])): : |
| 13462 | a (5 a^3 + 5 b^3 - 5 b^2 c - b c^2 + c^3 - a^2 (b + 5 c) - a (9 b^2 - 14 b c + c^2)): : |
| 13528 | a (2 a^6 - a^5 (b + 4 c) + a^4 (-8 b^2 + 8 b c + c^2) + 2 a^3 (4 b^3 + 3 b^2 c - 5 b c^2 + c^3) + (b - c)^3 (2 b^3 + 2 b^2 c + b c^2 + c^3) + a^2 (4 b^4 - 20 b^3 c + 8 b^2 c^2 + 6 b c^3 - 2 c^4) + a (-7 b^5 + 14 b^4 c - 4 b^3 c^2 - 5 b c^4 + 2 c^5)): : |
| 13600 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - 6 b c + c^2) - 2 a^3 c (-6 b^2 - 2 b c + c^2) + 2 a^2 b (b^3 - b^2 c - 8 b c^2 + 6 c^3) - a (b^5 + 4 b^4 c - 6 b^3 c^2 - 10 b^2 c^3 + 13 b c^4 - 2 c^5)): : |
| 13601 | a (a^5 b + 2 a^2 b (b - 2 c)^2 (b + c) + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - 2 b c + c^2) + a^3 (8 b^2 c - 2 c^3) + a (-b^5 + 2 b^3 c^2 + 6 b^2 c^3 - 9 b c^4 + 2 c^5)): : |
| 13624 | a (4 a^3 + 4 b^3 - 4 b^2 c - b c^2 + c^3 - a^2 (b + 4 c) - a (7 b^2 - 5 b c + c^2)): : |
| 13750 | a (a^5 b + 2 a^2 b^3 (b - 3 c) + (b - c)^3 c^2 (b + c) - 2 a^3 c^2 (2 b + c) + a^4 (-2 b^2 + 2 b c + c^2) - a (b - c)^2 (b^3 - 2 b^2 c - 3 b c^2 - 2 c^3)): : |
| 13751 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + 4 b c + c^2) - a^3 c (b^2 + 6 b c + 2 c^2) + a^2 b (2 b^3 - 9 b^2 c + 9 b c^2 - c^3) - a (b^5 - 6 b^4 c + 4 b^3 c^2 + 3 b^2 c^3 - 2 c^5)): : |
| 14000 | a (4 a^6 - a^5 (b + 10 c) + a^4 (-22 b^2 + 26 b c + 5 c^2) + a^3 (20 b^3 + 11 b^2 c - 34 b c^2 + 2 c^3) + (b - c)^2 (4 b^4 - 2 b^3 c - 3 b^2 c^2 - 2 b c^3 - 5 c^4) + a^2 (14 b^4 - 61 b^3 c + 39 b^2 c^2 + 11 b c^3 - 4 c^4) - a (19 b^5 - 44 b^4 c + 16 b^3 c^2 + 7 b^2 c^3 + 10 b c^4 - 8 c^5)): : |
| 14110 | a (a^5 b + (b - c)^3 c^2 (b + c) + 2 a^3 c (b^2 + b c - c^2) + a^4 (-2 b^2 - 4 b c + c^2) + 2 a^2 b (b^3 + 2 b^2 c - 2 b c^2 + c^3) - a (b^5 + 2 b^4 c - 4 b^3 c^2 + 3 b c^4 - 2 c^5)): : |
| 14115 | a (a^7 b (b - 3 c) + b (b - c)^3 c^3 (b + c)^2 + a^6 (-b^3 + 8 b c^2 + c^3) - a^5 (2 b^4 - 15 b^3 c + 20 b^2 c^2 + 4 b c^3 + c^4) + a^4 (2 b^5 - 14 b^4 c + 25 b^2 c^3 - 3 b c^4 - 2 c^5) + a^3 (b^6 - 7 b^5 c + 34 b^4 c^2 - 36 b^3 c^3 + b^2 c^4 + 3 b c^5 + 2 c^6) + a^2 (-b^7 + 14 b^6 c - 30 b^5 c^2 + 11 b^4 c^3 + 13 b^3 c^4 - 4 b^2 c^5 - 4 b c^6 + c^7) - a c (5 b^7 - 8 b^6 c + 3 b^4 c^3 - b^3 c^4 + 4 b^2 c^5 - 4 b c^6 + c^7)): : |
| 14122 | a (2 a^6 + 2 b^6 - 4 b^5 c + b^4 c^2 + b^3 c^3 - 2 b^2 c^4 + 3 b c^5 - c^6 - a^5 (b + 4 c) + a^4 (-9 b^2 + 13 b c + c^2) + a^3 (8 b^3 + 5 b^2 c - 19 b c^2 + c^3) + a^2 (5 b^4 - 33 b^3 c + 31 b^2 c^2 + 4 b c^3 - 2 c^4) - a (7 b^5 - 21 b^4 c + 11 b^3 c^2 + 2 b^2 c^3 + 6 b c^4 - 3 c^5)): : |
| 14131 | a (a^4 b (b - 7 c) + a^3 c^2 (9 b + c) + b c^3 (b^2 - c^2) + a^2 b (-b^3 + 14 b^2 c - 8 b c^2 + c^3) + a c (-9 b^4 + 7 b^3 c + b^2 c^2 - c^4)): : |
| 14132 | a (a^8 b + (b - c)^3 c^2 (b + c)^4 + a^7 (b^2 + b c + c^2) + a^6 (-3 b^3 - b^2 c + 2 b c^2 + c^3) - a^5 (3 b^4 + 3 b^3 c + 2 b^2 c^2 + 2 b c^3 + 3 c^4) + a^4 (3 b^5 - 3 b^3 c^2 + b^2 c^3 - 6 b c^4 - 3 c^5) - a (b - c)^2 (b^6 + 5 b^5 c + 5 b^4 c^2 - b^3 c^3 - 3 b^2 c^4 + c^6) + a^3 (3 b^6 + 5 b^5 c - 5 b^4 c^2 - 4 b^3 c^3 + b^2 c^4 - b c^5 + 3 c^6) - a^2 (b^7 - b^6 c - 2 b^5 c^2 + b^4 c^3 + 3 b^3 c^4 + 5 b^2 c^5 - 4 b c^6 - 3 c^7)): : |
| 14792 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) - a b (b - c)^2 (3 b^2 - c^2) + 2 a^3 (2 b^3 - 2 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 7 b^2 c^2 - c^4)): : |
| 14793 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) - a b (b - c)^2 (3 b^2 - c^2) + 2 a^3 (2 b^3 - 2 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 8 b^2 c^2 - c^4)): : |
| 14794 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - b c^2 + c^3) + a^2 (b^4 - 2 b^3 c + 5 b^2 c^2 - c^4) + a b (-3 b^4 + 4 b^3 c - 2 b c^3 + c^4)): : |
| 14795 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + a^2 (b - c)^2 (b^2 - b c - c^2) - a b^2 (3 b^3 - 4 b^2 c + c^3) + a^3 (4 b^3 + b^2 c - 2 b c^2 + 2 c^3)): : |
| 14796 | a (a^3 + b^2 (b - c) - a^2 c - a b (2 b + Sqrt[2] c)): : |
| 14797 | a (a^3 + b^2 (b - c) - a^2 c + a b (-2 b + Sqrt[2] c)): : |
| 14798 | a (a^6 + a^4 b (-3 b + c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a b^2 (-3 b^3 + 3 b^2 c + b c^2 - c^3) + a^3 (4 b^3 + b^2 c - b c^2 + 2 c^3) + a^2 (b^4 - b^3 c + b c^3 - c^4)): : |
| 14799 | a (a^6 - 3 a^4 b^2 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a b^2 (3 b^3 - 2 b^2 c - 2 b c^2 + c^3) + a^3 (4 b^3 + b^2 c + 2 c^3) + a^2 (b^4 + b^3 c + 2 b^2 c^2 + b c^3 - c^4)): : |
| 14800 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 - b^2 c - 6 b c^2 + 2 c^3) + a^2 (b^4 - 9 b^3 c + 8 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + 8 b^3 c - 4 b^2 c^2 - 3 b c^3 + 2 c^4)): : |
| 14801 | a (a^12 + b^2 (b - c)^7 (b + c)^3 - a^11 (3 b + 4 c) + a^10 (-2 b^2 - 2 (-10 + Sqrt[2]) b c + 3 c^2) + a^9 (15 b^3 + (-19 + 3 Sqrt[2]) b^2 c + 3 (-13 + 2 Sqrt[2]) b c^2 + 8 c^3) - a b (b - c)^5 (b + c)^2 (5 b^3 + (-11 + 2 Sqrt[2]) b^2 c + b c^2 + (2 + Sqrt[2]) c^3) - a^8 (9 b^4 + (53 - 9 Sqrt[2]) b^3 c + 3 (-36 + 7 Sqrt[2]) b^2 c^2 + 3 (-1 + Sqrt[2]) b c^3 + 14 c^4) - a^7 b (22 b^4 + (-115 + 19 Sqrt[2]) b^3 c + 33 b^2 c^2 - 4 (-37 + 9 Sqrt[2]) b c^3 + (-73 + 7 Sqrt[2]) c^4) + a^2 (b - c)^3 (b + c) (6 b^6 + (-43 + 9 Sqrt[2]) b^5 c + (58 - 15 Sqrt[2]) b^4 c^2 + 2 b^3 c^3 - (20 + 3 Sqrt[2]) b^2 c^4 + (5 + 3 Sqrt[2]) b c^5 + c^6) + a^6 (28 b^6 - (17 + 3 Sqrt[2]) b^5 c + 3 (-79 + 23 Sqrt[2]) b^4 c^2 + 2 (145 - 31 Sqrt[2]) b^3 c^3 - (20 + 9 Sqrt[2]) b^2 c^4 + 3 (-23 + 3 Sqrt[2]) b c^5 + 14 c^6) + a^5 (6 b^7 + (-131 + 27 Sqrt[2]) b^6 c + 18 (17 - 4 Sqrt[2]) b^5 c^2 - 6 (7 + 3 Sqrt[2]) b^4 c^3 + (-285 + 77 Sqrt[2]) b^3 c^4 - 6 (-31 + 4 Sqrt[2]) b^2 c^5 - 3 (5 + Sqrt[2]) b c^6 - 8 c^7) + a^3 (b - c) (9 b^8 + (22 - 9 Sqrt[2]) b^7 c + (-173 + 51 Sqrt[2]) b^6 c^2 + (177 - 41 Sqrt[2]) b^5 c^3 + 6 (11 - 4 Sqrt[2]) b^4 c^4 + 12 (-11 + Sqrt[2]) b^3 c^5 + (28 + 9 Sqrt[2]) b^2 c^6 + (14 - 3 Sqrt[2]) b c^7 - 4 c^8) - a^4 (25 b^8 + (-109 + 13 Sqrt[2]) b^7 c + 3 (7 + 5 Sqrt[2]) b^6 c^2 + 2 (177 - 56 Sqrt[2]) b^5 c^3 + (-392 + 79 Sqrt[2]) b^4 c^4 + 6 (7 + 3 Sqrt[2]) b^3 c^5 + (115 - 21 Sqrt[2]) b^2 c^6 + (-49 + Sqrt[2]) b c^7 + 3 c^8)): : |
| 14802 | a (a^12 + b^2 (b - c)^7 (b + c)^3 - a^11 (3 b + 4 c) + a^10 (-2 b^2 + 2 (10 + Sqrt[2]) b c + 3 c^2) + a^9 (15 b^3 - (19 + 3 Sqrt[2]) b^2 c - 3 (13 + 2 Sqrt[2]) b c^2 + 8 c^3) - a b (b - c)^5 (b + c)^2 (5 b^3 - (11 + 2 Sqrt[2]) b^2 c + b c^2 - (-2 + Sqrt[2]) c^3) + a^8 (-9 b^4 - (53 + 9 Sqrt[2]) b^3 c + 3 (36 + 7 Sqrt[2]) b^2 c^2 + 3 (1 + Sqrt[2]) b c^3 - 14 c^4) + a^7 b (-22 b^4 + (115 + 19 Sqrt[2]) b^3 c - 33 b^2 c^2 - 4 (37 + 9 Sqrt[2]) b c^3 + (73 + 7 Sqrt[2]) c^4) + a^2 (b - c)^3 (b + c) (6 b^6 - (43 + 9 Sqrt[2]) b^5 c + (58 + 15 Sqrt[2]) b^4 c^2 + 2 b^3 c^3 + (-20 + 3 Sqrt[2]) b^2 c^4 + (5 - 3 Sqrt[2]) b c^5 + c^6) + a^6 (28 b^6 + (-17 + 3 Sqrt[2]) b^5 c - 3 (79 + 23 Sqrt[2]) b^4 c^2 + 2 (145 + 31 Sqrt[2]) b^3 c^3 + (-20 + 9 Sqrt[2]) b^2 c^4 - 3 (23 + 3 Sqrt[2]) b c^5 + 14 c^6) + a^5 (6 b^7 - (131 + 27 Sqrt[2]) b^6 c + 18 (17 + 4 Sqrt[2]) b^5 c^2 + 6 (-7 + 3 Sqrt[2]) b^4 c^3 - (285 + 77 Sqrt[2]) b^3 c^4 + 6 (31 + 4 Sqrt[2]) b^2 c^5 + 3 (-5 + Sqrt[2]) b c^6 - 8 c^7) + a^3 (b - c) (9 b^8 + (22 + 9 Sqrt[2]) b^7 c - (173 + 51 Sqrt[2]) b^6 c^2 + (177 + 41 Sqrt[2]) b^5 c^3 + 6 (11 + 4 Sqrt[2]) b^4 c^4 - 12 (11 + Sqrt[2]) b^3 c^5 + (28 - 9 Sqrt[2]) b^2 c^6 + (14 + 3 Sqrt[2]) b c^7 - 4 c^8) + a^4 (-25 b^8 + (109 + 13 Sqrt[2]) b^7 c + 3 (-7 + 5 Sqrt[2]) b^6 c^2 - 2 (177 + 56 Sqrt[2]) b^5 c^3 + (392 + 79 Sqrt[2]) b^4 c^4 + 6 (-7 + 3 Sqrt[2]) b^3 c^5 - (115 + 21 Sqrt[2]) b^2 c^6 + (49 + Sqrt[2]) b c^7 - 3 c^8)): : |
| 14803 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 7 c) + a^3 (4 b^3 - b^2 c - 7 b c^2 + 2 c^3) + a^2 (b^4 - 11 b^3 c + 8 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + 9 b^3 c - 5 b^2 c^2 - 3 b c^3 + 2 c^4)): : |
| 14804 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + a^3 (4 b^3 - b^2 c - 4 b c^2 + 2 c^3) + a^2 (b^4 - 5 b^3 c + 4 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 3 b c^3 + 2 c^4)): : |
| 14882 | a (a^6 - 3 a^4 b (b - c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^3 (4 b^3 + 2 b^2 c - 3 b c^2 + 2 c^3) + a^2 (b^4 - 6 b^3 c + 5 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 5 b^3 c + b^2 c^2 + c^4)): : |
| 15016 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^3 c (b^2 - 5 b c - 2 c^2) + a^4 (-2 b^2 + 3 b c + c^2) + a^2 b (2 b^3 - 9 b^2 c + 4 b c^2 + c^3) - a (b^5 - 5 b^4 c + 3 b^3 c^2 + b^2 c^3 + 2 b c^4 - 2 c^5)): : |
| 15177 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c + 2 b^2 c^2 - b c^3 - c^4) + a^4 (-b^5 + 2 b^4 c - 3 b^3 c^2 + b^2 c^3 + c^5) + a^3 (3 b^6 - b^5 c + b^4 c^2 + 2 b^3 c^3 - b^2 c^4 - b c^5 + c^6) - a^2 (b^7 - b^4 c^3 + 3 b^3 c^4 - 4 b^2 c^5 + c^7)): : |
| 15178 | a (4 a^3 + 4 b^3 - 4 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 4 c) + a (-5 b^2 + 7 b c - 3 c^2)): : |
| 15803 | a (3 a^3 + 3 b^3 + a^2 (b - 3 c) - 3 b^2 c + b c^2 - c^3 + a (-7 b^2 + 6 b c + c^2)): : |
| 15804 | a (a^9 + b^2 (b - c)^5 (b + c)^2 - a^8 (2 b + 3 c) - a b (b - c)^3 (b + c)^2 (4 b^2 - b c + c^2) + a^7 (-3 b^2 + b c + c^2) + a^6 (9 b^3 + 6 b^2 c + 4 b c^2 + 5 c^3) - a^5 (b^4 - 3 b^3 c + 16 b^2 c^2 + b c^3 + 5 c^4) - a^4 (11 b^5 + 6 b^4 c + 11 b^3 c^2 - 15 b^2 c^3 + 2 b c^4 + c^5) + a^3 (7 b^6 - 9 b^5 c + 41 b^4 c^2 - 46 b^3 c^3 - 11 b^2 c^4 - b c^5 + 3 c^6) + a^2 (3 b^7 + 6 b^6 c - 26 b^5 c^2 + 15 b^4 c^3 - 9 b^3 c^4 + 12 b^2 c^5 - c^7)): : |
| 15931 | a (a^6 + b^2 (b - c)^3 (b + c) - a^4 b (3 b + c) - a^5 (b + 2 c) + a b^2 (-3 b^3 + b^2 c + 3 b c^2 - c^3) + a^3 (4 b^3 + b^2 c + b c^2 + 2 c^3) + a^2 (b^4 + 3 b^3 c + b c^3 - c^4)): : |
| 15932 | a (a^6 - 2 a^5 c + a^3 b (4 b^2 - b c - 5 c^2) + a^4 (-5 b^2 + 3 b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 5 b^3 c - b c^3 - c^4) + a (-4 b^5 + 7 b^4 c - b^3 c^2 - 5 b^2 c^3 + b c^4 + 2 c^5)): : |
| 15934 | a (a^3 + b^3 - b^2 c - 2 b c^2 + 2 c^3 - a^2 (2 b + c) - a c (5 b + 2 c)): : |
| 15941 | a (a^9 + a^8 (b - c) - 2 a^7 b (2 b + c) + 2 a^6 b c (b + 2 c) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3)^2 + 2 a^5 (b^4 + 3 b^3 c + 2 b^2 c^2 - c^4) + 2 a^2 b^2 c (3 b^4 - 2 b^3 c - 2 b^2 c^2 + 2 b c^3 - c^4) - 2 a^4 (b^5 + 3 b^4 c + 3 b c^4 - c^5) + 2 a^3 b (2 b^5 - b^4 c - 6 b^3 c^2 - 2 b^2 c^3 + 2 b c^4 + c^5) + a (-3 b^8 - 2 b^7 c + 8 b^6 c^2 - 2 b^4 c^4 + 2 b^3 c^5 - 4 b^2 c^6 + c^8)): : |
| 16189 | a (5 a^3 + 5 b^3 - 5 b^2 c - 9 b c^2 + 9 c^3 - a^2 (9 b + 5 c) - a (b^2 - 14 b c + 9 c^2)): : |
| 16191 | a (9 a^3 + 9 b^3 - 9 b^2 c - 17 b c^2 + 17 c^3 - a^2 (17 b + 9 c) - a (b^2 - 26 b c + 17 c^2)): : |
| 16192 | a (7 a^3 + 7 b^3 + a^2 (b - 7 c) - 7 b^2 c + b c^2 - c^3 + a (-15 b^2 + 6 b c + c^2)): : |
| 16193 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (2 b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) - a (b - c)^2 (b^3 - 6 b^2 c - 7 b c^2 - 2 c^3) + 2 a^2 b (b^3 - 5 b^2 c + 2 b c^2 - 2 c^3)): : |
| 16200 | a (3 a^3 + 3 b^3 - 3 b^2 c - 5 b c^2 + 5 c^3 - a^2 (5 b + 3 c) - a (b^2 - 8 b c + 5 c^2)): : |
| 16201 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (2 b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) + 2 a^2 b (b^3 - 5 b^2 c - 10 b c^2 - 2 c^3) - a (b - c)^2 (b^3 - 6 b^2 c - 7 b c^2 - 2 c^3)): : |
| 16202 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a^4 b (3 b + 2 c) + 2 a^3 (2 b^3 + 2 b^2 c + b c^2 + c^3) + a b (-3 b^4 + 4 b^2 c^2 + 2 b c^3 - 3 c^4) + a^2 (b^4 + 2 b^3 c - 4 b^2 c^2 + 4 b c^3 - c^4)): : |
| 16203 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 10 c) + 2 a^3 (2 b^3 - 2 b^2 c - 5 b c^2 + c^3) + a^2 (b^4 - 14 b^3 c + 16 b^2 c^2 - 4 b c^3 - c^4) + a b (-3 b^4 + 12 b^3 c - 8 b^2 c^2 - 6 b c^3 + 5 c^4)): : |
| 16204 | a (5 a^6 - 2 a^5 (7 b + 5 c) + 3 a^4 (b^2 + 10 b c - 3 c^2) + (b - c)^3 (5 b^3 + 5 b^2 c - 9 b c^2 - 9 c^3) + 4 a^3 (5 b^3 - 5 b^2 c - 3 b c^2 + 7 c^3) - a^2 (13 b^4 + 12 b^3 c - 42 b^2 c^2 + 20 b c^3 + 5 c^4) - 2 a (3 b^5 - 11 b^4 c + 10 b^3 c^2 + 6 b^2 c^3 - 17 b c^4 + 9 c^5)): : |
| 16205 | a (5 a^6 - 2 a^5 (7 b + 5 c) + a^4 (3 b^2 + 46 b c - 9 c^2) + (b - c)^3 (5 b^3 + 5 b^2 c - 9 b c^2 - 9 c^3) + 4 a^3 (5 b^3 - 13 b^2 c - 7 b c^2 + 7 c^3) - a^2 (13 b^4 + 12 b^3 c - 90 b^2 c^2 + 52 b c^3 + 5 c^4) - 2 a (3 b^5 - 19 b^4 c + 18 b^3 c^2 + 22 b^2 c^3 - 33 b c^4 + 9 c^5)): : |
| 16206 | a (5 a^6 - 2 a^5 (7 b + 5 c) + a^4 (3 b^2 + 32 b c - 9 c^2) + (b - c)^3 (5 b^3 + 5 b^2 c - 9 b c^2 - 9 c^3) + 2 a^3 (10 b^3 - 11 b^2 c - 7 b c^2 + 14 c^3) - a^2 (13 b^4 + 14 b^3 c - 46 b^2 c^2 + 22 b c^3 + 5 c^4) - 2 a (3 b^5 - 12 b^4 c + 11 b^3 c^2 + 7 b^2 c^3 - 18 b c^4 + 9 c^5)): : |
| 16207 | a (5 a^6 - 2 a^5 (7 b + 5 c) + a^4 (3 b^2 + 44 b c - 9 c^2) + (b - c)^3 (5 b^3 + 5 b^2 c - 9 b c^2 - 9 c^3) + a^3 (20 b^3 - 50 b^2 c - 26 b c^2 + 28 c^3) - a^2 (13 b^4 + 10 b^3 c - 86 b^2 c^2 + 50 b c^3 + 5 c^4) - 2 a (3 b^5 - 18 b^4 c + 17 b^3 c^2 + 21 b^2 c^3 - 32 b c^4 + 9 c^5)): : |
| 16208 | a (3 a^6 - 2 a^5 (b + 3 c) + a^4 (-11 b^2 + c^2) + (b - c)^3 (3 b^3 + 3 b^2 c + b c^2 + c^3) + 2 a^3 (6 b^3 + 3 b^2 c - b c^2 + 2 c^3) + a^2 (5 b^4 - 2 b^3 c + 2 b^2 c^2 + 6 b c^3 - 3 c^4) - 2 a (5 b^5 - 4 b^4 c - 3 b^3 c^2 + b^2 c^3 + 2 b c^4 - c^5)): : |
| 16209 | a (3 a^6 - 2 a^5 (b + 3 c) + a^4 (-11 b^2 + 20 b c + c^2) + (b - c)^3 (3 b^3 + 3 b^2 c + b c^2 + c^3) + 2 a^3 (6 b^3 + b^2 c - 11 b c^2 + 2 c^3) + a^2 (5 b^4 - 38 b^3 c + 26 b^2 c^2 + 2 b c^3 - 3 c^4) - 2 a (5 b^5 - 14 b^4 c + 7 b^3 c^2 + 3 b^2 c^3 - c^5)): : |
| 16215 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (2 b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) - a (b - c)^2 (b^3 - 6 b^2 c - 7 b c^2 - 2 c^3) + 2 a^2 b (b^3 - 5 b^2 c + 14 b c^2 - 2 c^3)): : |
| 16216 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (3 b^2 + 4 b c + c^2) + a^4 (-2 b^2 + 6 b c + c^2) + 2 a^2 b (b^3 - 4 b^2 c - 9 b c^2 - 3 c^3) - a (b^5 - 8 b^4 c + 6 b^3 c^2 + 8 b^2 c^3 - 5 b c^4 - 2 c^5)): : |
| 16217 | a (a^8 b + (b - c)^5 c^2 (b + c)^2 + a^7 (-3 b^2 + 5 b c + c^2) + a^6 (b^3 - 8 b^2 c - 16 b c^2 - 3 c^3) + a^5 (5 b^4 - 13 b^3 c + 8 b^2 c^2 + b c^3 + c^4) + a^2 (b - c)^2 (3 b^5 - 14 b^4 c - 21 b^3 c^2 - 17 b^2 c^3 - 10 b c^4 - c^5) - a (b - c)^3 (b^5 - 6 b^4 c - 7 b^3 c^2 + 5 b^2 c^3 + 8 b c^4 + 3 c^5) + a^4 (-5 b^5 + 28 b^4 c + 13 b^3 c^2 - b^2 c^3 + 20 b c^4 + 5 c^5) - a^3 (b^6 + b^5 c + 3 b^4 c^2 + 30 b^3 c^3 - 13 b^2 c^4 + 5 b c^5 + 5 c^6)): : |
| 16218 | a (a^8 b + (b - c)^5 c^2 (b + c)^2 + a^7 (-3 b^2 + 5 b c + c^2) + a^6 (b^3 - 4 b^2 c - 16 b c^2 - 3 c^3) + a^5 (5 b^4 - 21 b^3 c + 32 b^2 c^2 + 5 b c^3 + c^4) + a^2 (b - c)^2 (3 b^5 - 18 b^4 c + 3 b^3 c^2 + 11 b^2 c^3 - 2 b c^4 - c^5) - a (b - c)^3 (b^5 - 6 b^4 c - 7 b^3 c^2 + b^2 c^3 + 4 b c^4 + 3 c^5) + a^4 (-5 b^5 + 28 b^4 c - 3 b^3 c^2 - 33 b^2 c^3 + 12 b c^4 + 5 c^5) - a^3 (b^6 - 7 b^5 c + 43 b^4 c^2 - 82 b^3 c^3 + 3 b^2 c^4 + 5 b c^5 + 5 c^6)): : |
| 16541 | a (a^9 - a^8 c + b^2 (b - c)^3 (b + c)^2 (b^2 + c^2) - a^2 (b - c)^2 (b + c)^3 (b^2 - b c + c^2) - a^7 (3 b^2 - b c + c^2) - a b (b^2 - c^2)^2 (2 b^3 - b^2 c + 2 b c^2 - c^3) + a^6 (b^3 + c^3) + a^5 (b^4 - b^3 c + 4 b^2 c^2 - b c^3 - c^4) - a^4 (b^5 - 2 b^4 c + b^3 c^2 + b^2 c^3 - c^5) + a^3 (3 b^6 - b^5 c - 5 b^4 c^2 - 14 b^3 c^3 + b^2 c^4 - b c^5 + c^6)): : |
| 16678 | a (a^5 (b + c) + a^4 b (b + c) - a^2 b^3 (b + 3 c) + a b^3 (b^2 - b c - 2 c^2) + b^3 c (b^2 - c^2) - a^3 (2 b^3 + b^2 c + c^3)): : |
| 16687 | a (a^5 (b + c) + a^4 b (b + 3 c) + b^3 c (b^2 - c^2) + a^3 (-2 b^3 + b^2 c + 2 b c^2 - c^3) - a^2 (b^4 + b^3 c - 2 b c^3) + a b (b^4 + b^3 c + 2 b c^3 + 2 c^4)): : |
| 16763 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 6 b c + c^2) + 4 a^3 (b^3 - 2 b c^2) - 2 a (b - c)^2 (2 b^3 - b^2 c - 2 b c^2 - c^3) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 12 b^3 c + 7 b^2 c^2 - c^4)): : |
| 16778 | a (2 a^5 (b + c) + a^4 b (2 b + 3 c) + 2 b^3 c (b^2 - c^2) + a b (b - c)^2 (2 b^2 + 3 b c + c^2) - a^3 (4 b^3 + b^2 c - b c^2 + 2 c^3) + a^2 (-2 b^4 - 5 b^3 c + b c^3)): : |
| 16877 | a (a^7 (b + c) + a^6 b (b + c) + a b^4 (b - c)^2 (b + c) + a^4 b c^2 (b + 3 c) + a^5 (-b^3 + b c^2) - a^2 b^3 (b^3 + 2 b^2 c + b c^2 + 2 c^3) + b^3 c (b^4 - c^4) - a^3 (b^5 + 2 b^3 c^2 - 2 b c^4 + c^5)): : |
| 16878 | a (2 a^5 (b + c) + a^4 b (2 b + 3 c) + 2 b^3 c (b^2 - c^2) + a^3 (-4 b^3 + b^2 c + 3 b c^2 - 2 c^3) + a^2 b (-2 b^3 - 3 b^2 c + 6 b c^2 + 3 c^3) + a b (2 b^4 - b^3 c - b^2 c^2 + 3 b c^3 + c^4)): : |
| 17102 | a (a^5 (b + 2 c) + a b (b - c)^2 (3 b^2 - c^2) + a^4 (2 b^2 - 4 b c - c^2) - 2 a^2 b^2 (b^2 - 3 b c + 2 c^2) - 2 a^3 (2 b^3 - 2 b c^2 + c^3) + c (2 b^5 - b^4 c - 2 b^3 c^2 + c^5)): : |
| 17437 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 6 b c + c^2) + 4 a^3 (b^3 - 2 b c^2) - 2 a (b - c)^2 (2 b^3 - b^2 c - 2 b c^2 - c^3) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 12 b^3 c + 14 b^2 c^2 - c^4)): : |
| 17502 | a (6 a^3 + 6 b^3 - 6 b^2 c - b c^2 + c^3 - a^2 (b + 6 c) - a (11 b^2 - 7 b c + c^2)): : |
| 17591 | a (a^2 (b + 3 c) + a (5 b^2 - b c + c^2) + c (3 b^2 + b c + 2 c^2)): : |
| 17592 | a (a^2 (2 b + 3 c) + 2 a (2 b^2 + 2 b c + c^2) + c (3 b^2 + 2 b c + c^2)): : |
| 17593 | a (a^3 + b^3 - 4 b^2 c - b c^2 - 2 c^3 - a^2 (b + 4 c) - a (7 b^2 + c^2)): : |
| 17594 | a (a^3 + b^3 - 3 b^2 c - b c^2 - c^3 - a^2 (b + 3 c) - a (5 b^2 + 2 b c + c^2)): : |
| 17595 | a (a^3 + b^3 - 3 a^2 c - 3 b^2 c - 2 c^3 + 3 a b (-2 b + c)): : |
| 17596 | a (a^3 + b^3 - 2 a^2 c - 2 b^2 c - c^3 + a b (-4 b + c)): : |
| 17597 | a (a^3 + b^3 + a b (2 b - 5 c) + a^2 c + b^2 c + 2 c^3): : |
| 17598 | a (a^3 + b^3 + 2 b^2 c + b c^2 + 2 c^3 + a^2 (b + 2 c) + a (3 b^2 - 2 b c + c^2)): : |
| 17599 | a (a^3 + b^3 + 3 b^2 c + 2 b c^2 + 2 c^3 + a^2 (2 b + 3 c) + a (4 b^2 + b c + 2 c^2)): : |
| 17600 | a (a^3 + b^3 + 4 b^2 c + 3 b c^2 + 2 c^3 + a^2 (3 b + 4 c) + a (5 b^2 + 4 b c + 3 c^2)): : |
| 17601 | a (2 a^3 - 6 a b^2 + 2 b^3 - 3 a^2 c - 3 b^2 c - c^3): : |
| 17603 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (b^2 + 5 b c + c^2) + a^4 (-2 b^2 + 8 b c + c^2) + 2 a^2 b (b^3 - 8 b^2 c + 2 b c^2 - c^3) + a (-b^5 + 10 b^4 c - 8 b^3 c^2 - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 17609 | a (a^2 b + (b - c) c^2 + a (-b^2 + 9 b c + c^2)): : |
| 17642 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + c^2) - 2 a^3 c (b^2 + b c + c^2) + 2 a^2 b (b^3 + 6 b c^2 - c^3) + a (-b^5 + 2 b^4 c - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 17699 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 6 b c + c^2) + 4 a^3 (b^3 - 2 b c^2) - 2 a (b - c)^2 (2 b^3 - b^2 c - 2 b c^2 - c^3) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 12 b^3 c - 2 b^2 c^2 - c^4)): : |
| 17700 | a (a^6 - 2 a^5 c + a^4 (-5 b^2 + 6 b c + c^2) + 4 a^3 (b^3 - 2 b c^2) - 2 a (b - c)^2 (2 b^3 - b^2 c - 2 b c^2 - c^3) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - 12 b^3 c + 6 b^2 c^2 - c^4)): : |
| 17715 | a (2 a^3 + 2 b^3 - a^2 c - b^2 c + c^3 - 2 a b (b + 2 c)): : |
| 17716 | a (2 a^3 + 2 b^3 + b^2 c + 2 b c^2 + c^3 + 2 a c (b + c) + a^2 (2 b + c)): : |
| 17798 | a (a^5 + a^4 b + b^5 - b^2 c^3 + a^3 b (-b + c) - a^2 (b^3 + b^2 c - 2 b c^2 + c^3) - a (b^4 + b^3 c - b c^3)): : |
| 18115 | -(a (a^8 c + a^7 (b^2 - 2 b c - 2 c^2) + (b - c)^3 c (b + c)^2 (b^3 - b^2 c - c^3) - a^6 (3 b^3 - 4 b c^2 + c^3) + a^5 c (6 b^3 - 4 b^2 c - b c^2 + 3 c^3) + a^4 b (6 b^4 - 8 b^3 c - b^2 c^2 + 5 b c^3 - 3 c^4) + a^3 b (-3 b^5 + 7 b^3 c^2 - 5 b^2 c^3 - 2 b c^4 + 2 c^5) + a (b - c)^2 (2 b^6 + 3 b^3 c^3 + b^2 c^4 - b c^5 - c^6) - a^2 (3 b^7 - 6 b^6 c + 4 b^5 c^2 + b^4 c^3 - 4 b^3 c^4 + b^2 c^5 + c^7))): : |
| 18193 | a (a^3 + b^3 + a^2 (b - 3 c) - 3 b^2 c + b c^2 - 3 c^3 + a (-7 b^2 + 8 b c + c^2)): : |
| 18201 | a (a^3 + b^3 + a^2 (b - 2 c) - 2 b^2 c + b c^2 - 2 c^3 + a (-5 b^2 + 6 b c + c^2)): : |
| 18208 | -(a (a^4 c + a^3 (b^2 - 2 b c - c^2) + a b (2 b^3 - 2 b^2 c + b c^2 - 2 c^3) + a^2 (-b^3 + b^2 c - b c^2 + c^3) + c (b^4 - b^3 c + b^2 c^2 + c^4))): : |
| 18280 | a (a^12 + a^11 b - a b (b - c)^5 (b + c)^4 (b + 2 c) + a^10 (-6 b^2 + b c - 5 c^2) + b^2 (b^2 - c^2)^5 - a^9 b (5 b^2 + b c + 2 c^2) + a^7 b (10 b^4 + 4 b^3 c + b^2 c^2 + 6 b c^3 - 2 c^4) + a^8 (15 b^4 - 4 b^3 c + 14 b^2 c^2 - 4 b c^3 + 10 c^4) + a^6 (-20 b^6 + 6 b^5 c - 7 b^4 c^2 + 7 b^3 c^3 - 8 b^2 c^4 + 6 b c^5 - 10 c^6) + a^3 b (b + c)^2 (5 b^6 - 6 b^5 c - 6 b^4 c^2 + 15 b^3 c^3 - 19 b^2 c^4 + 18 b c^5 - 7 c^6) + a^5 b (-10 b^6 - 6 b^5 c + 8 b^4 c^2 - 7 b^3 c^3 + 3 b^2 c^4 - 8 b c^5 + 8 c^6) - a^2 (b - c)^3 (6 b^7 + 17 b^6 c + 19 b^5 c^2 + 14 b^4 c^3 + 10 b^3 c^4 + 3 b^2 c^5 - 2 b c^6 - c^7) + a^4 (15 b^8 - 4 b^7 c - 11 b^6 c^2 - b^5 c^3 + b^3 c^5 - 5 b^2 c^6 - 4 b c^7 + 5 c^8)): : |
| 18330 | a (a^7 b^2 + b (b - c)^3 c^3 (b + c)^2 + a^6 (-b^3 - 2 b^2 c + 2 b c^2 + c^3) - a^5 (2 b^4 - 4 b^3 c + 3 b^2 c^2 + 3 b c^3 + c^4) + a^4 (2 b^5 - 2 b^4 c - 2 b^3 c^2 + 6 b^2 c^3 + b c^4 - 2 c^5) - a (b - c)^2 c (2 b^5 + 2 b^4 c + b^3 c^2 - b^2 c^3 - b c^4 + c^5) + a^3 (b^6 - 2 b^5 c + 6 b^4 c^2 - 5 b^3 c^3 - b^2 c^4 + 2 c^6) + a^2 (-b^7 + 4 b^6 c - 5 b^5 c^2 + 3 b^3 c^4 - 2 b c^6 + c^7)): : |
| 18398 | a (a^2 b + (b - c) c^2 + a (-b^2 + 4 b c + c^2)): : |
| 18421 | a (a^3 + b^3 - b^2 c - 5 b c^2 + 5 c^3 - a^2 (5 b + c) + a (3 b^2 - 2 b c - 5 c^2)): : |
| 18443 | a (a^6 - 2 a^5 (b + c) - a^4 (b + c)^2 + (b - c)^4 (b + c)^2 + 4 a^3 (b^3 + b c^2 + c^3) - a^2 (b^4 - 8 b^3 c + 2 b^2 c^2 + c^4) - 2 a (b^5 + b^4 c - 2 b^3 c^2 - b c^4 + c^5)): : |
| 18447 | a (a^6 + a b^3 (b - c) c - a^3 b c^2 + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 - b c + c^2) - a^2 (b^4 + 2 b^3 c - 3 b^2 c^2 + c^4)): : |
| 18453 | a (a^9 + a^8 (b - c) + a^7 b (-4 b + c) - a^6 b c (b + 2 c) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3)^2 + a^5 (2 b^4 - 3 b^3 c + 4 b^2 c^2 - 2 c^4) + a^2 b^2 c (-3 b^4 + 2 b^3 c + 2 b^2 c^2 - 2 b c^3 + c^4) + a^3 b (4 b^5 + b^4 c - 6 b^3 c^2 + 2 b^2 c^3 + 4 b c^4 - c^5) + a^4 (-2 b^5 + 6 b^4 c + 2 c^5) + a (-3 b^8 + b^7 c + 2 b^6 c^2 + 4 b^4 c^4 - b^3 c^5 - 4 b^2 c^6 + c^8)): : |
| 18455 | a (a^6 + a^3 b c^2 + a b^3 c (-b + c) + (b^2 - c^2)^2 (b^2 + c^2) - a^4 (b^2 + b c + c^2) - a^2 (b^4 - 2 b^3 c - b^2 c^2 + c^4)): : |
| 18758 | a (a^4 (b - c) c^2 + b^4 (b - c) c^2 + a^5 (b^2 + c^2) + a b^2 c^2 (-b^2 + b c + c^2) + a^3 (-2 b^4 + b^3 c + b c^3) + a^2 b (b^4 + 2 b^2 c^2 - b c^3 + c^4)): : |
| 18788 | a (a^5 + b^5 - 2 a^4 c - 2 b^4 c + 3 b^3 c^2 - b^2 c^3 - c^5 + a^3 (-b^2 + b c + 3 c^2) + a^2 (3 b^3 - 2 b^2 c + 2 b c^2 - c^3) + a b (-4 b^3 + b^2 c - 2 b c^2 + c^3)): : |
| 18838 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + 2 b c + c^2) - 2 a^3 c (-b^2 + 2 b c + c^2) + 2 a^2 b (b^3 - 4 b^2 c + 3 b c^2 + c^3) - a (b^5 - 4 b^4 c + 2 b^3 c^2 + 3 b c^4 - 2 c^5)): : |
| 18839 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (b + c)^2 + a^4 (-2 b^2 + 2 b c + c^2) + 2 a^2 b (b^3 - 2 b^2 c + 5 b c^2 - c^3) + a (-b^5 + 4 b^4 c - 2 b^3 c^2 - 4 b^2 c^3 + b c^4 + 2 c^5)): : |
| 18856 | a (a^8 b + (b - c)^5 c^2 (b + c)^2 + a^7 (-3 b^2 + 5 b c + c^2) + a^6 (b^3 - 16 b c^2 - 3 c^3) + a^5 (5 b^4 - 29 b^3 c + 32 b^2 c^2 + 9 b c^3 + c^4) - a (b - c)^3 (b^5 - 6 b^4 c - 7 b^3 c^2 - 3 b^2 c^3 + 3 c^5) + a^4 (-5 b^5 + 28 b^4 c + 9 b^3 c^2 - 41 b^2 c^3 + 4 b c^4 + 5 c^5) - a^3 (b^6 - 15 b^5 c + 63 b^4 c^2 - 46 b^3 c^3 - 9 b^2 c^4 + 5 b c^5 + 5 c^6) + a^2 (3 b^7 - 28 b^6 c + 50 b^5 c^2 - 13 b^4 c^3 - 17 b^3 c^4 - 2 b^2 c^5 + 8 b c^6 - c^7)): : |
| 18857 | a (4 a^6 - a^5 (5 b + 8 c) - a^4 (10 b^2 - 22 b c + c^2) + (b - c)^3 (4 b^3 + 4 b^2 c - b c^2 - c^3) + 2 a^3 (8 b^3 - 3 b^2 c - 10 b c^2 + 5 c^3) + 2 a^2 (b^4 - 14 b^3 c + 17 b^2 c^2 - 3 b c^3 - 2 c^4) - a (11 b^5 - 28 b^4 c + 14 b^3 c^2 + 12 b^2 c^3 - 11 b c^4 + 2 c^5)): : |
| 18967 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 8 c) + 2 a^3 (2 b^3 - 3 b^2 c - 4 b c^2 + c^3) + a^2 (b^4 - 8 b^3 c + 12 b^2 c^2 - 6 b c^3 - c^4) + a b (-3 b^4 + 10 b^3 c - 6 b^2 c^2 - 8 b c^3 + 7 c^4)): : |
| 19758 | a (a^5 - a^4 c - 3 a^3 (b^2 + b c + c^2) - a^2 (5 b^3 + 8 b^2 c + 4 b c^2 + 3 c^3) + b (b^4 - b^3 c - 3 b^2 c^2 - 3 b c^3 - 2 c^4) - a (2 b^4 + 7 b^3 c + 6 b^2 c^2 + 3 b c^3 + 2 c^4)): : |
| 19761 | a (a^5 + a^4 (4 b + 3 c) + a^3 (b^2 + 5 b c + c^2) + a^2 (-b^3 + 4 b c^2 + c^3) + b (b^4 + 3 b^3 c + b^2 c^2 + b c^3 + 2 c^4) + a (2 b^4 + b^3 c + 2 b^2 c^2 + 5 b c^3 + 2 c^4)): : |
| 19765 | a (a^3 - a^2 (2 b + 3 c) + b (b^2 - 3 b c - 2 c^2) - a (4 b^2 + 3 b c + 2 c^2)): : |
| 19782 | a (a^6 - a^4 b^2 - a^5 (b + 2 c) + 4 a^3 (b^3 + b c^2 + c^3) - a^2 (b^4 - 2 b^3 c - 2 b c^3 + c^4) + b (b^5 - 2 b^4 c + 4 b^2 c^3 - b c^4 - 2 c^5) + a (-3 b^5 - 2 b^4 c + 2 b^3 c^2 + b c^4 - 2 c^5)): : |
| 20182 | a (a^3 + b^3 + 5 b^2 c + 4 b c^2 + 2 c^3 + a^2 (4 b + 5 c) + a (6 b^2 + 7 b c + 4 c^2)): : |
| 20254 | -(a (a^5 c + a^4 (b^2 - 2 b c - c^2) + a^2 b^2 (-b^2 + 3 b c + c^2) + a^3 (-2 b^3 + b^2 c + b c^2 - c^3) + a b (2 b^4 - 2 b^3 c + b^2 c^2 + 2 b c^3 - c^4) + c (b^5 - b^4 c - b^3 c^2 + c^5))): : |
| 20323 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - 9 b c + c^2)): : |
| 20358 | a (a^3 b (b - c) + b (b - c) c^3 - a c (3 b^3 - 2 b^2 c + b c^2 + c^3) + a^2 (-b^3 + b^2 c + 2 b c^2 + c^3)): : |
| 20359 | a (a^4 b (b - 3 c) + b c^3 (b^2 - c^2) + a^3 c (-b^2 + 3 b c + c^2) - a^2 b^2 (b^2 - 3 b c + 3 c^2) - a c (5 b^4 - b^3 c + b c^3 + c^4)): : |
| 20367 | a (a^4 (b + c) + a^3 (b^2 - c^2) + b c (b^3 - b^2 c + b c^2 - c^3) + a^2 (-3 b^3 + 2 b c^2 + c^3) + a (b^4 - 4 b^3 c + 2 b^2 c^2 - c^4)): : |
| 20368 | a (a^4 b (2 b - 3 c) + a^5 (b + c) - 2 a^3 b (b^2 + b c - 3 c^2) - 2 a^2 b^2 (b^2 - 3 b c + 3 c^2) + b c (b^4 - c^4) + a (b^5 - 7 b^4 c + 2 b^3 c^2 + b c^4 - c^5)): : |
| 20764 | a (-(a^7 c^2) + a^8 (b + c) + b^3 (b - c)^3 c (b + c)^2 - a^6 (4 b^3 + b^2 c - 2 b c^2 + 2 c^3) - a^2 b^2 (b - c)^2 (2 b^3 + b^2 c + 2 b c^2 + 3 c^3) + a^5 (b^4 + 2 b^3 c - 2 b^2 c^2 - 2 b c^3 + 2 c^4) + a^4 (5 b^5 - 4 b^4 c + b^3 c^2 + 4 b^2 c^3 - 3 b c^4 + c^5) + a b (b - c)^2 (b^5 + b^3 c^2 + 4 b^2 c^3 + 4 b c^4 + 2 c^5) + a^3 (-2 b^6 + b^4 c^2 + 2 b^2 c^4 - c^6)): : |
| 20788 | a (b^2 (b - c) c^4 (b + c)^2 + a^6 (b^3 - b c^2) + a^5 (b^4 + b^3 c + 3 b^2 c^2 + 3 b c^3 + c^4) + a^4 (-b^5 + 2 b^4 c + 3 b^3 c^2 + 4 b^2 c^3 + 6 b c^4 + c^5) - a b c^2 (3 b^5 + b^4 c - 4 b^3 c^2 - b^2 c^3 + 3 b c^4 + 2 c^5) - a^3 (b^6 + 3 b^5 c + 3 b^4 c^2 - 5 b^3 c^3 - 5 b^2 c^4 - b c^5 + c^6) - a^2 c (4 b^6 + 3 b^5 c - 3 b^3 c^3 + 3 b c^5 + c^6)): : |
| 20789 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - 10 b c + c^2) - 2 a^3 c (-6 b^2 - 4 b c + c^2) - a (b - c)^2 (b^3 + 10 b^2 c + 9 b c^2 - 2 c^3) + 2 a^2 b (b^3 + 3 b^2 c - 18 b c^2 + 6 c^3)): : |
| 20790 | a (a^5 b + (b - c)^3 c^2 (b + c) - 2 a^3 c (6 b^2 + 8 b c + c^2) + a^4 (-2 b^2 + 14 b c + c^2) + 2 a^2 b (b^3 - 9 b^2 c - 18 b c^2 - 6 c^3) - a (b - c)^2 (b^3 - 14 b^2 c - 15 b c^2 - 2 c^3)): : |
| 20878 | a (a^5 b^2 (b - c) + b^4 c^2 (b^2 - c^2) + a^6 (b^2 + c^2) + a b^3 c^2 (-2 b^2 - b c + c^2) + a^2 b^2 (b^4 - b^3 c + 2 b c^3 - 2 c^4) - a^4 (2 b^4 + 2 b^2 c^2 - b c^3 + c^4) + a^3 (-b^5 + 4 b^3 c^2 + b c^4)): : |
| 21010 | a (b^3 (b - c) c + a^3 (2 b - c) c + a^4 (b + c) + a^2 b (-2 b^2 + b c + 2 c^2) + a b (b^3 + 2 b c^2 + 2 c^3)): : |
| 21164 | a (3 a^6 - 2 a^5 (b + 3 c) + a^4 (-11 b^2 + 22 b c + c^2) + 4 a^3 (3 b^3 - 6 b c^2 + c^3) + (b - c)^3 (3 b^3 + 3 b^2 c + b c^2 + c^3) + a^2 (5 b^4 - 40 b^3 c + 30 b^2 c^2 - 3 c^4) - 2 a (5 b^5 - 15 b^4 c + 8 b^3 c^2 + 4 b^2 c^3 - b c^4 - c^5)): : |
| 21334 | a (a^4 b (b - c) + b c^3 (b^2 - c^2) + a^3 c (-b^2 + b c + c^2) - a^2 b^2 (b^2 + b c + 5 c^2) - a c (3 b^4 + b^3 c + b c^3 + c^4)): : |
| 21842 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - 4 b c + c^2)): : |
| 22341 | a (a^8 (b + c) - a^7 c (b + c) + b^3 (b - c)^3 c (b + c)^2 - a^6 (4 b^3 + b^2 c - 2 b c^2 + 2 c^3) - a^2 b^2 (b - c)^2 (2 b^3 + b^2 c + 2 b c^2 + 3 c^3) + a^5 (b^4 + 3 b^3 c - 2 b^2 c^2 - b c^3 + 2 c^4) + a^4 (5 b^5 - 4 b^4 c + b^3 c^2 + 4 b^2 c^3 - 3 b c^4 + c^5) + a b (b - c)^2 (b^5 - b^4 c - b^3 c^2 + 2 b^2 c^3 + 2 b c^4 + c^5) + a^3 (-2 b^6 + b^5 c + b^4 c^2 - 2 b^3 c^3 + 2 b^2 c^4 + b c^5 - c^6)): : |
| 22765 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 5 c) + a^3 (4 b^3 - 2 b^2 c - 5 b c^2 + 2 c^3) + a^2 (b^4 - 6 b^3 c + 9 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 7 b^3 c - 3 b^2 c^2 - 4 b c^3 + 3 c^4)): : |
| 22766 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a b (b - c)^2 (3 b^2 - 2 b c - 3 c^2) + 2 a^3 (2 b^3 - b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 8 b^3 c + 6 b^2 c^2 - 2 b c^3 - c^4)): : |
| 22767 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) - a b (b - c)^2 (3 b^2 - 2 b c - 3 c^2) + 2 a^3 (2 b^3 - b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 8 b^3 c + 14 b^2 c^2 - 2 b c^3 - c^4)): : |
| 22768 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 8 c) + 2 a^3 (2 b^3 - b^2 c - 4 b c^2 + c^3) + a^2 (b^4 - 12 b^3 c + 8 b^2 c^2 - 2 b c^3 - c^4) + a b (-3 b^4 + 10 b^3 c - 6 b^2 c^2 - 4 b c^3 + 3 c^4)): : |
| 22770 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + 2 a^3 (2 b^3 - 2 b^2 c - 2 b c^2 + c^3) + a^2 (b^4 - 2 b^3 c + 10 b^2 c^2 - 4 b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 6 b c^3 + 5 c^4)): : |
| 23171 | a (a^7 (b - c) c + a^8 (b + c) + b^3 (b - c)^3 c (b + c)^2 - 2 a^6 (2 b^3 + b^2 c + c^3) + a^5 (b^4 - b^3 c - 2 b^2 c^2 - 2 b c^3 + 2 c^4) - 2 a^2 b^2 (b^5 - b^2 c^3 - b c^4 + c^5) + a^4 (5 b^5 + b^3 c^2 + 4 b^2 c^3 - b c^4 + c^5) + a^3 (-2 b^6 + b^5 c + 3 b^4 c^2 + 2 b^3 c^3 + 2 b^2 c^4 - b c^5 - c^6) + a (b^8 - b^7 c + 2 b^5 c^3 - b^4 c^4 - 3 b^3 c^5 + 2 b c^7)): : |
| 23207 | a (a^7 (b - c) c + a^8 (b + c) + b^3 (b - c)^3 c (b + c)^2 - a^2 b^2 (b + c)^3 (2 b^2 - 3 b c + c^2) + a b (b^2 - c^2)^2 (b^3 - b^2 c + c^3) - a^6 (4 b^3 + 3 b^2 c + 2 b c^2 + 2 c^3) + a^5 (b^4 - 3 b^3 c - 2 b^2 c^2 - b c^3 + 2 c^4) + a^4 (5 b^5 + 4 b^4 c + b^3 c^2 + 4 b^2 c^3 + b c^4 + c^5) - a^3 (2 b^6 - 3 b^5 c - 5 b^4 c^2 - 2 b^3 c^3 - 2 b^2 c^4 + b c^5 + c^6)): : |
| 23340 | a (a^5 b + (b - c)^3 c^2 (b + c) + 2 a^3 c (4 b^2 + b c - c^2) + a^4 (-2 b^2 - 4 b c + c^2) + 2 a^2 b (b^3 - b^2 c - 5 b c^2 + 4 c^3) - a (b^5 + 2 b^4 c - 4 b^3 c^2 - 6 b^2 c^3 + 9 b c^4 - 2 c^5)): : |
| 23703 | a (2 a^6 - 6 a^4 b (b - c) - a^5 (b + 3 c) + b (b - c)^2 (2 b^3 + b^2 c + c^3) + a^3 (6 b^3 + 3 b^2 c - 7 b c^2 + 2 c^3) + a^2 (2 b^4 - 13 b^3 c + 8 b^2 c^2 + 3 b c^3 - 2 c^4) + a (-5 b^5 + 10 b^4 c - 3 b^3 c^2 - b^2 c^3 - 2 b c^4 + c^5)): : |
| 23832 | a (a^4 b (b - 5 c) + a^5 (b + c) + b^3 c (b^2 - c^2) - a^3 (2 b^3 + 3 b^2 c - 6 b c^2 + c^3) - a^2 b (b^3 - 11 b^2 c + 4 b c^2 + 2 c^3) + a b (b^4 - 7 b^3 c + 4 b^2 c^2 - 2 b c^3 + 2 c^4)): : |
| 23853 | a (a^4 b^2 + a^5 (b + c) + b^3 c (b^2 - c^2) + a b^3 (b^2 - 2 b c - c^2) - a^2 b^2 (b^2 + b c - c^2) - a^3 (2 b^3 + b^2 c - b c^2 + c^3)): : |
| 23890 | a (2 a^7 - a^6 (b + 3 c) + a^4 b (6 b^2 + b c - 3 c^2) - a^5 (7 b^2 - 8 b c + c^2) + b (b - c)^3 (2 b^3 + 3 b^2 c + 2 b c^2 - c^3) - a (b - c)^2 (5 b^4 - 2 b^3 c - 6 b^2 c^2 - 6 b c^3 - c^4) + 2 a^3 (b^4 - 4 b^3 c + 3 b^2 c^2 - 4 b c^3 + 3 c^4) + a^2 (b^5 - 7 b^4 c + 2 b^3 c^2 + 10 b^2 c^3 - b c^4 - 5 c^5)): : |
| 23960 | a (2 a^6 - 2 a^5 (3 b + 2 c) + 2 a^4 (b^2 + 9 b c - 2 c^2) + 2 (b - c)^3 (b^3 + b^2 c - 2 b c^2 - 2 c^3) + a^3 (8 b^3 - 19 b^2 c - 10 b c^2 + 12 c^3) - a^2 (6 b^4 + 5 b^3 c - 33 b^2 c^2 + 19 b c^3 + 2 c^4) - a (2 b^5 - 14 b^4 c + 14 b^3 c^2 + 15 b^2 c^3 - 25 b c^4 + 8 c^5)): : |
| 23961 | -(a (2 a^6 + 2 b^2 (b - c)^3 (b + c) - 2 a^5 (b + 2 c) + 2 a^4 b (-3 b + 5 c) + a^3 (8 b^3 - b^2 c - 10 b c^2 + 4 c^3) + a^2 (2 b^4 - 15 b^3 c + 15 b^2 c^2 - b c^3 - 2 c^4) + a b (-6 b^4 + 14 b^3 c - 6 b^2 c^2 - 5 b c^3 + 3 c^4))): : |
| 23981 | a (a^8 (b + c) + b^3 (b - c)^3 c (b + c)^2 - a^7 c (3 b + c) - 2 a^6 (2 b^3 - 3 b c^2 + c^3) - 2 a^2 b (b - c)^2 (b^4 - 3 b^3 c + 2 b c^3 + c^4) + a^5 (b^4 + 11 b^3 c - 8 b^2 c^2 - 2 b c^3 + 2 c^4) + a^4 (5 b^5 - 12 b^4 c - 3 b^3 c^2 + 12 b^2 c^3 - 5 b c^4 + c^5) + a b (b - c)^2 (b^5 - 3 b^4 c - b^3 c^2 + 3 b^2 c^3 + 2 b c^4 + 2 c^5) - a^3 (2 b^6 + 3 b^5 c - 15 b^4 c^2 + 10 b^3 c^3 + 2 b^2 c^4 - 3 b c^5 + c^6)): : |
| 24299 | a (2 a^6 - a^4 (-2 b + c)^2 - a^5 (3 b + 4 c) + (b - c)^3 (2 b^3 + 2 b^2 c - b c^2 - c^3) - 2 a^2 c (b^3 - 3 b^2 c + c^3) + a^3 (8 b^3 - 2 b c^2 + 6 c^3) + a (-5 b^5 + 6 b^4 c - 2 b^2 c^3 + 3 b c^4 - 2 c^5)): : |
| 24301 | -(a (2 a^9 - a^8 (b + 2 c) + a^7 (-5 b^2 + 3 b c - 3 c^2) + 3 a^6 (b^3 + c^3) + (b - c)^3 (b + c)^2 (2 b^4 + b^2 c^2 - c^4) + a^5 (b^4 - 3 b^3 c + 4 b^2 c^2 - 3 b c^3 - c^4) - a (b^2 - c^2)^2 (3 b^4 - 3 b^3 c + 4 b^2 c^2 - 3 b c^3 + c^4) + a^4 (-b^5 + 4 b^4 c - 3 b^3 c^2 + b^2 c^3 + 2 b c^4 + c^5) + a^3 (5 b^6 - 3 b^5 c + b^4 c^2 + 2 b^3 c^3 - b^2 c^4 - 3 b c^5 + 3 c^6) + a^2 (-3 b^7 + 2 b^5 c^2 + b^4 c^3 - 3 b^3 c^4 + 6 b^2 c^5 - 3 c^7))): : |
| 24310 | a (a^5 (b + c) + a^4 b (2 b + c) - 2 a^3 (b^3 - b c^2) - 2 a^2 (b^4 + 2 b^3 c - b c^3) + b c (b^4 - c^4) + a (b^5 - 3 b^4 c - 2 b^3 c^2 + 2 b^2 c^3 - b c^4 - c^5)): : |
| 24464 | -(a (a^3 c^2 + a^2 b^2 (2 b + c) + b c^2 (b^2 + c^2) + a (2 b^3 c + c^4))): : |
| 24468 | a (a^6 - 2 a^5 c + a^3 b (4 b^2 - b c - 3 c^2) + a^4 (-5 b^2 + b c + c^2) + (b - c)^3 (b^3 + b^2 c + b c^2 + c^3) + a^2 (3 b^4 - b^3 c + 6 b^2 c^2 - b c^3 - c^4) + a (-4 b^5 + 5 b^4 c + b^3 c^2 - 5 b^2 c^3 + b c^4 + 2 c^5)): : |
| 24474 | a (a^5 b - 2 a^3 c^2 (b + c) + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 + c^2) + 2 a^2 b^2 (b^2 - b c + c^2) - a (b^5 - 2 b^4 c + 2 b^2 c^3 + b c^4 - 2 c^5)): : |
| 24806 | a (-(a^4 b c) + a^5 (b + c) + b c (b^2 - c^2)^2 - 2 a^2 b c (b^2 + b c - c^2) - 2 a^3 (b^3 - b^2 c + c^3) + a (b^5 - b^4 c + 2 b^2 c^3 - 3 b c^4 + c^5)): : |
| 24926 | a (3 a^3 + 3 b^3 - 3 b^2 c - 2 b c^2 + 2 c^3 - a^2 (2 b + 3 c) - 2 a (2 b^2 - 2 b c + c^2)): : |
| 24927 | a (2 a^6 - a^5 (3 b + 4 c) - a^4 (4 b^2 - 16 b c + c^2) + (b - c)^3 (2 b^3 + 2 b^2 c - b c^2 - c^3) - 2 a^2 c (9 b^3 - 13 b^2 c + 4 b c^2 + c^3) + 2 a^3 (4 b^3 - 4 b^2 c - 7 b c^2 + 3 c^3) - a (5 b^5 - 18 b^4 c + 12 b^3 c^2 + 10 b^2 c^3 - 11 b c^4 + 2 c^5)): : |
| 24928 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 - 7 b c + c^2)): : |
| 24929 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 + b c + c^2)): : |
| 25405 | a (4 a^3 + 4 b^3 - 4 b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + 4 c) + a (-5 b^2 + 11 b c - 3 c^2)): : |
| 25413 | a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - b c + c^2) - a^3 c (-4 b^2 + b c + 2 c^2) + a^2 b (2 b^3 - 4 b^2 c - 3 b c^2 + 4 c^3) + a (-b^5 + b^4 c + b^3 c^2 + 2 b^2 c^3 - 5 b c^4 + 2 c^5)): : |
| 25414 | -(a (a^5 b + (b - c)^3 c^2 (b + c) + a^4 (-2 b^2 - 2 b c + c^2) + a^3 (5 b^2 c - 2 c^3) + a^2 b (2 b^3 - 3 b^2 c - 7 b c^2 + 5 c^3) + a (-b^5 + 2 b^3 c^2 + 3 b^2 c^3 - 6 b c^4 + 2 c^5))): : |
| 25415 | a (a^3 + b^3 - b^2 c - 3 b c^2 + 3 c^3 - a^2 (3 b + c) + a (b^2 + 2 b c - 3 c^2)): : |
| 26086 | a (2 a^6 + 2 b^2 (b - c)^3 (b + c) - 2 a^5 (b + 2 c) + a^4 (-6 b^2 + 8 b c) + a^3 (8 b^3 + b^2 c - 8 b c^2 + 4 c^3) + a^2 (2 b^4 - 13 b^3 c + 11 b^2 c^2 + b c^3 - 2 c^4) + a b (-6 b^4 + 12 b^3 c - 4 b^2 c^2 - 3 b c^3 + c^4)): : |
| 26087 | a (2 a^6 - 4 a^5 (b + c) + 2 (b - c)^4 (b + c)^2 - 2 a^4 (b^2 - 6 b c + c^2) + a^3 (8 b^3 - 9 b^2 c - 8 b c^2 + 8 c^3) - a^2 (2 b^4 + 7 b^3 c - 21 b^2 c^2 + 9 b c^3 + 2 c^4) - a (4 b^5 - 12 b^4 c + 8 b^3 c^2 + 9 b^2 c^3 - 13 b c^4 + 4 c^5)): : |
| 26285 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) - a b^2 (3 b^3 - 6 b^2 c + 2 b c^2 + c^3) + a^3 (4 b^3 + b^2 c - 4 b c^2 + 2 c^3) + a^2 (b^4 - 7 b^3 c + 5 b^2 c^2 + b c^3 - c^4)): : |
| 26286 | a (a^6 + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + a^4 b (-3 b + 4 c) + a^3 (4 b^3 - b^2 c - 4 b c^2 + 2 c^3) + a^2 (b^4 - 5 b^3 c + 7 b^2 c^2 - b c^3 - c^4) + a b (-3 b^4 + 6 b^3 c - 2 b^2 c^2 - 3 b c^3 + 2 c^4)): : |
| 26287 | a (2 a^6 - a^5 (3 b + 4 c) - a^4 (4 b^2 - 10 b c + c^2) + (b - c)^3 (2 b^3 + 2 b^2 c - b c^2 - c^3) - a^2 c (11 b^3 - 15 b^2 c + 3 b c^2 + 2 c^3) + a^3 (8 b^3 - 3 b^2 c - 8 b c^2 + 6 c^3) - a (5 b^5 - 12 b^4 c + 6 b^3 c^2 + 5 b^2 c^3 - 6 b c^4 + 2 c^5)): : |
| 26290 | a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-4 b^3 + 2 b^2 c + 2 b c^2 - 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (-3 b^4 + b^3 c + b^2 c^2 - 3 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (b^4 + 6 b^2 c^2 - 2 b c^3 - c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26291 | a (a^6 + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + (b - c)^2 (b + c) (b^3 - b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (4 b^3 - 2 b^2 c - 2 b c^2 + 2 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (b - c) (3 b^4 - b^3 c - b^2 c^2 + 3 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-b^4 - 6 b^2 c^2 + 2 b c^3 + c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26296 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 - 2 b c + c^2) + 2 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26297 | a (a^3 + b^3 + a^2 (b - c) - b^2 c + b c^2 - c^3 + a (-3 b^2 - 2 b c + c^2) - 2 Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26319 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - b^2 c - b c^2 + c^3) + a^2 (b^4 + 6 b^2 c^2 - 2 b c^3 - c^4) - a b (3 b^4 - 4 b^3 c + 4 b c^3 - 3 c^4 + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26320 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - b^2 c - b c^2 + c^3) + a^2 (b^4 + 6 b^2 c^2 - 2 b c^3 - c^4) - a b (3 b^4 - 4 b^3 c + 4 b c^3 - 3 c^4 - 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26351 | a (2 a^4 b c + Sqrt[2] (b - c)^2 (b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^3 (-2 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (2 b^3 c - Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (4 b^3 c + 2 b^2 c^2 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26352 | a (2 a^4 b c - Sqrt[2] (b - c)^2 (b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^3 (2 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (2 b^3 c + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (-4 b^3 c - 2 b^2 c^2 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26357 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - b c^2 + c^3) + a^2 (b^4 - 2 b^3 c + 8 b^2 c^2 - c^4) + a b (-3 b^4 + 4 b^3 c - 2 b c^3 + c^4)): : |
| 26358 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + 2 b^2 c - b c^2 + c^3) + a b (-3 b^4 + 4 b^3 c + 2 b c^3 - 3 c^4) + a^2 (b^4 - 6 b^3 c - 4 b^2 c^2 + 4 b c^3 - c^4)): : |
| 26365 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 + b c + c^2) + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26366 | a (2 a^3 + 2 b^3 - 2 b^2 c - b c^2 + c^3 - a^2 (b + 2 c) - a (3 b^2 + b c + c^2) - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26380 | a (2 a^4 b c - Sqrt[2] (b - c)^2 (b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - a^3 (4 b^2 c + 2 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (2 b^3 c - 4 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (2 b^2 c^2 - 4 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26393 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 2 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 4 b^3 c + c^4 - 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26395 | a (a^3 + b^3 - b^2 c + a (b - 2 c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c) - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26398 | a (2 a^6 - 2 a^5 (b + 2 c) + a^4 (-6 b^2 + 4 b c) + (b - c)^2 (b + c) (2 b^3 - 2 b^2 c + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^3 (8 b^3 + 2 b^2 c - 4 b c^2 + 4 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a (b - c) (6 b^4 - 2 b^3 c - 2 b^2 c^2 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-2 b^4 + 6 b^3 c - 6 b^2 c^2 - 2 b c^3 + 2 c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26399 | a (a^3 + b^3 - a^2 c - b^2 c + a b (-2 b + c) + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26401 | a (a^3 + b^3 - a^2 c - b^2 c + a b (-2 b + 3 c) + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26404 | a (2 a^4 b c + Sqrt[2] (b - c)^2 (b + c) Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + a^3 (-4 b^2 c - 2 b c^2 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^2 (-2 b^2 c^2 + 4 b c^3 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (2 b^3 c + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - b (4 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]))): : |
| 26417 | a (a^6 + b^2 (b - c)^3 (b + c) + a^4 b (-3 b + 2 c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 + b^2 c - b c^2 + c^3) + a^2 (b^4 - 4 b^3 c + 2 b^2 c^2 + 2 b c^3 - c^4) - a b (3 b^4 - 4 b^3 c + c^4 + 2 Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26419 | a (a^3 + b^3 - b^2 c + a (b - 2 c) c - 2 b c^2 + 2 c^3 - a^2 (2 b + c) + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26422 | a (2 a^6 - 2 a^5 (b + 2 c) + a^4 (-6 b^2 + 4 b c) + (b - c)^2 (b + c) (2 b^3 - 2 b^2 c - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) - a^3 (-8 b^3 - 2 b^2 c + 4 b c^2 - 4 c^3 + Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a (b - c) (-6 b^4 + 2 b^3 c + 2 b^2 c^2 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] - Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]) + a^2 (2 b^4 - 6 b^3 c + 6 b^2 c^2 + 2 b c^3 - 2 c^4 + Sqrt[2] b Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))] + Sqrt[2] c Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))])): : |
| 26423 | a (a^3 + b^3 - a^2 c - b^2 c + a b (-2 b + c) - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26425 | a (a^3 + b^3 - a^2 c - b^2 c + a b (-2 b + 3 c) - Sqrt[2] Sqrt[-(a b c (a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 + 6 b c + c^2)))]): : |
| 26437 | a (a^6 - 3 a^4 b (b - 2 c) + b^2 (b - c)^3 (b + c) - a^5 (b + 2 c) + 2 a^3 (2 b^3 - 2 b^2 c - 3 b c^2 + c^3) + a^2 (b^4 - 6 b^3 c + 8 b^2 c^2 - 4 b c^3 - c^4) + a b (-3 b^4 + 8 b^3 c - 4 b^2 c^2 - 6 b c^3 + 5 c^4)): : |
| 26903 | a (2 b^4 (b - c)^5 c^2 (b + c)^4 - 2 a^12 c (b^2 + c^2) - 2 a^3 b^2 (b^2 - c^2)^4 (2 b^2 + c^2) + a^13 (2 b^2 + b c + 2 c^2) + 2 a^2 b^2 (b^2 - c^2)^4 (b^3 - b^2 c + b c^2 - 2 c^3) + a b c (b^2 - c^2)^4 (b^4 - 4 b^3 c + 4 b^2 c^2 + c^4) - 2 a^11 (6 b^4 + 5 b^2 c^2 + 4 c^4) + 2 a^10 (b^5 + 3 b^4 c + b^3 c^2 + 2 b^2 c^3 + 4 c^5) - 2 a^4 (b - c)^3 (b + c)^2 (4 b^6 + b^5 c + 7 b^4 c^2 + 4 b^2 c^4 - b c^5 - c^6) + a^5 (b^2 - c^2)^2 (18 b^6 - 9 b^5 c + 22 b^4 c^2 - 18 b^3 c^3 + 14 b^2 c^4 - 9 b c^5 + 2 c^6) + a^9 (28 b^6 - 9 b^5 c + 16 b^4 c^2 + 20 b^2 c^4 - 9 b c^5 + 12 c^6) - 2 a^8 (4 b^7 + 2 b^6 c + 3 b^5 c^2 - b^4 c^3 + 4 b^3 c^4 - 2 b^2 c^5 + 6 c^7) - 4 a^7 (8 b^8 - 4 b^7 c + b^6 c^2 + 5 b^2 c^6 - 4 b c^7 + 2 c^8) + 4 a^6 (3 b^9 - b^8 c + b^7 c^2 - 2 b^6 c^3 + b^5 c^4 - 3 b^4 c^5 + 3 b^3 c^6 - 4 b^2 c^7 + 2 c^9)): : |
| 26904 | a (2 b^4 (b - c)^5 c^2 (b + c)^4 - 2 a^12 c (b^2 + c^2) + a^13 (2 b^2 - b c + 2 c^2) - 2 a^3 b (b^2 - c^2)^4 (2 b^3 - 2 b^2 c + b c^2 - 2 c^3) + 2 a^2 b^2 (b^2 - c^2)^4 (b^3 - b^2 c + b c^2 - 2 c^3) - a b c (b^2 - c^2)^4 (b^4 + 4 b^3 c + c^4) - 2 a^11 (6 b^4 - 2 b^3 c + 5 b^2 c^2 - 2 b c^3 + 4 c^4) + 2 a^10 (b^5 + 3 b^4 c + b^3 c^2 + 2 b^2 c^3 + 4 c^5) - 2 a^4 (b - c)^3 (b + c)^2 (4 b^6 + b^5 c + 7 b^4 c^2 + 4 b^2 c^4 - b c^5 - c^6) + a^5 (b^2 - c^2)^2 (18 b^6 - 7 b^5 c + 22 b^4 c^2 - 6 b^3 c^3 + 14 b^2 c^4 - 7 b c^5 + 2 c^6) + a^9 (28 b^6 - 7 b^5 c + 16 b^4 c^2 - 12 b^3 c^3 + 20 b^2 c^4 - 7 b c^5 + 12 c^6) - 2 a^8 (4 b^7 + 2 b^6 c + 3 b^5 c^2 - b^4 c^3 + 4 b^3 c^4 - 2 b^2 c^5 + 6 c^7) - 4 a^7 (8 b^8 - 2 b^7 c + b^6 c^2 - 2 b^5 c^3 - 2 b^3 c^5 + 5 b^2 c^6 - 2 b c^7 + 2 c^8) + 4 a^6 (3 b^9 - b^8 c + b^7 c^2 - 2 b^6 c^3 + b^5 c^4 - 3 b^4 c^5 + 3 b^3 c^6 - 4 b^2 c^7 + 2 c^9)): : |
| 26908 | a (-2 a^12 c^3 + 2 b^4 (b - c)^5 c^2 (b + c)^4 + a^13 (2 b^2 + b c + 2 c^2) + 2 a^2 b^2 (b^2 - c^2)^4 (b^3 - 2 b^2 c - b c^2 - c^3) + a b c (b^2 - c^2)^4 (b^4 - 4 b^3 c - 2 b^2 c^2 - c^4) - 2 a^11 (6 b^4 + 4 b^3 c + 5 b^2 c^2 + 3 b c^3 + 4 c^4) - 2 a^3 b (b^2 - c^2)^3 (2 b^5 + 4 b^4 c - b^3 c^2 + 3 b^2 c^3 - b c^4 + c^5) + 2 a^10 (b^5 - 2 b^4 c - b^3 c^2 - b^2 c^3 + 4 c^5) + a^9 (28 b^6 + 23 b^5 c + 16 b^4 c^2 + 18 b^3 c^3 + 20 b^2 c^4 + 13 b c^5 + 12 c^6) + 2 a^8 (-4 b^7 + 8 b^6 c + 5 b^5 c^2 + 5 b^4 c^3 + 4 b^3 c^4 + 4 b^2 c^5 - 6 c^7) - 2 a^4 (b^2 - c^2)^2 (4 b^7 - 8 b^6 c - 2 b^5 c^2 - 5 b^4 c^3 - 4 b^3 c^4 - 2 b^2 c^5 + c^7) - 4 a^7 (8 b^8 + 8 b^7 c + b^6 c^2 + 3 b^5 c^3 + 2 b^3 c^5 + 5 b^2 c^6 + 3 b c^7 + 2 c^8) + 4 a^6 (3 b^9 - 6 b^8 c - 5 b^7 c^2 + b^6 c^3 - 3 b^5 c^4 - 2 b^4 c^5 - 3 b^3 c^6 - 3 b^2 c^7 + 2 c^9) + a^5 (18 b^10 + 23 b^9 c - 14 b^8 c^2 - 12 b^7 c^3 - 12 b^6 c^4 - 10 b^5 c^5 - 4 b^4 c^6 - 4 b^3 c^7 + 10 b^2 c^8 + 3 b c^9 + 2 c^10)): : |
El 6 de abril de 1896, en Atenas (Grecia), se inauguran los I Juegos Olímpicos de la Era Moderna, 1.500 años después de su prohibición por el emperador romano Teodosio I. El barón Pierre de Coubertin, pretende así recuperar los ideales deportivos de la Grecia clásica.
Ab=(a^2 : -b^2 + c (-a + c) : -a c),
Ac=(-a^2 : a b : a b - b^2 + c^2),
Oa=(-a^3 : -b (-a^2 + (b - c)^2 +
a (-b + c)) : -(-a^2 + a (b - c) + (b - c)^2) c).
IaOa: 2 b c x + c (a + b - c) y + b (a - b + c) z=0.
D = (a (a^2 + (b - c)^2 - 2 a (b + c)) : b (a^2 - 2 a b + b^2 + 2 a c +
2 b c - 3 c^2) : c (a^2 - 3 b^2 + 2 a (b - c) + 2 b c + c^2)).
(a/(3 a^2 - 2 a (b + c)- (b - c)^2) : ... : ...).
El de ABC y DEF es:b (-a + b - c) (a + b - c) c x + a (a - b - c) (a + b - c) c y + a b (a - b - c) (a - b + c) z = 0,
que pasa por pos centros Xi, para i∈{650, 663, 861, 2340, 3689, 3900, 4041, 4105, 4162, 4433, 4435, 4477, 4814, 4895, 4959, 6603, 6608, 8611, 10397, 14392, 33969}.El 30 de marzo de 1853 nació Vicent van Gogh, pintor holandés, cuyos cuadros se consideran postimpresionistas, su estilo fue tomado como ejemplo en el desarrollo posterior del abstracto, fauvista y expresionista.
[ =c^2 (a^2+b^2-c^2)/(b^2 (-a^2+b^2-c^2)) ].
Cuando las rectas paralelas dadas varían, el punto A' recorre una circunferenciaAb = (a^2 (-1 + t) t : -b^2 (-1 + t) : c^2 t),
y entonces:Ac = (a^2 (c^2 + a^2 (-1 + t) - b^2 (-1 + t)) (-1 + t) : -(c^2 + a^2 (-1 + t)) (c^2 + a^2 (-1 + t) - b^2 (-1 + t)) : -c^2 (c^2 + a^2 (-1 + t)) (-1 + t)).
Obteniéndose:
A' = (a^2 (a^2-b^2-c^2) (-b^2+c^2+a^2 (-1+t)) (-1+t) :
c^6-b^6 (-1+t)+2 b^4 c^2 (-1+t)-a^6 (-1+t)^2-b^2 c^4 t+a^4 c^2 (3-4 t+t^2)+a^2 (b^4 (-1+t) t-b^2 c^2 (-1+t) t+c^4 (-3+2 t)) :
c^2 (-a^4 (-1+t)^2+(b^2-c^2) (-c^2 (-1+t)+b^2 t)+a^2 (b^2 (-1+t-t^2)+c^2 (2-3 t+t^2)))).
gN2 = ( a^2/((b^2 - c^2)^2 - a^2 (b^2 + c^2))^2 : ... : ...),
que tiene números de búsqueda en (1.95048335767224, 3.92784392504975, 0.0211648302550592).El 26 de marzo de 1913 nació Natalicio de Paul Erdős, matemático húngaro inmensamente prolífico y famoso por su excentricidad que, con cientos de colaboradores, trabajó en problemas sobre combinatoria, teoría de grafos, teoría de números, análisis clásico, teoría de aproximación, teoría de conjuntos y probabilidad. Su vida fue documentada en la película "N es un número: El retrato de Paul Erdős", hecha mientras él todavía estaba vivo, y el libro "El hombre que solo amaba a los números" (1998).
W1 = ( a (a^3 (b+c)+3 a (b-c)^2 (b+c)-(b-c)^2 (b^2-4 b c+c^2)-a^2 (3 b^2+4 b c+3 c^2)) : ... : ...),
que tiene números de búsqueda en (1.16362607785634, 1.22659354531071, 2.25442614537404).W4 = ( (a^4-(b^2-c^2)^2) (b^2 c^2 (b^2-c^2)^2+2 a^6 (b^2+c^2)-3 a^4 (b^2+c^2)^2+a^2 (b^6-5 b^4 c^2-5 b^2 c^4+c^6)) : ... : ...),
que tiene números de búsqueda en ETC (6.47220107285024, 8.49069141822153, -5.22467622586910).Joseph Liouville nació el 24 de marzo de 1809, matemático francés, demostró que las longitudes de las tangentes trazadas desde un punto a una cónica, son proporcionales a las raíces cúbicas de los radios de curvatura de la cónica en los correspondientes puntos de tangencia. Estudió las superficies de revolución de curvatura constante. Prosiguió las investigaciones de Gauss y Jacobí acerca de los triángulos geodésicos, las coordenadas geodésicas polares y la representación conforme.
a^2 y z+b^2 z x+c^2 x y-c(x+y+z) ( c y+ bz)/2 = 0.
Su centro es:Oac = (2 a^4 + (b - c)^2 c (b + c) - a^2 (2 b^2 + b c + 3 c^2): b (2 b^3 - b^2 c - c^3 + a^2 (-2 b + c)): c^2 (-a^2 - 3 b^2 + 2 b c + c^2)),
y el segundo punto de intersección con AC es A2 =(-c : 0 : -2 b + c).a^2 y z+b^2 z x+c^2 x y-b(x+y+z) ( c y+ bz)/2 = 0.
Su centro es:Oab = ( -2 a^4 - b (b - c)^2 (b + c) + a^2 (3 b^2 + b c + 2 c^2) : -b^2 (-a^2 + b^2 + 2 b c - 3 c^2) : c (b^3 - a^2 (b - 2 c) + b c^2 - 2 c^3)}),
y el segundo punto de intersección con AB es A3 =(-b : b - 2 c : 0).Ab = (a^4 - 2 a^2 c^2 - (b - c)^3 (b + c) : b (2 b^3 - 3 b^2 c + 2 b c^2 - c^3 + a^2 (-2 b + c)) : b c (-a^2 + b^2 - 4 b c + 3 c^2)}),
y a la perpendicular por A3 a AB en:Ac = (a^4 - 2 a^2 b^2 - (-b + c)^3 (b + c) : b c (-a^2 + 3 b^2 - 4 b c + c^2) : c (-b^3 + a^2 (b - 2 c) + 2 b^2 c - 3 b c^2 + 2 c^3)).
Los puntos Bc y Ba, Ca y Cb, se definen cíclicamente.45 aniversario del nacimiento de mi hija Marta
(u (v - w)^2 : v (u - w)^2 : w(u - v)^2),
que está en la si y solo si u^2v+uv^2+u^2w-6uvw+v^2w+uw^2+vw^2=0.
ℳ[1,1] = 0,
ℳ[1,2] = u (u + v) (v + w) ,
ℳ[1,3] = u (u + w) (v + w).
λ = (u + v) (u + w) (v + w),
esPo = (u (v + w) : v (u + w) : (u + v) w).
Po es el complemento del de P y también el de G y P.P'=σ(P) = (u (v + w) (v (u + v) + w (u + w)) : ... : ...).
Este punto es la reflexión de Q en P, donde Q está definido en:σ(X3) = ( a^2 (a^2-b^2-c^2) (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+a^6 c^2-3 a^2 b^4 c^2+2 b^6 c^2-3 a^4 c^4-3 a^2 b^2 c^4-2 b^4 c^4+3 a^2 c^6+2 b^2 c^6-c^8) : ... : ...),
que tiene números de búsqueda en (-66.2015389592357, 33.2392913887276, 11.1834038093587).σ(X5) = ( (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (2 a^4-3 a^2 b^2+b^4-3 a^2 c^2-2 b^2 c^2+c^4) (a^8-4 a^6 b^2+6 a^4 b^4-4 a^2 b^6+b^8-4 a^6 c^2+3 a^4 b^2 c^2+4 a^2 b^4 c^2-3 b^6 c^2+6 a^4 c^4+4 a^2 b^2 c^4+4 b^4 c^4-4 a^2 c^6-3 b^2 c^6+c^8) : ... : ...),
que tiene números de búsqueda en ETC (57.0171130987073, -32.8481460917056, 0.0660980383002817).El 14 de marzo de 1882 nació Waclaw Sierpinski, matemático polaco. Trabajó en teoría de conjuntos, la teoría de números, la topología y la teoría de funciones. Tres conocidos fractales llevan su nombre: el triángulo de Sierpinski, la alfombra de Sierpinski y la curva de Sierpinski. También los números de Sierpinski en teoría de números han sido nombrados así en su honor.
V = (a^4 (u+v) (u+w) (-4 v w+u (v+w))-2 a^2 u^2 (v+w) (b^2 (u+v)+c^2 (u+w))+(b^2-c^2) u (v+w) (-c^2 (u+3 v) (u+w)+b^2 (u+v) (u+3 w)): ... : ...).
Pares de centros del triángulo {P=Xi, V=Xj}, para los índices {i, j}: {2, 381}, {4, 4}, {5, 31868}, {7, 4312}, {8, 5881}, {20, 5925}, {69, 5921}, {110, 9934}, {189, 5923}, {253, 5922}, {329, 5924}.k = (a^2+b^2+c^2)/(2√3S).
La matriz ℳ asociada de la transformación afín σ, que aplica ABC en A'B'C', tiene las entradas (las demás se deducen cíclicamente):
ℳ[1,1] = 3 a^4 + 3 a^2 b^2 - 2 b^4 + 3 a^2 c^2 + 4 b^2 c^2 - 2 c^4,
ℳ[1,2] = -(b - c) (b + c) (a^2 + 3 b^2 - c^2),
ℳ[1,3] = (b - c) (b + c) (a^2 - b^2 + 3 c^2).
λ = 3 (-a + b + c) (a + b - c) (a - b + c) (a + b + c).
Otra propiedad: La recta Xσ(X), cuando X recorre la hipérbola de Kiepert de ABC, es tangente en X'=σ(X) a la hipérbola de Kiepert de A'B'C'.El 4 de marzo de 1918, en la base militar de Fort Riley, Kansas, EE.UU., se registra el primer caso de Gripe Española. En total, el 2,5% de la población mundial perecerá y un 20% padecerá este virus.
ℳ[1,1] = -a^2 v (b^2 u^2+a^2 u v+b^2 u v-c^2 u v+a^2 v^2) w (c^2 u^2+a^2 u w-b^2 u w+c^2 u w+a^2 w^2),
ℳ[1,2] = u (b^2 u^2+a^2 u v+b^2 u v-c^2 u v+a^2 v^2) (c^2 u+a^2 w) (c^2 v^2-a^2 v w+b^2 v w+c^2 v w+b^2 w^2),
ℳ[1,3] = u (b^2 u+a^2 v) (c^2 u^2+a^2 u w-b^2 u w+c^2 u w+a^2 w^2) (c^2 v^2-a^2 v w+b^2 v w+c^2 v w+b^2 w^2).
λ = (b^2 u^2 + a^2 u v + b^2 u v - c^2 u v + a^2 v^2) (c^2 u^2+ a^2 u w- b^2 u w + c^2 u w + a^2 w^2) (c^2 v^2 - a^2 v w + b^2 v w + c^2 v w + b^2 w^2),
ℓ esPo = (u (b^2 u + a^2 v) (c^2 u + a^2 w) (c^2 v (v + w) + b^2 w (v + w)-a^2 v w ) : ... : ...).
Si ℓ es una recta que pasa por P, sea ℓ'=σ(ℓ). La aplicación afín σ induce una proyectividad σℓ:ℓ→ℓ'; sea pℓ su eje de perspectividad.Q = (1/(b^6 u (u+v) w^2+c^2 (-a^2+c^2) v^2 (u+w) (c^2 u+a^2 w)+b^4 w (c^2 u (-u^2+u v+v (v-2 w))+a^2 (-u^2+v^2) w)+b^2 v (-a^4 (u+v) w^2+c^4 u (-u^2+u w+w (-2 v+w))+a^2 c^2 w (-2 u^2+v^2+w^2+u (v+w)))) : ... : ...).
Pares {P=Xi, Q=Xj} de centros que figuran actualmente en , para los índices {i, j}: {1, 104}, {2, 6325}, {4, 74}, {6, 6323}, {15, 2378}, {16, 2379}, {30, 477}, {36, 953}, {54, 32749}, {186, 477}, {187, 9831}, {371, 32437}, {372, 32434}, {511, 2698}, {512, 2698}, {513, 953}, {514, 2724}, {515, 2734}, {516, 2724}, {517, 953}, {518, 28914}, {522, 2734}, {523, 477}, {524, 6093}, {526, 16169}, {1154, 15907}, {1157, 6345}, {1499, 6093}, {1510, 15907}, {2574, 74}, {2575, 74}, {3307, 104}, {3308, 104}, {3309, 28914}, {3413, 98}, {3414, 98}, {5663, 16169}.El 3 de marzo de 1919 nación Alekséi Vasílievich Pogorélov, matemático soviético y ucraniano. Es conocido por sus contribuciones a la geometría convexa y diferencial. Fue también autor de numerosas monografías de investigación, así como libros de texto. Pogorelov demostró en 1949 que ninguna superficie convexa cerrada se puede deformar como un todo conservando su convexidad.
σ(t)=t'=- (a+b+c)(a^2+(b-c)^2-2a(b+c))/(3(a^3-a^2(b+c)+(b-c)^2(b+c)-a(b^2+c^2-2b c(1+t)))).
Como las rectas ℒ y ℒ' se cortan en X57 yIX57:X57O = 2 (a + b - c) (a^2 - 2 a b + b^2 - c^2) /(-a^3 + a^2 (b + c) - (b - c)^2 (b + c) + a (b + c)^2),
se tiene que:Gσ(X57):σ(X57)Ge=-((a^3-a^2 b-a b^2+b^3-a^2 c-2 a b c-b^2 c-a c^2-b c^2+c^3)/(3 (a-b-c) (a+b-c) (a-b+c))).
De aquí se deduce que σ(X57)=X1145, punto de tangencia de ℒ' y 𝒞.σ(t)= IX57:X57O= -(((a-b-c) (a+b+c) (a^2+(b-c)^2-2 a (b+c)))/(3 (a+b-c) (a-b+c) (-a+b+c)^2)),
se obtiene para t=0; es decir, se trata del incentro, que es, por tanto, el punto de tangencia de ℒ y 𝒞.
𝔖abc xyz
b^2 c^2 (b-c)^2(a-b-c)^2 (2 a^2-a (b+c)-(b-c)^2)^2x^2
-2 a^2b c (a-b)(a-c) (a+b-c) (a-b+c) (a^4-a^3 (b+c)+a^2 (b^2-b c+c^2)-3 a (b-c)^2 (b+c)+(b-c)^2 (2 b^2+3 b c+2 c^2))y z = 0.
W = ( a (-2 a^5+4 a b (b-c)^2 c+3 a^4 (b+c)+2 a^3 (b^2-5 b c+c^2)+a^2 (-4 b^3+5 b^2 c+5 b c^2-4 c^3)+(b-c)^2 (b^3+c^3)) : ... : ...),
que tiene números de búsqueda en (11.4186534661763, 11.6881293515845, -9.72126513050165).El 28 de febrero de 1803 nació Christian Heinrich von Nagel, matemático alemán. Publicó varios artículos en los que estudió varios puntos en un triángulo que se obtinen como la intersección de tres rectas concurrentes. Es más famoso por uno de estos puntos de intersección que hoy se llama el punto Nagel. Este se construye de una manera sencilla. En un triángulo ABC, sea s su semiperímetro, esto es la mitad de la suma de las longitudes de los tres lados. Comenzando en A, se recorre una distancia s alrededor del triángulo hasta un punto A' sobre BC. De manera similar, comenzando en B, se recorre una distancia s alrededor del triángulo hasta un punto B' en AC y comenzando en C se recorre una distancia s alrededor del triángulo hasta un punto C' en AB. Entonces las líneas AA', BB', CC' son concurrentes en Na, el punto Nagel. Hay otra forma de construir A', B', C' ya que son los puntos donde los tres excirculos tocan a los segmentos BC, CA y AB, respectivamente.
b^2 c^2 v w x y + b^2 c^2 w^2 x y + c^4 v^2 y^2 + b^2 c^2 v w y^2 - b^2 c^2 v^2 x z - b^2 c^2 v w x z - a^2 c^2 v^2 y z + c^4 v^2 y z + a^2 b^2 w^2 y z - b^4 w^2 y z - b^2 c^2 v w z^2 - b^4 w^2 z^2 = 0.
La ecuación de la tangente en Qa a Γa es:
ta: b^2 c^2 (v+w) (-c^2 v^2+b^2 w^2) x
+c^2 v (-a^2 c^2 v^2+(c^2 v+b^2 w)^2) y
-b^2 w (c^4 v^2+2 b^2 c^2 v w+b^2 (-a^2+b^2) w^2) z = 0.
𝔖abc xyz a^4 (b^2 + c^2-a^2) y z (c y - b z) (c y + b z) = 0,
esta última es la ecuación de la cuártica Euler-Morley (Q002).W6 = ( a^6 - a^2 (b^4 + 16 b^2 c^2 + c^4)+ 4 b^2 c^2 (b^2 + c^2) : ... : ...),
que tiene números de búsqueda en (-11.2432285470671, 7.81672079938954, 3.41827095020723).𝔖abc xyz 4 b^2 (b-c)^2 c^2 (b+c)^2 x^4+2 b^2 c^2 (11 a^4+b^4-2 b^2 c^2+c^4+a^2 (24 b^2+24 c^2)) x^2 y z+a^2 (a^6+12 b^4 c^2+12 b^2 c^4+a^4 (-2 b^2-2 c^2)+a^2 (b^4+38 b^2 c^2+c^4)) y^2 z^2+4 a^2 y z (c^2 (a^4+a^2 (5 b^2-2 c^2)+c^2 (3 b^2+c^2)) y^2+b^2 (a^4+b^2 (b^2+3 c^2)+a^2 (-2 b^2+5 c^2)) z^2) = 0.
= 0)En Madrid, a las 18:24 horas de 23 de Febrero de 1981, un numeroso grupo de guardias civiles a cuyo mando se encontraba el teniente coronel Antonio Tejero asaltó el Palacio de las Cortes durante la votación para la investidura del candidato a la Presidencia del Gobierno, Leopoldo Calvo-Sotelo, y anuncia a los guardias que lo custodian que "La II, III, IV y V Región Militar han dicho sí al teniente general Milans del Bosch como Presidente del Gobierno". Los diputados y el Gobierno de España al completo fueron secuestrados en su interior. La ciudad de Valencia fue ocupada militarmente, en virtud del estado de excepción proclamado por el teniente general Jaime Milans del Bosch, capitán general de la III región militar. Dos mil hombres y cincuenta carros de combate fueron desplegados en las calles de la ciudad.
A1 = (a c t - b (-a t + c (1 + t)^2) : -a b t : -a c t),
A2 = (a^2 (a - b - c) t (1 + t) :
a (-a^2 + c^2) t + b^3 t (1 + t) - b^2 (c + a t^2 - c t^2) -
b c (a (-1 + t) t + c (1 + t)) : t (-a^3 t + c (b + c) (1 + t) (c - b t) + a (b + c) (-c + b t))).
Oa = (a^2 (c (1 + t) + t (-2 a + b + b t)) : a^3 t + a (b^2 - c^2) t + a^2 b (1 + t) - b^2 (b - c) (1 + t)^2 : a^3 t - a b^2 t + a c^2 t + a^2 c t (1 + t) + b c^2 (1 + t)^2 - c^3 (1 + t)^2).
El lugar geométrico de Oa, cuando M recorre la recta BC, es una parábola,da: (a^5 + a^4 (b + c) + 2 (b - c)^2 (b + c)^3 - a^3 (b^2 + 3 b c + c^2) - a^2 (3 b^3 + b^2 c + b c^2 + 3 c^3))x + a^2 (a^3 - a^2 (b + c) + (b + c)^3 - a (b^2 + 3 b c + c^2))y + a^2 (a^3 - a^2 (b + c) + (b + c)^3 - a (b^2 + 3 b c + c^2))z = 0.
Procediendo cíclicamente, se obtienen las ecuaciones de las directrices db y dc de las parábolas 𝒫b y 𝒫c, respectivamente.Z = ( a^2(a+b)(a+c)(a^3-a^2(b+c)-a(b^2+3b c+c^2)+(b+c)^3) : ... : ...),
que tiene números de búsqueda en (6.48121975901121, 3.65247178598485, -1.87930202793338).El 20 de febrero de 1931 nació John Milnor, matemático estadounidense conocido por sus trabajos en la topología diferencial y sistemas dinámicos. Ha sido galardonado con el premio Abel 2011, la medalla Fields en 1962 (por sus estudios relacionado con al estructura de ciertas esferas 7-dimensionales) y otros premios importantes en el ámbito de las Matemáticas. El nombre de Milnor aparece entre otros en: número de Milnor, fibración de Milnor, bola de Milnor, esferas exóticas deMilnor, invariante de Kervaire-Milnor y torsión de Milnor. Entre sus publicaciones figuran: Differential Topology (1958), Morse Theory (1963).
A2 = (2 c^2 : b^2 : -c^2) A3 = (2 b^2 : -b^2 : c^2)
Ab = (c^2 - b^2 : b^2 : b^2) Ac = (b^2 - c^2 : c^2 : c^2)
A' = ((b^2 - c^2)^2 : 2 b^2 c^2 : 2 b^2 c^2).
M[1,1] = (a^2+b^2)^2 (b^2-c^2)^2 (a^2+c^2)^2,
M[1,2] = 2 a^2 (a^2+b^2)^2 c^2 (b^2+c^2)^2,
M[1,3] = 2 a^2 b^2 (a^2+c^2)^2 (b^2+c^2)^2.
(a^2 (b^2+c^2)^2 : b^2 (c^2+a^2)^2 : c^2(a^2+b^2)^2).
Se tiene que σ(X7794)=X7765. No existen actualmente en otros pares de centros del triangulo que se correspondan mediante σ.El 19 de febrero de 1951 muere en París, el escritor y Premio Nobel de Literatura en 1947, André Gide, defensor de los derechos de los homosexuales. Un año después de su muerte, la Iglesia Católica incluirá sus libros en el Índice de libros prohibidos. Fue inspiración para escritores como Sartre o Camus.
P = (b^2 c^2 (b^2-c^2-3 a^2) : c^2 a^2 (c^2-a^2-3 b^2) : a^2 b^2 (a^2-b^2-3 c^2)).
Sea ℓac el eje (paralelo a BC) de la parábola 𝒫ab,U = (b^2 c^2 (c^2-b^2-3 a^2) : c^2 a^2 (a^2-c^2-3 b^2) : a^2 b^2 (b^2-a^2-3 c^2)).
W = ( (b^2-c^2)(3 a^4 - 3 a^2 (b^2 + c^2)- 2 b^2 c^2 ) : ... : ...),
que tiene números de búsqueda en (-16.6361942772876, 14.0432196871557, 1.59667898031707).El 15 de febrero de 1847 fallece Germinal Pierre Dandelin (a los 52 años de edad), matemático francés. El teorema de Dandelin en geometría, descubierto en 1822, demuestra que si un cono es cortado por un plano en una cónica, los focos de dicha cónica son los puntos donde este plano es tocado por las esferas inscritas en el cono.
Ab=(-a^2 w (2 v + w) : c^2 (v + w)^2 + a^2 w (2 v + w) : 0),
Ac=(-a^2 v (v + 2 w) : 0 : b^2 (v + w)^2 + a^2 v (v + 2 w)).
A2 = (-a^2 w (v + w) : -(b^2 - c^2) (v + w)^2 +
a^2 (v^2 + 5 v w + 3 w^2) : -a^2 w (2 v + w)),
A3 = (-a^2 v (v + w) : -a^2 v (v + 2 w) : (b^2 - c^2) (v + w)^2 +
a^2 (3 v^2 + 5 v w + w^2)).
A' = ( a^8 (u+v)^2 (u+w)^2-3 c^8 (u^2+4 u v+v^2) (u+w)^2+b^2 c^6 (u+w) (3 u^3+u^2 (19 v-8 w)+8 u v (v-3 w)-4 v^2 w)-3 b^8 (u+v)^2 (u^2+4 u w+w^2)-4 a^6 (u+v) (u+w) (b^2 (u+v) w+c^2 v (u+w))+a^4 (-2 c^4 (3 u^2+5 u v-v^2) (u+w)^2+3 b^2 c^2 (u+v) (u+w) (u^2+4 v w)-2 b^4 (u+v)^2 (3 u^2+5 u w-w^2))+2 b^4 c^4 (6 u^4+7 v^2 w^2+16 u^3 (v+w)+19 u v w (v+w)+u^2 (3 v^2+61 v w+3 w^2))+b^6 c^2 (3 u^4-4 v^2 w^2+4 u v w (-6 v+w)+u^3 (-5 v+19 w)+u^2 (-8 v^2-5 v w+8 w^2))+2 a^2 (2 c^6 (2 u^2+6 u v+v^2) (u+w)^2-b^2 c^4 (u+w) (3 u^3+u^2 (11 v-6 w)+2 u v (2 v-5 w)+2 v^2 w)+2 b^6 (u+v)^2 (2 u^2+6 u w+w^2)-b^4 c^2 (3 u^4+2 v^2 w^2+2 u v w (-5 v+3 w)+u^3 (-3 v+11 w)+u^2 (-6 v^2+v w+4 w^2))) :
b^2 (a^6 (u+v)^2 w (u+w)+b^6 (u+v)^2 w (5 u+w)+c^6 (u+w) (3 v^2 w+u^2 (5 v+3 w)+u v (v+12 w))+b^2 c^4 (u^3 (4 v-13 w)-5 v^2 w^2-u^2 w (36 v+w)-u v w (13 v+12 w))-a^4 (u+v) (-b^2 (u+v) (3 u-w) w+c^2 (u+w) (u (v-w)+3 v w))-b^4 c^2 (-v^2 w^2+2 u v w (-2 v+w)+u^3 (v+11 w)+u^2 (v^2+7 v w+3 w^2))-a^2 (b^4 (u+v)^2 w (9 u+w)+c^4 (u+w) (12 u v w+v^2 w+u^2 (4 v+5 w))-2 b^2 c^2 (2 u v w^2+v^2 w^2+u^3 (v+5 w)+u^2 (v^2+5 v w+w^2)))) :
c^2 (a^6 v (u+v) (u+w)^2+c^6 v (5 u+v) (u+w)^2-b^2 c^4 (u+w) (u v (3 v-4 w)-v^2 w+u^2 (11 v+w))-b^4 c^2 (u^3 (13 v-4 w)+5 v^2 w^2+u v w (12 v+13 w)+u^2 v (v+36 w))-a^4 (u+w) (-c^2 (3 u-v) v (u+w)-b^2 (u+v) (u (v-w)-3 v w))+b^6 (3 v^2 w^2+4 u v w (3 v+w)+u^3 (3 v+5 w)+u^2 (3 v^2+17 v w+w^2))-a^2 (c^4 v (9 u+v) (u+w)^2-2 b^2 c^2 (u+w) (u v^2+v^2 w+u^2 (5 v+w))+b^4 (v^2 w^2+u v w (12 v+w)+u^3 (5 v+4 w)+u^2 v (5 v+16 w))))).
El 12 de febrero de 1984, muere en París el escritor argentino Julio Cortázar, autor de obras como "Bestiario", "Historias de cronopios y de famas" y "Rayuela". Renovó el género narrativo, poniendo especial cuidado en el cuento breve.
Kab = (-(a+b-c) (3 a^2+a b-4 b^2+a c+8 b c-4 c^2) : -b (a+b-c) (-a+b+c) : (a-b-c) (a^2+2 a b-3 b^2+a c+5 b c-2 c^2)),
Ab = (-(a+b-c) (a^2-2 (b-c)^2+a (b+c))^2 : (a+b-c)^3 (a^2-2 a b+b^2-c^2) : (a-b-c) ((b-c)^2-a (b+c))^2).
Kac = ((a-b+c) (3 a^2+a b-4 b^2+a c+8 b c-4 c^2) :-(a-b-c) (a^2+a b-2 b^2+2 a c+5 b c-3 c^2) : c (a-b+c) (-a+b+c)),
Ac = (-(a-b+c) (a^2-2 (b-c)^2+a (b+c))^2 : (a-b-c) ((b-c)^2-a (b+c))^2 : (a-b+c)^3 (a^2-b^2-2 a c+c^2)).
(-a^5+a^4 (b+c)+2 (b-c)^4 (b+c)+a^2 (b+c)^3-4 a (b-c)^2 (b^2+c^2)+a^3 (b^2-6 b c+c^2)) x-(a-b+c) (a^2-2 (b-c)^2+a (b+c))^2 y-(a+b-c) (a^2-2 (b-c)^2+a (b+c))^2 z = 0.
Procediendo cíclicamente, se obtienen las ecuaciones de las rectas ℓb=BcBa y ℓc=CaCb.Z = ( (a^2+a b-2 b^2+a c+4 b c-2 c^2)^2 /((a-b-c)(a^4-2 a^2 (b^2-4 b c+c^2)-3 a (b-c)^2 (b+c)+3 (b-c)^4+a^3 (b+c))) : ... : ...),
que tiene números de búsqueda en (0.658096887691987, 0.734894512322484, 2.82815433290328).W = ( (a^4+a^3 b-2 a^2 b^2-3 a b^3+3 b^4+a^3 c+8 a^2 b c+3 a b^2 c-12 b^3 c-2 a^2 c^2+3 a b c^2+18 b^2 c^2-3 a c^3-12 b c^3+3 c^4) (6 a^7-24 a^6 b+31 a^5 b^2-5 a^4 b^3-20 a^3 b^4+14 a^2 b^5-a b^6-b^7-24 a^6 c+66 a^5 b c-52 a^4 b^2 c+2 a^3 b^3 c+6 a^2 b^4 c+4 a b^5 c-2 b^6 c+31 a^5 c^2-52 a^4 b c^2+36 a^3 b^2 c^2-20 a^2 b^3 c^2-7 a b^4 c^2+12 b^5 c^2-5 a^4 c^3+2 a^3 b c^3-20 a^2 b^2 c^3+8 a b^3 c^3-9 b^4 c^3-20 a^3 c^4+6 a^2 b c^4-7 a b^2 c^4-9 b^3 c^4+14 a^2 c^5+4 a b c^5+12 b^2 c^5-a c^6-2 b c^6-c^7) : ... : ...),
que tiene números de búsqueda en ETC (1.03827473220076, 0.994977505348996, 2.47263017872703).Ka = (2 a^2 + a (b + c)- 3 (b - c)^2 : b (-a + b + c) : c (-a + b + c)).
Los puntos de Brocard de AB'C' son:
A1 = (-(a+2 b-c)^2 (a-b+c):-b^2 (-a+b+c):a^3-a (b-c)^2-a^2 (b+c)+(b-c)^2 (b+c)),
A2 = (-(a+b-c) (a-b+2 c)^2:a^3-a (b-c)^2-a^2 (b+c)+(b-c)^2 (b+c):(a-b-c) c^2}).
(a^3+b^3-2 b^2 c-2 b c^2+c^3-a^2 (b+c)-a (b^2-3 b c+c^2)) x+
(a^3+b^3-a^2 (b-3 c)-6 b^2 c+8 b c^2-3 c^3-a (b^2-3 b c+c^2)) y+
(a^3-3 b^3+8 b^2 c-6 b c^2+c^3-a^2 (-3 b+c)-a (b^2-3 b c+c^2)) z = 0.
T = ( a(a+b-c) (a-b+c) (4 a-5 b-5 c) (2 a^2-2 b^2+5 b c-2 c^2) : ... : ...),
que tiene números de búsqueda en ETC (0.582917746259555, 0.578721360173314, 2.97097227274460).El 10 de febrero de 1886, nació Pia Nalli, matemática italiana, catedrática de la Universidad de Catania. Conocida por su trabajo en sumabilidad de series de Fourier. A partir de 1928 se dedica casi exclusivamente al cálculo diferencial absoluto, manteniendo una estrecha correspondencia con Tullio Levi-Civita, quien fue el creador de ese cálculo con Gregorio Ricci.
Q = (a^2 (a^2 - b^2 - c^2) (v + w) /(a^4 v w (u + v + w) - a^2 (b^2 w (v (v + w) + u (3 v + w)) + c^2 v (w (v + w) + u (v + 3 w))) + u (b^4 w (2 v + w) + c^4 v (v + 2 w) + 2 b^2 c^2 (v^2 + 3 v w + w^2))):...:...).
El único par {P, Q} que consta de centros del triángulo, listados actualmente en , es {X1176, X9969}.
Q2 = ( a^2(a^2-b^2-c^2)/(3a^4-6a^2b^2+3b^4-6a^2c^2+10b^2c^2+3c^4) : ... : ...) =
( : ... : ...),
W = ((a^4 v w (u+v+w)-a^2 (b^2 w (v (v+w)+u (3 v+w))+c^2 v (w (v+w)+u (v+3 w)))+u (b^4 w (2 v+w)+c^4 v (v+2 w)+2 b^2 c^2 (v^2+3 v w+w^2)))
(a^8 v (2 u+v) w (2 u+w)+a^6 (c^2 v (4 u^3+v w^2+u w (4 v+w)+2 u^2 (v+3 w))+b^2 w (4 u^3+v^2 w+2 u^2 (3 v+w)+u v (v+4 w)))-a^4 (b^4 w (4 u^3+2 v^2 w+u^2 (12 v+w)+u v (5 v+4 w))+c^4 v (4 u^3+2 v w^2+u w (4 v+5 w)+u^2 (v+12 w))-b^2 c^2 (3 u^4+5 v^2 w^2+9 u^3 (v+w)+12 u v w (v+w)+u^2 (3 v^2+32 v w+3 w^2)))-a^2 (b^2-c^2) u (-c^4 v (u^2+u v+2 (v-w) w)+b^4 w (u^2+u w+2 v (-v+w))+b^2 c^2 (v-w) (2 u^2+5 v w+2 u (v+w)))+(b^2-c^2)^3 u^2 (b^2 (u+2 v) w-c^2 v (u+2 w))) : ... : ...).
El teorema de Johnson establece que si tres círculos iguales se cortan mutuamente en un solo punto, entonces el círculo que pasa por sus otros tres puntos de intersección por pares de estos círculos es congruente con los tres círculos originales. Se dice que el matemático rumano Gheorghe Titeica (4 de Octubre de 1873 - 5 de Febrero de 1939) lo descubrió accidentalmente mientras dibujaba círculos con una moneda rumana de 5 lei en 1908 (Problema piesei de cinci lei), y lo propuso el mismo año en un concurso organizado por Rumanian Mathematical Gazette.
Ab = BC∩DF, Ac = BC∩DE,
Bc = CA∩ED, Ba = CA∩EF,
Ca = AB∩FE, Cb = AB∩FD.
W = ( a^2 (2 a^4-2 a^2 (b^2+c^2)-b^4-5 b^2 c^2-c^4) : ... : ...),
que tiene números de búsqueda en ETC (2.90899278978645, 2.94744112903368, 0.257516258828851).Z = ( a^2 (a^6 - 10 a^4 (b^2 + c^2) + a^2 (11 b^4 + 12 b^2 c^2 + 11 c^4) - 2 (b^6 - 4 b^4 c^2 - 4 b^2 c^4 + c^6)) : ... : ...),
que tiene números de búsqueda en (5.53925573925679, 4.94898645135094, -2.34213647945402).T = ( a^2(5 a^4 - 7 a^2 (b^2 + c^2) + 2 (b^4 - 5 b^2 c^2 + c^4)) : ... : ...),
que tiene números de búsqueda en ETC (2.72974481480487, 2.81103919783837, 0.434678199647871).
El 1 de febrero de 1894 nace John Ford, actor, director y productor cinematográfico estadounidense.
En los años treinta cuando las películas de Hollywood mostraban a los indios como salvajes, era un éxito. Desde entonces, los nativos pasaron a aparecer en el cine como seres brutales.
John Ford ya había rodado una película en estos términos, "El caballo de hierro", en 1924, en la que los blancos construían el ferrocarril, eran la civilización, ante la amenaza de los indios, los salvajes.
El paradigma de este modelo de película fue "La diligencia", en 1939, de John Ford. «Una de las que más daño ha hecho a la imagen de los nativos a lo largo de la historia». La diligencia atraviesa el lado salvaje de Norteamérica acosada por los nativos. Los indios son unos salvajes que impiden el progreso. Están atrasados y son sanguinarios.
Son asesinos, depredadores que atacan en manada la diligencia hasta que llega el 7º de caballería, los arrasan en una nube de polvo, y se acabó.
HA1/AtD = HB1/BtE = HC1/CtF = t.
Sea PaPbPc el de un punto P.
Q = ((a^4 (b^2 (u+v)+c^2 (u+w)))-2 a^2 (b^4 (u+v)+c^4 (u+w)-b^2 c^2 (v+w))+(b^2-c^2)^2 (b^2 (u+v)+c^2 (u+w))
(a^6 (2 v w+u (v+w))+a^4 u (c^2 (u+v-2 w)+b^2 (u-2 v+w))-a^2 (-4 b^2 c^2 v w+c^4 (2 u^2+u v-u w+2 v w)+b^4 (2 u^2-u v+u w+2 v w))+(b^2-c^2)^2 u (c^2 (u-v)+b^2 (u-w))) : ... : ...).
𝔖abc xyz b^2 c^2 (-b^4 + c^4 + a^2 (b^2 - c^2))^2 (4 a^20 + b^2 c^2 (b^2 - c^2)^8 - 16 a^18 (b^2 + c^2) + 8 a^16 (2 b^4 + 9 b^2 c^2 + 2 c^4) + 8 a^14 (2 b^6 - 13 b^4 c^2 - 13 b^2 c^4 + 2 c^6) + 2 a^4 (b^2 - c^2)^4 (2 b^8 + 5 b^6 c^2 + 12 b^4 c^4 + 5 b^2 c^6 + 2 c^8) - 4 a^12 (10 b^8 - 5 b^6 c^2 - 51 b^4 c^4 - 5 b^2 c^6 + 10 c^8) + a^8 (b^2 + c^2)^2 (16 b^8 - 111 b^6 c^2 + 194 b^4 c^4 - 111 b^2 c^6 + 16 c^8) - 4 a^6 (b^2 - c^2)^2 (4 b^10 + b^8 c^2 - 11 b^6 c^4 - 11 b^4 c^6 + b^2 c^8 + 4 c^10) + 4 a^10 (4 b^10 + 21 b^8 c^2 - 35 b^6 c^4 - 35 b^4 c^6 + 21 b^2 c^8 + 4 c^10))x^2 -2 a^2 b^2 c^2 (a^2 - b^2)(a^2 - c^2) (a^22 - 2 a^20 (b^2 + c^2) - 2 (b^2 - c^2)^8 (b^2 + c^2)^3 - 2 a^18 (2 b^4 - 7 b^2 c^2 + 2 c^4) + 2 a^16 (4 b^6 - 5 b^4 c^2 - 5 b^2 c^4 + 4 c^6) - 2 a^12 (b^2 - c^2)^2 (21 b^6 - 4 b^4 c^2 - 4 b^2 c^4 + 21 c^6) + a^2 (b^2 - c^2)^6 (6 b^8 - 6 b^6 c^2 - 25 b^4 c^4 - 6 b^2 c^6 + 6 c^8) + a^10 (b^2 - c^2)^2 (14 b^8 + 80 b^6 c^2 - 103 b^4 c^4 + 80 b^2 c^6 + 14 c^8) + a^14 (16 b^8 - 60 b^6 c^2 + 89 b^4 c^4 - 60 b^2 c^6 + 16 c^8) - a^6 (b^2 - c^2)^4 (33 b^8 + 32 b^6 c^2 - 69 b^4 c^4 + 32 b^2 c^6 + 33 c^8) + 2 a^4 (b^2 - c^2)^4 (2 b^10 + 23 b^8 c^2 - 17 b^6 c^4 - 17 b^4 c^6 + 23 b^2 c^8 + 2 c^10) + 2 a^8 (b^2 - c^2)^2 (17 b^10 - 58 b^8 c^2 + 33 b^6 c^4 + 33 b^4 c^6 - 58 b^2 c^8 + 17 c^10))y z = 0.
)T = ( a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^8 (b^2+c^2)-2 a^6 (2 b^4+b^2 c^2+2 c^4)+6 a^4 (b^6+c^6)+a^2 (-4 b^8+2 b^6 c^2+2 b^2 c^6-4 c^8)+b^10-b^8 c^2-b^2 c^8+c^10) : ... : ...),
que tiene números de búsqueda en (0.730887315161516, 0.514920822362869, 2.94684822865862).El 28 de enero de 1540, nació Ludolph van Ceulen matemático alemán. Es conocido principalmente por haber calculado el valor de π, utilizando esencialmente el mismo método con el que Arquímedes había obtenido 35. De hecho, este número fue conocido en el continente durante mucho tiempo como número ludolphino
Tab = ((a^2+b^2-c^2) (4 a^6 b^2-2 a^2 (b^2-c^2)^3-(b^2-c^2)^4-a^4 (b^2+c^2)^2) :
-4 a^2 b^2 (a^2+b^2-c^2) (a^4-b^4-2 a^2 c^2+c^4) :
-(a^2-b^2-c^2) (-2 a^2 (b^2-c^2)^3-(b^2-c^2)^4+a^4 (3 b^4+2 b^2 c^2-c^4))),
Oab = (-(a^2 + b^2 - c^2)^2 (-(b^2 - c^2)^2 + a^2 (b^2 + c^2)) :
2 a^2 b^2 (a^2 - b^2 - c^2) (a^2 + b^2 - c^2) :
-(b^2 - c^2)^4 + a^6 (3 b^2 + c^2) - a^4 (7 b^4 + 2 b^2 c^2 + 3 c^4) +
a^2 (5 b^6 - 3 b^4 c^2 - 5 b^2 c^4 + 3 c^6)).
Ab = (-(b - c) (b + c) (a^2 + b^2 - c^2) : 0 : (b^2 - c^2)^2 - a^2 (b^2 + c^2)).
El punto de tangencia de la otra tangente por C a Γac es:
Tac = ((a^2 - b^2 + c^2) (4 a^6 c^2 + 2 a^2 (b^2 - c^2)^3 - (b^2 - c^2)^4 -
a^4 (b^2 + c^2)^2) :
(a^2 - b^2 - c^2) (-2 a^2 (b^2 - c^2)^3 + (b^2 - c^2)^4 +
a^4 (b^4 - 2 b^2 c^2 - 3 c^4)) :
-4 a^2 c^2 (a^2 - b^2 - c^2) (a^2 - b^2 + c^2)^2).
Oac = ((a^2-b^2+c^2)^2 (-(b^2-c^2)^2+a^2 (b^2+c^2)) :
(b^2-c^2)^4-a^6 (b^2+3 c^2)+a^4 (3 b^4+2 b^2 c^2+7 c^4)+a^2 (-3 b^6+5 b^4 c^2+3 b^2 c^4-5 c^6) :
-2 a^2 c^2 (a^2-b^2-c^2) (a^2-b^2+c^2)).
Ac = ((b - c) (b + c) (-a^2 + b^2 - c^2) : -(b^2 - c^2)^2 + a^2 (b^2 + c^2) : 0).
La recta AbAc pasa por D y es paralela a la tangente en A a la circunferencia circunscrita a ABC.
Ao = (a^8 (b^2 + c^2) + 3 a^4 (b^2 - c^2)^2 (b^2 + c^2) -
a^2 (b^2 - c^2)^2 (b^4 - 4 b^2 c^2 + c^4) -
a^6 (3 b^4 + 4 b^2 c^2 + 3 c^4) :
b^2 (-a^8 + c^2 (-b^2 + c^2)^3 + a^6 (3 b^2 + 4 c^2) +
a^2 (b^3 - b c^2)^2 - a^4 (3 b^4 + b^2 c^2 + 4 c^4)) :
c^2 (-a^8 + b^2 (b^2 - c^2)^3 + a^6 (4 b^2 + 3 c^2) +
a^2 (-b^2 c + c^3)^2 - a^4 (4 b^4 + b^2 c^2 + 3 c^4))),
A1 = (-a^2 (b^2 - c^2)^2 +
a^4 (b^2 + c^2) : -b^2 (a^2 - c^2) (a^2 - b^2 +
c^2) : -(a^2 - b^2) c^2 (a^2 + b^2 - c^2)).
El 24 de enero de 1977, en Madrid, durante la transición democrática, un grupo de extrema derecha asesina a cinco abogados laboralistas de CCOO. Hecho conocido como la Matanza de Atocha.
((a + b - c) (a - b + c) (b + c)^2 : b^2 (a + b - c) (b + c-a) : c^2 (a - b + c) (b + c-a)).
El punto de intersección A' de las tangentes tb y tb es:A' = (a^2 (-a^2 + (b - c)^2) : b (a + c) (-a^2 + b^2 + 2 a c - c^2) : -(a + b) c (a^2 - 2 a b + b^2 - c^2)).
El centro de la ""W = ( a^2 (b + c) (a^2 - (b - c)^2)(a^2 (b + c) - b c (b + c) - a (b^2 + c^2)) : ... : ...),
que tiene números de búsqueda en (7.15669680131694, 8.08134630993316, -5.25720456403870).El 19 de enero de 1809 nace Edgar Allan Poe, escritor, poeta, crítico y periodista romántico estadounidense, generalmente reconocido como uno de los maestros universales del relato corto, del cual fue uno de los primeros practicantes en su país. Fue renovador de la novela gótica, recordado especialmente por sus cuentos de terror.
a Aye, por su "cumple"
b^2c^2 (b - c)^2 x^2+ c^2 (a^4 + 8 a b^2 c + (-2 b^2 + b c + c^2)^2 - 2 a^2 (2 b^2 + b c + c^2)y^2 + b^2 (a^4 + 8 a b c^2 + (b^2 + b c - 2 c^2)^2 - 2 a^2 (b^2 + b c + 2 c^2) z^2 + 2 b c (a^4 + 4 a b c (b + c) + (b - c)^2 (2 b^2 + 5 b c + 2 c^2) - a^2 (3 b^2 + 4 b c + 3 c^2)) y z + 2 b^2 c (b^3 + 4 a b c - 2 b^2 c - 3 b c^2 + 2 c^3 - a^2 (b + c)) z x + 2 b c^2 (2 b^3 + 4 a b c - 3 b^2 c - 2 b c^2 + c^3 - a^2 (b + c))x y =0,
y su centro es:
Ao = (a^6 + 2 a^3 b c (b + c) -
2 a b (b - c)^2 c (b + c) - (b - c)^4 (b + c)^2 -
a^4 (3 b^2 + b c + 3 c^2) +
a^2 (3 b^4 - b^3 c - 2 b^2 c^2 - b c^3 + 3 c^4) :
b c (a^4 -
2 a^3 b - 2 b^4 + 2 a b (b - c)^2 + 2 b^3 c + b^2 c^2 - 2 b c^3 +
c^4 + a^2 (b^2 + 2 b c - 2 c^2))
b c (a^4 + b^4 - 2 a^3 c -
2 b^3 c + 2 a (b - c)^2 c + b^2 c^2 + 2 b c^3 - 2 c^4 +
a^2 (-2 b^2 + 2 b c + c^2))).
Hoy martes 12 de enero de 2021, el Gobierno irlandés analiza el informe de una investigación sobre las condiciones de vida de madres solteras y bebés internados en 18 instituciones estatales entre 1922 y 1998, se estima
que hasta 9.000 menores fallecieron en casas de acogidas regentadas por órdenes religiosas católicas. El Gobierno estableció la comisión de investigación en 2014, tras el hallazgo ese año de casi 800 esqueletos de niños en cámaras subterráneas de un convento regentado por monjas del Buen Socorro.
Otras investigaciones han relevado en los últimos años los abusos sexuales cometidos por religiosos contra miles de menores durante gran parte del pasado siglo.
Otra pesquisa oficial reveló el comportamiento de las monjas católicas en las llamadas 'Lavanderías de la Madgalena', donde entre 1922 y 1996 miles de internas trabajaron en un régimen de semiesclavitud y abusos.
Las congregaciones a cargo de estas casas eran las Hermanas de Nuestra Señora de la Caridad, la congregación de las Hermanas de la Piedad, las Hermanas Religiosas de la Caridad y las Hermanas del Buen Pastor.
Bc = (a:0:b-a), Cb = (a:c-a:0)
Las rectas BcCb, CaAc, AbBa son paralelas, con punto en el infinito X513, conjugado isogonal de X100 ( del )Γa: c^2 x y - a c y^2- a b z^2 +a(a - b - c) y z +a(b- a )z x -a c x y =0.
El centro de Γa es:
Oa=(a (-a^3 + a^2 (b + c) - (b - c)^2 (b + c) + a (b^2 + c^2)) :
b (-a^3 +
a^2 b - b^3 + a (b - c)^2 + b c^2) : c (-a^3 + a (b - c)^2 + a^2 c +
c (b^2 - c^2))).
ta: a (4 b c - (-a + b + c)^2) x - b (a^2 + b^2 + b c - 2 c^2 + a (-2 b + c)) y + (-2 (a - b) b c + (a - c) c (-a + b + c)) z = 0.
Las ecuaciones de las tangentes tb y tc se obtienen cíclicamente, entonces ta∩tb∩tc=X100.A' = (a (a^2 + (b - c)^2 - 2 a (b + c)) : b (a^2 + b^2 + b c - 2 c^2 + a (-2 b + c)) : c (a^2 - 2 b^2 + a (b - 2 c) + b c + c^2)).
El 8 de enero de 1942 nació Stephen William Hawking, físico teórico, astrofísico, cosmólogo y divulgador científico británico. Sus trabajos más importantes consistieron en aportar, junto con Roger Penrose, teoremas respecto a las singularidades espaciotemporales en el marco de la relatividad general y la predicción teórica de que los agujeros negros emitirían radiación, lo que se conoce hoy en día como radiación de Hawking.
(a^6+a^4(b^2+c^2)+
a^2(b^4+12b^2c^2+c^4)+b^6+c^6+b^4c^2+b^2c^4)x^2y^2z^2 +
𝔖abc xyz
y z(-a^4(b^2+c^2-a^2)y^2z^2-
x^3(c^2((b^2-c^2)(2b^2-c^2)+a^2(2b^2+c^2))y+
b^2((b^2-2c^2)(b^2-c^2)+a^2(b^2+2c^2))z)) = 0,
Que alguien te haga sentir cosas sin ponerte un dedo encima, eso es admirable. Mario Benedetti
Ab = (-a^4 t - (b^2 - c^2)^2 t - a^2 (b^2 - 2 c^2 t) : 0 :
a^4 t + (b^2 - c^2)^2 t - a^2 (2 c^2 t + b^2 (1 + 2 t))),
Ac = (-a^4 t - (b^2 - c^2)^2 t - a^2 (c^2 - 2 b^2 t) :
a^4 t + (b^2 - c^2)^2 t - a^2 (2 b^2 t + c^2 (1 + 2 t)) : 0).
𝔖abc xyz
(b^2 c^2+a^4 t-2 a^2 b^2 t+b^4 t-2 a^2 c^2 t+c^4 t) (-a^2 b^2+a^4 t-2 a^2 b^2 t+b^4 t-2 a^2 c^2 t-2 b^2 c^2 t+c^4 t) (-a^2 c^2+a^4 t-2 a^2 b^2 t+b^4 t-2 a^2 c^2 t-2 b^2 c^2 t+c^4 t)x^2+
2 (-b^2 c^2+a^4 t-2 a^2 b^2 t+b^4 t-2 a^2 c^2 t-2 b^2 c^2 t+c^4 t) (a^4 b^2 c^2+2 a^4 b^2 c^2 t+a^8 t^2-3 a^6 b^2 t^2+4 a^4 b^4 t^2-3 a^2 b^6 t^2+b^8 t^2-3 a^6 c^2 t^2+2 a^4 b^2 c^2 t^2+3 a^2 b^4 c^2 t^2-4 b^6 c^2 t^2+4 a^4 c^4 t^2+3 a^2 b^2 c^4 t^2+6 b^4 c^4 t^2-3 a^2 c^6 t^2-4 b^2 c^6 t^2+c^8 t^2)y z = 0.
Po = ( a^2 (a^4+(b^2-c^2)^2-2 a^2 (b^2+c^2))^2 (a^6 (b^2+c^2)-)-a^4 (3 b^4+2 b^2 c^2+3 c^4)+a^2 (3 b^6-b^4 c^2-b^2 c^4+3 c^6)(b^2-c^2)^2 (b^4+c^4) +
a^2 b^2 c^2 (-2 a^10 (b^2+c^2)+a^8 (9 b^4+16 b^2 c^2+9 c^4)-2 a^6 (8 b^6+11 b^4 c^2+11 b^2 c^4+8 c^6)+2 a^4 (7 b^8-6 b^4 c^4+7 c^8)-6 a^2 (b^2-c^2)^2 (b^6+c^6)+(b^2-c^2)^4 (b^4+c^4))t +
a^4 b^4 c^4 (2 a^6-3 a^4 (b^2+c^2)-10 a^2 b^2 c^2+(b^2-c^2)^2 (b^2+c^2))t^2
-2 a^6 b^6 c^6 t^3 : ... : ...),
Go = (a^2 (a^4 + b^4 - 4 b^2 c^2 + c^4 - 2 a^2 (b^2 + c^2)) (a^10 (b^2 + c^2) - (b^2 - c^2)^4 (b^4 + c^4) - a^8 (5 b^4 + 6 b^2 c^2 + 5 c^4) + a^2 (b^2 - c^2)^2 (5 b^6 - b^4 c^2 - b^2 c^4 + 5 c^6) + 2 a^6 (5 b^6 + 3 b^4 c^2 + 3 b^2 c^4 + 5 c^6) + a^4 (-10 b^8 + 6 b^6 c^2 + 20 b^4 c^4 + 6 b^2 c^6 - 10 c^8)) : ... : ...)
𝔖abc xyz (a^6-3 a^2 b^4+2 b^6-a^4 c^2-4 a^2 b^2 c^2-3 b^4 c^2-a^2 c^4+c^6) (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2-2 a^2 b^2 c^2-b^4 c^2-2 a^2 c^4-b^2 c^4+c^6) (a^6-a^4 b^2-a^2 b^4+b^6-4 a^2 b^2 c^2-3 a^2 c^4-3 b^2 c^4+2 c^6)x^2-2 (2 a^6-3 a^4 b^2+b^6-3 a^4 c^2-4 a^2 b^2 c^2-b^4 c^2-b^2 c^4+c^6) (a^12-2 a^10 b^2-a^8 b^4+4 a^6 b^6-a^4 b^8-2 a^2 b^10+b^12-2 a^10 c^2-3 a^8 b^2 c^2+3 a^6 b^4 c^2+10 a^4 b^6 c^2-7 a^2 b^8 c^2-b^10 c^2-a^8 c^4+3 a^6 b^2 c^4+16 a^4 b^4 c^4+9 a^2 b^6 c^4-5 b^8 c^4+4 a^6 c^6+10 a^4 b^2 c^6+9 a^2 b^4 c^6+10 b^6 c^6-a^4 c^8-7 a^2 b^2 c^8-5 b^4 c^8-2 a^2 c^10-b^2 c^10+c^12)y z = 0.
)( a^2 (a^10 (b^2 + c^2) - a^8 (5 b^4 + 6 b^2 c^2 + 5 c^4) + 10 a^6 (b^6 + b^4 c^2 + b^2 c^4 + c^6) - (b^2 - c^2)^2 (b^8 - b^6 c^2 + 2 b^4 c^4 - b^2 c^6 + c^8) - a^4 (10 b^8 + 3 b^6 c^2 + 6 b^4 c^4 + 3 b^2 c^6 + 10 c^8) + a^2 (5 b^10 - 5 b^8 c^2 + 3 b^6 c^4 + 3 b^4 c^6 - 5 b^2 c^8 + 5 c^10)) : ... : ...),
que tiene números de búsqueda en (-25.3112468940511, 15.3919826743027, 1.02612594581403).𝔖abc xyz (a - b - c) (a + b - c) (a - b + c) (a + b + c) (a^4 - a^2 b^2 + 2 b^4 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2 + 2 c^4) (3 a^6 b^2 - 7 a^4 b^4 + 5 a^2 b^6 - b^8 + 3 a^6 c^2 - 8 a^4 b^2 c^2 - 3 a^2 b^4 c^2 + 4 b^6 c^2 - 7 a^4 c^4 - 3 a^2 b^2 c^4 - 6 b^4 c^4 + 5 a^2 c^6 + 4 b^2 c^6 - c^8)x^2+ 2 (2 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^16 - 8 a^14 b^2 + 28 a^12 b^4 - 56 a^10 b^6 + 70 a^8 b^8 - 56 a^6 b^10 + 28 a^4 b^12 - 8 a^2 b^14 + b^16 - 8 a^14 c^2 + 39 a^12 b^2 c^2 - 67 a^10 b^4 c^2 + 35 a^8 b^6 c^2 + 38 a^6 b^8 c^2 - 67 a^4 b^10 c^2 + 37 a^2 b^12 c^2 - 7 b^14 c^2 + 28 a^12 c^4 - 67 a^10 b^2 c^4 + 36 a^8 b^4 c^4 - 6 a^6 b^6 c^4 + 50 a^4 b^8 c^4 - 75 a^2 b^10 c^4 + 26 b^12 c^4 - 56 a^10 c^6 + 35 a^8 b^2 c^6 - 6 a^6 b^4 c^6 + 18 a^4 b^6 c^6 + 46 a^2 b^8 c^6 - 57 b^10 c^6 + 70 a^8 c^8 + 38 a^6 b^2 c^8 + 50 a^4 b^4 c^8 + 46 a^2 b^6 c^8 + 74 b^8 c^8 - 56 a^6 c^10 - 67 a^4 b^2 c^10 - 75 a^2 b^4 c^10 - 57 b^6 c^10 + 28 a^4 c^12 + 37 a^2 b^2 c^12 + 26 b^4 c^12 - 8 a^2 c^14 - 7 b^2 c^14 + c^16)y z = 0.
)W = ( a^2 (a^10-5 a^8 (b^2+c^2)+a^6 (10 b^4+13 b^2 c^2+10 c^4)-5 a^4 (2 b^6+b^4 c^2+b^2 c^4+2 c^6)+5 a^2 (b^8-b^6 c^2-b^2 c^6+c^8)-(b^2-c^2)^2 (b^6+c^6)) : ... : ...),
que tiene números de búsqueda en ETC (-22.1655966878598, -22.9766432070208, 29.7778467119341.t1 = -b^2c^2/(16 r^2 s^2), t2 = -c^2a^2/(16 r^2 s^2), t3 = -a^2b^2/(16 r^2 s^2),
donde r es el radio de la circunferencia inscrita y s el semiperímetro de ABC.
(a^2 - b^2) (a^2 - c^2) (a - b - c) (a + b - c) (a + c) (a - b + c) (a + b + c)x
-(a^2 - c^2) (a^6 - a^4 (b^2 + 2 c^2) +
a^2 (-b^4 - 2 b^2 c^2 + c^4)+ (b^3 - b c^2)^2)y
+( -a^8 +
a^6 (3 b^2 + c^2) + a^4 (-3 b^4 + b^2 c^2 + c^4) +
a^2 (b^6 - 3 b^4 c^2 + b^2 c^4 - c^6)+ b^2 c^2 (b^2 - c^2)^2)z=0.
Sa = (0 : a^8 - b^2 c^2 (b^2 - c^2)^2 - a^6 (3 b^2 + c^2) + a^4 (3 b^4 - b^2 c^2 - c^4) + a^2 (-b^6 + 3 b^4 c^2 - b^2 c^4 + c^6) : -(a^2 - c^2) (a^6 - a^4 (b^2 + 2 c^2) + (b^3 - b c^2)^2 + a^2 (-b^4 - 2 b^2 c^2 + c^4))).
Las rectas ℓb, ℓc y los puntos Sb, Sc, se obtienen por permutación cíclica.W = ( (a^2 - b^2)(a^2 - c^2) (a^4 (b^2 + c^2) + (b^2 - c^2)^2 (b^2 + c^2) - 2 a^2 (b^4 + b^2 c^2 + c^4)) : ... : ...),
que tiene números de búsqueda en ETC (12.1582244063209, -3.63918542705645, 0.548612359259956).El 4 de enero de 1643 nació Isaac Newton, físico, teólogo, inventor, alquimista y matemático inglés. Es autor de los Philosophiæ naturalis principia mathematica, más conocidos como los Principia, donde describe la ley de la gravitación universal y estableció las bases de la mecánica clásica mediante las leyes que llevan su nombre.
Hoy 2 de enero de 2021, a las 13.51 UTC (hora Universal), la Tierra está más cerca del Sol (147.093.162 Km) en lo que se conoce como perihelio, del griego «peri» (en torno a) y «hélios» (Sol). Desde el último perihelio han transcurrido 363 días; el próximo será dentro de 366 días, el 4 de enero de 2022.
a^2 b^2 (a^2 - b^2 + c^2)y^2+ a^2 c^2 (a^2 + b^2 - c^2)z^2 + a^2 ((b^2 - c^2)^2 - a^2 (b^2 + c^2))y z -(a^2 - b^2) (b^2 - c^2) (a^2 + b^2 - c^2)z x + (a^2 - c^2) (b^2 - c^2) (a^2 - b^2 + c^2) x y = 0.
Su centro es:
Ao = (a^2 (a^2 - b^2 - c^2) (a^4 - 3 (b^2 - c^2)^2 +
2 a^2 (b^2 + c^2)) :
-(a^2 + b^2 - c^2) (a^6 -
a^4 (b^2 + 2 c^2) + (b^3 - b c^2)^2 +
a^2 (-b^4 + 4 b^2 c^2 + c^4)) :
-(a^2 - b^2 + c^2) (a^6 -
a^4 (2 b^2 + c^2) + (-b^2 c + c^3)^2 +
a^2 (b^4 + 4 b^2 c^2 - c^4))).
∗ ∗ ∗ ∗ ∗
∗ ∗ ∗ ∗ ∗
El 1 de enero de 1899, en Cuba, el ejército español entrega la isla a Estados Unidos, que la había mantenido ocupada durante tres años.
A2 = (-a^2 (a^2 + (b - c)^2) : b (b - c) (a^2 + b^2 - c^2) : -(b - c) c (a^2 - b^2 + c^2)).
Sean A'B'C' el triángulo formado por las rectas ℓa, ℓb, ℓc, y A"B"C" el triángulo formado por las de A', B', C', respecto a la .
A' = (a (-a^4 + (b^2 - c^2)^2) : b (-a^4 + b^4 + 2 a^2 c^2 - c^4) :
c (-a^4 + 2 a^2 b^2 - b^4 + c^4)),
A" = (-a^2 (b - c)^2 + a^3 (b + c) + a (b - c)^2 (b + c) - (b^2 - c^2)^2 :
b (-a^3 + a^2 (b + c) + (b - c) (b + c)^2 + a (-b^2 + c^2)) :
c (-a^3 + a^2 (b + c) - (b - c) (b + c)^2 + a (b^2 - c^2))).
(a^7 - a^5 (b - c)^2 - a^6 (b + c) +
a (b - c)^4 (b + c)^2 - (b - c)^2 (b + c)^3 (b^2 + c^2) +
a^4 (b^3 - 3 b^2 c - 3 b c^2 + c^3) +
a^2 (b - c)^2 (b^3 + 7 b^2 c + 7 b c^2 + c^3) -
a^3 (b^4 - 10 b^2 c^2 + c^4)) x +
(a^7 - a^5 (b - c)^2 -
a^6 (b + c) +
a^4 (b^3 + b^2 c - 3 b c^2 + c^3) - (b - c)^4 (b^3 + b^2 c +
b c^2 + c^3) - a^3 (b^4 - 6 b^2 c^2 + 4 b c^3 + c^4) +
a (b - c)^2 (b^4 + 2 b^2 c^2 + 4 b c^3 + c^4) +
a^2 (b^5 - 3 b^4 c - 2 b^3 c^2 + 2 b^2 c^3 + b c^4 +
c^5)) y +
(a^7 - a^5 (b - c)^2 - a^6 (b + c) +
a^4 (b^3 - 3 b^2 c + b c^2 + c^3) - (b - c)^4 (b^3 + b^2 c +
b c^2 + c^3) - a^3 (b^4 + 4 b^3 c - 6 b^2 c^2 + c^4) +
a (b - c)^2 (b^4 + 4 b^3 c + 2 b^2 c^2 + c^4) +
a^2 (b^5 + b^4 c + 2 b^3 c^2 - 2 b^2 c^3 - 3 b c^4 + c^5)) z = 0.
T = ( a (b-c)(a^3-a^2 (b+c)-(b-c)^2 (b+c)+a (b+c)^2)(a^6+a^4 (b-c)^2-2 a^5 (b+c)+2 a^3 b c (b+c)-a^2 (b-c)^2 (b^2+c^2)-(b^2-c^2)^2 (b^2+c^2)+2 a (b^5-b^3 c^2-b^2 c^3+c^5)) : ... : ...),
que tiene números de búsqueda en (-0.373079963472450, 1.73817240228519, 2.60950510962038).W = ( a (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^6 + a^4 (b - c)^2 - 2 a^5 (b + c) + 2 a^3 b c (b + c) - a^2 (b - c)^2 (b^2 + c^2) - (b^2 - c^2)^2 (b^2 + c^2) + 2 a (b^5 - b^3 c^2 - b^2 c^3 + c^5)) : ... : ...),
que tiene números de búsqueda en ETC (0.102383815594064, 0.616398926106776, 3.16667269509781)..png)
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