Последний раз редактировалось _Ivana 19.07.2014, 13:29, всего редактировалось 2 раз(а).
Подробно расписана, Ваша система для  и  И это получается ровно та же система, которую я получал в своем методе (что и неудивительно). Скрипт Матлаба символьных преобразований и сравнения вариантов: (Оффтоп)
Код: function Main() clear all; close all;
syms x y x0 y0 x1 y1 x2 y2 x3 y3 x4 y4 X1 Y1 X2 Y2 X3 Y3 X4 Y4
% через определители матриц
A = [2*x0, 1, 0, 0; x0^2+y0^2, x0, y0, 1; X1^2+Y1^2, X1, Y1, 1; X2^2+Y2^2, X2, Y2, 1]; B = [2*y0, 0, 1, 0; x0^2+y0^2, x0, y0, 1; X3^2+Y3^2, X3, Y3, 1; X4^2+Y4^2, X4, Y4, 1]; C = [2*x0, 1, 0, 0; x0^2+y0^2, x0, y0, 1; X3^2+Y3^2, X3, Y3, 1; X4^2+Y4^2, X4, Y4, 1]; D = [2*y0, 0, 1, 0; x0^2+y0^2, x0, y0, 1; X1^2+Y1^2, X1, Y1, 1; X2^2+Y2^2, X2, Y2, 1];
g = det(A)*det(B) - det(C)*det(D);
% напрямую через уравнения прямых
a(x) = x0 - x; b(y) = y0 - y; c(x, y) = (x0 - x)*x + (y0 - y)*y;
zp(x1, y1, x2, y2) = a(x1)*b(y2) - a(x2)*b(y1); xp(x1, y1, x2, y2) = (b(y2)*c(x1, y1) - b(y1)*c(x2, y2)); yp(x1, y1, x2, y2) = (a(x1)*c(x2, y2) - a(x2)*c(x1, y1));
zp12 = zp(X1, Y1, X2, Y2); zp34 = zp(X3, Y3, X4, Y4); xp12 = xp(X1, Y1, X2, Y2); xp34 = xp(X3, Y3, X4, Y4); yp12 = yp(X1, Y1, X2, Y2); yp34 = yp(X3, Y3, X4, Y4);
f = y0*(xp34*zp12 - xp12*zp34) - x0*(yp34*zp12 - yp12*zp34) - yp12*xp34 + xp12*yp34;
% сравнение результатов
factor(g) factor(f) simplify(f - g)
end
Результаты (Оффтоп)
Код: ans = X1^2*X2*X3^2*Y4 - X1^2*X2*X3^2*y0 - 2*X1^2*X2*X3*Y4*x0 + 2*X1^2*X2*X3*x0*y0 - X1^2*X2*X4^2*Y3 + X1^2*X2*X4^2*y0 + 2*X1^2*X2*X4*Y3*x0 - 2*X1^2*X2*X4*x0*y0 + X1^2*X2*Y3^2*Y4 - X1^2*X2*Y3^2*y0 - X1^2*X2*Y3*Y4^2 - X1^2*X2*Y3*x0^2 + X1^2*X2*Y3*y0^2 + X1^2*X2*Y4^2*y0 + X1^2*X2*Y4*x0^2 - X1^2*X2*Y4*y0^2 - X1^2*X3^2*X4*Y2 + X1^2*X3^2*X4*y0 + X1^2*X3^2*Y2*x0 - X1^2*X3^2*Y4*x0 + X1^2*X3*X4^2*Y2 - X1^2*X3*X4^2*y0 + X1^2*X3*Y2*Y4^2 - 2*X1^2*X3*Y2*Y4*y0 - X1^2*X3*Y2*x0^2 + X1^2*X3*Y2*y0^2 - X1^2*X3*Y4^2*y0 + 2*X1^2*X3*Y4*x0^2 + 2*X1^2*X3*Y4*y0^2 - X1^2*X3*x0^2*y0 - X1^2*X3*y0^3 - X1^2*X4^2*Y2*x0 + X1^2*X4^2*Y3*x0 - X1^2*X4*Y2*Y3^2 + 2*X1^2*X4*Y2*Y3*y0 + X1^2*X4*Y2*x0^2 - X1^2*X4*Y2*y0^2 + X1^2*X4*Y3^2*y0 - 2*X1^2*X4*Y3*x0^2 - 2*X1^2*X4*Y3*y0^2 + X1^2*X4*x0^2*y0 + X1^2*X4*y0^3 + X1^2*Y2*Y3^2*x0 - 2*X1^2*Y2*Y3*x0*y0 - X1^2*Y2*Y4^2*x0 + 2*X1^2*Y2*Y4*x0*y0 - X1^2*Y3^2*Y4*x0 + X1^2*Y3*Y4^2*x0 + X1^2*Y3*x0^3 + X1^2*Y3*x0*y0^2 - X1^2*Y4*x0^3 - X1^2*Y4*x0*y0^2 - X1*X2^2*X3^2*Y4 + X1*X2^2*X3^2*y0 + 2*X1*X2^2*X3*Y4*x0 - 2*X1*X2^2*X3*x0*y0 + X1*X2^2*X4^2*Y3 - X1*X2^2*X4^2*y0 - 2*X1*X2^2*X4*Y3*x0 + 2*X1*X2^2*X4*x0*y0 - X1*X2^2*Y3^2*Y4 + X1*X2^2*Y3^2*y0 + X1*X2^2*Y3*Y4^2 + X1*X2^2*Y3*x0^2 - X1*X2^2*Y3*y0^2 - X1*X2^2*Y4^2*y0 - X1*X2^2*Y4*x0^2 + X1*X2^2*Y4*y0^2 + 2*X1*X3^2*X4*Y2*x0 - 2*X1*X3^2*X4*x0*y0 - X1*X3^2*Y2^2*Y4 + X1*X3^2*Y2^2*y0 + 2*X1*X3^2*Y2*Y4*y0 - 2*X1*X3^2*Y2*x0^2 - 2*X1*X3^2*Y2*y0^2 + X1*X3^2*Y4*x0^2 - X1*X3^2*Y4*y0^2 + X1*X3^2*x0^2*y0 + X1*X3^2*y0^3 - 2*X1*X3*X4^2*Y2*x0 + 2*X1*X3*X4^2*x0*y0 + 2*X1*X3*Y2^2*Y4*x0 - 2*X1*X3*Y2^2*x0*y0 - 2*X1*X3*Y2*Y4^2*x0 + 2*X1*X3*Y2*x0^3 + 2*X1*X3*Y2*x0*y0^2 + 2*X1*X3*Y4^2*x0*y0 - 2*X1*X3*Y4*x0^3 - 2*X1*X3*Y4*x0*y0^2 + X1*X4^2*Y2^2*Y3 - X1*X4^2*Y2^2*y0 - 2*X1*X4^2*Y2*Y3*y0 + 2*X1*X4^2*Y2*x0^2 + 2*X1*X4^2*Y2*y0^2 - X1*X4^2*Y3*x0^2 + X1*X4^2*Y3*y0^2 - X1*X4^2*x0^2*y0 - X1*X4^2*y0^3 - 2*X1*X4*Y2^2*Y3*x0 + 2*X1*X4*Y2^2*x0*y0 + 2*X1*X4*Y2*Y3^2*x0 - 2*X1*X4*Y2*x0^3 - 2*X1*X4*Y2*x0*y0^2 - 2*X1*X4*Y3^2*x0*y0 + 2*X1*X4*Y3*x0^3 + 2*X1*X4*Y3*x0*y0^2 - X1*Y2^2*Y3^2*Y4 + X1*Y2^2*Y3^2*y0 + X1*Y2^2*Y3*Y4^2 + X1*Y2^2*Y3*x0^2 - X1*Y2^2*Y3*y0^2 - X1*Y2^2*Y4^2*y0 - X1*Y2^2*Y4*x0^2 + X1*Y2^2*Y4*y0^2 + 2*X1*Y2*Y3^2*Y4*y0 - 2*X1*Y2*Y3^2*x0^2 - 2*X1*Y2*Y3^2*y0^2 - 2*X1*Y2*Y3*Y4^2*y0 + 2*X1*Y2*Y3*x0^2*y0 + 2*X1*Y2*Y3*y0^3 + 2*X1*Y2*Y4^2*x0^2 + 2*X1*Y2*Y4^2*y0^2 - 2*X1*Y2*Y4*x0^2*y0 - 2*X1*Y2*Y4*y0^3 + X1*Y3^2*Y4*x0^2 - X1*Y3^2*Y4*y0^2 + X1*Y3^2*x0^2*y0 + X1*Y3^2*y0^3 - X1*Y3*Y4^2*x0^2 + X1*Y3*Y4^2*y0^2 - X1*Y3*x0^4 - 2*X1*Y3*x0^2*y0^2 - X1*Y3*y0^4 - X1*Y4^2*x0^2*y0 - X1*Y4^2*y0^3 + X1*Y4*x0^4 + 2*X1*Y4*x0^2*y0^2 + X1*Y4*y0^4 + X2^2*X3^2*X4*Y1 - X2^2*X3^2*X4*y0 - X2^2*X3^2*Y1*x0 + X2^2*X3^2*Y4*x0 - X2^2*X3*X4^2*Y1 + X2^2*X3*X4^2*y0 - X2^2*X3*Y1*Y4^2 + 2*X2^2*X3*Y1*Y4*y0 + X2^2*X3*Y1*x0^2 - X2^2*X3*Y1*y0^2 + X2^2*X3*Y4^2*y0 - 2*X2^2*X3*Y4*x0^2 - 2*X2^2*X3*Y4*y0^2 + X2^2*X3*x0^2*y0 + X2^2*X3*y0^3 + X2^2*X4^2*Y1*x0 - X2^2*X4^2*Y3*x0 + X2^2*X4*Y1*Y3^2 - 2*X2^2*X4*Y1*Y3*y0 - X2^2*X4*Y1*x0^2 + X2^2*X4*Y1*y0^2 - X2^2*X4*Y3^2*y0 + 2*X2^2*X4*Y3*x0^2 + 2*X2^2*X4*Y3*y0^2 - X2^2*X4*x0^2*y0 - X2^2*X4*y0^3 - X2^2*Y1*Y3^2*x0 + 2*X2^2*Y1*Y3*x0*y0 + X2^2*Y1*Y4^2*x0 - 2*X2^2*Y1*Y4*x0*y0 + X2^2*Y3^2*Y4*x0 - X2^2*Y3*Y4^2*x0 - X2^2*Y3*x0^3 - X2^2*Y3*x0*y0^2 + X2^2*Y4*x0^3 + X2^2*Y4*x0*y0^2 - 2*X2*X3^2*X4*Y1*x0 + 2*X2*X3^2*X4*x0*y0 + X2*X3^2*Y1^2*Y4 - X2*X3^2*Y1^2*y0 - 2*X2*X3^2*Y1*Y4*y0 + 2*X2*X3^2*Y1*x0^2 + 2*X2*X3^2*Y1*y0^2 - X2*X3^2*Y4*x0^2 + X2*X3^2*Y4*y0^2 - X2*X3^2*x0^2*y0 - X2*X3^2*y0^3 + 2*X2*X3*X4^2*Y1*x0 - 2*X2*X3*X4^2*x0*y0 - 2*X2*X3*Y1^2*Y4*x0 + 2*X2*X3*Y1^2*x0*y0 + 2*X2*X3*Y1*Y4^2*x0 - 2*X2*X3*Y1*x0^3 - 2*X2*X3*Y1*x0*y0^2 - 2*X2*X3*Y4^2*x0*y0 + 2*X2*X3*Y4*x0^3 + 2*X2*X3*Y4*x0*y0^2 - X2*X4^2*Y1^2*Y3 + X2*X4^2*Y1^2*y0 + 2*X2*X4^2*Y1*Y3*y0 - 2*X2*X4^2*Y1*x0^2 - 2*X2*X4^2*Y1*y0^2 + X2*X4^2*Y3*x0^2 - X2*X4^2*Y3*y0^2 + X2*X4^2*x0^2*y0 + X2*X4^2*y0^3 + 2*X2*X4*Y1^2*Y3*x0 - 2*X2*X4*Y1^2*x0*y0 - 2*X2*X4*Y1*Y3^2*x0 + 2*X2*X4*Y1*x0^3 + 2*X2*X4*Y1*x0*y0^2 + 2*X2*X4*Y3^2*x0*y0 - 2*X2*X4*Y3*x0^3 - 2*X2*X4*Y3*x0*y0^2 + X2*Y1^2*Y3^2*Y4 - X2*Y1^2*Y3^2*y0 - X2*Y1^2*Y3*Y4^2 - X2*Y1^2*Y3*x0^2 + X2*Y1^2*Y3*y0^2 + X2*Y1^2*Y4^2*y0 + X2*Y1^2*Y4*x0^2 - X2*Y1^2*Y4*y0^2 - 2*X2*Y1*Y3^2*Y4*y0 + 2*X2*Y1*Y3^2*x0^2 + 2*X2*Y1*Y3^2*y0^2 + 2*X2*Y1*Y3*Y4^2*y0 - 2*X2*Y1*Y3*x0^2*y0 - 2*X2*Y1*Y3*y0^3 - 2*X2*Y1*Y4^2*x0^2 - 2*X2*Y1*Y4^2*y0^2 + 2*X2*Y1*Y4*x0^2*y0 + 2*X2*Y1*Y4*y0^3 - X2*Y3^2*Y4*x0^2 + X2*Y3^2*Y4*y0^2 - X2*Y3^2*x0^2*y0 - X2*Y3^2*y0^3 + X2*Y3*Y4^2*x0^2 - X2*Y3*Y4^2*y0^2 + X2*Y3*x0^4 + 2*X2*Y3*x0^2*y0^2 + X2*Y3*y0^4 + X2*Y4^2*x0^2*y0 + X2*Y4^2*y0^3 - X2*Y4*x0^4 - 2*X2*Y4*x0^2*y0^2 - X2*Y4*y0^4 - X3^2*X4*Y1^2*Y2 + X3^2*X4*Y1^2*y0 + X3^2*X4*Y1*Y2^2 + X3^2*X4*Y1*x0^2 - X3^2*X4*Y1*y0^2 - X3^2*X4*Y2^2*y0 - X3^2*X4*Y2*x0^2 + X3^2*X4*Y2*y0^2 + X3^2*Y1^2*Y2*x0 - X3^2*Y1^2*Y4*x0 - X3^2*Y1*Y2^2*x0 + 2*X3^2*Y1*Y4*x0*y0 - X3^2*Y1*x0^3 - X3^2*Y1*x0*y0^2 + X3^2*Y2^2*Y4*x0 - 2*X3^2*Y2*Y4*x0*y0 + X3^2*Y2*x0^3 + X3^2*Y2*x0*y0^2 + X3*X4^2*Y1^2*Y2 - X3*X4^2*Y1^2*y0 - X3*X4^2*Y1*Y2^2 - X3*X4^2*Y1*x0^2 + X3*X4^2*Y1*y0^2 + X3*X4^2*Y2^2*y0 + X3*X4^2*Y2*x0^2 - X3*X4^2*Y2*y0^2 + X3*Y1^2*Y2*Y4^2 - 2*X3*Y1^2*Y2*Y4*y0 - X3*Y1^2*Y2*x0^2 + X3*Y1^2*Y2*y0^2 - X3*Y1^2*Y4^2*y0 + 2*X3*Y1^2*Y4*x0^2 + 2*X3*Y1^2*Y4*y0^2 - X3*Y1^2*x0^2*y0 - X3*Y1^2*y0^3 - X3*Y1*Y2^2*Y4^2 + 2*X3*Y1*Y2^2*Y4*y0 + X3*Y1*Y2^2*x0^2 - X3*Y1*Y2^2*y0^2 - X3*Y1*Y4^2*x0^2 + X3*Y1*Y4^2*y0^2 - 2*X3*Y1*Y4*x0^2*y0 - 2*X3*Y1*Y4*y0^3 + X3*Y1*x0^4 + 2*X3*Y1*x0^2*y0^2 + X3*Y1*y0^4 + X3*Y2^2*Y4^2*y0 - 2*X3*Y2^2*Y4*x0^2 - 2*X3*Y2^2*Y4*y0^2 + X3*Y2^2*x0^2*y0 + X3*Y2^2*y0^3 + X3*Y2*Y4^2*x0^2 - X3*Y2*Y4^2*y0^2 + 2*X3*Y2*Y4*x0^2*y0 + 2*X3*Y2*Y4*y0^3 - X3*Y2*x0^4 - 2*X3*Y2*x0^2*y0^2 - X3*Y2*y0^4 - X4^2*Y1^2*Y2*x0 + X4^2*Y1^2*Y3*x0 + X4^2*Y1*Y2^2*x0 - 2*X4^2*Y1*Y3*x0*y0 + X4^2*Y1*x0^3 + X4^2*Y1*x0*y0^2 - X4^2*Y2^2*Y3*x0 + 2*X4^2*Y2*Y3*x0*y0 - X4^2*Y2*x0^3 - X4^2*Y2*x0*y0^2 - X4*Y1^2*Y2*Y3^2 + 2*X4*Y1^2*Y2*Y3*y0 + X4*Y1^2*Y2*x0^2 - X4*Y1^2*Y2*y0^2 + X4*Y1^2*Y3^2*y0 - 2*X4*Y1^2*Y3*x0^2 - 2*X4*Y1^2*Y3*y0^2 + X4*Y1^2*x0^2*y0 + X4*Y1^2*y0^3 + X4*Y1*Y2^2*Y3^2 - 2*X4*Y1*Y2^2*Y3*y0 - X4*Y1*Y2^2*x0^2 + X4*Y1*Y2^2*y0^2 + X4*Y1*Y3^2*x0^2 - X4*Y1*Y3^2*y0^2 + 2*X4*Y1*Y3*x0^2*y0 + 2*X4*Y1*Y3*y0^3 - X4*Y1*x0^4 - 2*X4*Y1*x0^2*y0^2 - X4*Y1*y0^4 - X4*Y2^2*Y3^2*y0 + 2*X4*Y2^2*Y3*x0^2 + 2*X4*Y2^2*Y3*y0^2 - X4*Y2^2*x0^2*y0 - X4*Y2^2*y0^3 - X4*Y2*Y3^2*x0^2 + X4*Y2*Y3^2*y0^2 - 2*X4*Y2*Y3*x0^2*y0 - 2*X4*Y2*Y3*y0^3 + X4*Y2*x0^4 + 2*X4*Y2*x0^2*y0^2 + X4*Y2*y0^4 + Y1^2*Y2*Y3^2*x0 - 2*Y1^2*Y2*Y3*x0*y0 - Y1^2*Y2*Y4^2*x0 + 2*Y1^2*Y2*Y4*x0*y0 - Y1^2*Y3^2*Y4*x0 + Y1^2*Y3*Y4^2*x0 + Y1^2*Y3*x0^3 + Y1^2*Y3*x0*y0^2 - Y1^2*Y4*x0^3 - Y1^2*Y4*x0*y0^2 - Y1*Y2^2*Y3^2*x0 + 2*Y1*Y2^2*Y3*x0*y0 + Y1*Y2^2*Y4^2*x0 - 2*Y1*Y2^2*Y4*x0*y0 + 2*Y1*Y3^2*Y4*x0*y0 - Y1*Y3^2*x0^3 - Y1*Y3^2*x0*y0^2 - 2*Y1*Y3*Y4^2*x0*y0 + Y1*Y4^2*x0^3 + Y1*Y4^2*x0*y0^2 + Y2^2*Y3^2*Y4*x0 - Y2^2*Y3*Y4^2*x0 - Y2^2*Y3*x0^3 - Y2^2*Y3*x0*y0^2 + Y2^2*Y4*x0^3 + Y2^2*Y4*x0*y0^2 - 2*Y2*Y3^2*Y4*x0*y0 + Y2*Y3^2*x0^3 + Y2*Y3^2*x0*y0^2 + 2*Y2*Y3*Y4^2*x0*y0 - Y2*Y4^2*x0^3 - Y2*Y4^2*x0*y0^2 ans = X1^2*X2*X3^2*Y4 - X1^2*X2*X3^2*y0 - 2*X1^2*X2*X3*Y4*x0 + 2*X1^2*X2*X3*x0*y0 - X1^2*X2*X4^2*Y3 + X1^2*X2*X4^2*y0 + 2*X1^2*X2*X4*Y3*x0 - 2*X1^2*X2*X4*x0*y0 + X1^2*X2*Y3^2*Y4 - X1^2*X2*Y3^2*y0 - X1^2*X2*Y3*Y4^2 - X1^2*X2*Y3*x0^2 + X1^2*X2*Y3*y0^2 + X1^2*X2*Y4^2*y0 + X1^2*X2*Y4*x0^2 - X1^2*X2*Y4*y0^2 - X1^2*X3^2*X4*Y2 + X1^2*X3^2*X4*y0 + X1^2*X3^2*Y2*x0 - X1^2*X3^2*Y4*x0 + X1^2*X3*X4^2*Y2 - X1^2*X3*X4^2*y0 + X1^2*X3*Y2*Y4^2 - 2*X1^2*X3*Y2*Y4*y0 - X1^2*X3*Y2*x0^2 + X1^2*X3*Y2*y0^2 - X1^2*X3*Y4^2*y0 + 2*X1^2*X3*Y4*x0^2 + 2*X1^2*X3*Y4*y0^2 - X1^2*X3*x0^2*y0 - X1^2*X3*y0^3 - X1^2*X4^2*Y2*x0 + X1^2*X4^2*Y3*x0 - X1^2*X4*Y2*Y3^2 + 2*X1^2*X4*Y2*Y3*y0 + X1^2*X4*Y2*x0^2 - X1^2*X4*Y2*y0^2 + X1^2*X4*Y3^2*y0 - 2*X1^2*X4*Y3*x0^2 - 2*X1^2*X4*Y3*y0^2 + X1^2*X4*x0^2*y0 + X1^2*X4*y0^3 + X1^2*Y2*Y3^2*x0 - 2*X1^2*Y2*Y3*x0*y0 - X1^2*Y2*Y4^2*x0 + 2*X1^2*Y2*Y4*x0*y0 - X1^2*Y3^2*Y4*x0 + X1^2*Y3*Y4^2*x0 + X1^2*Y3*x0^3 + X1^2*Y3*x0*y0^2 - X1^2*Y4*x0^3 - X1^2*Y4*x0*y0^2 - X1*X2^2*X3^2*Y4 + X1*X2^2*X3^2*y0 + 2*X1*X2^2*X3*Y4*x0 - 2*X1*X2^2*X3*x0*y0 + X1*X2^2*X4^2*Y3 - X1*X2^2*X4^2*y0 - 2*X1*X2^2*X4*Y3*x0 + 2*X1*X2^2*X4*x0*y0 - X1*X2^2*Y3^2*Y4 + X1*X2^2*Y3^2*y0 + X1*X2^2*Y3*Y4^2 + X1*X2^2*Y3*x0^2 - X1*X2^2*Y3*y0^2 - X1*X2^2*Y4^2*y0 - X1*X2^2*Y4*x0^2 + X1*X2^2*Y4*y0^2 + 2*X1*X3^2*X4*Y2*x0 - 2*X1*X3^2*X4*x0*y0 - X1*X3^2*Y2^2*Y4 + X1*X3^2*Y2^2*y0 + 2*X1*X3^2*Y2*Y4*y0 - 2*X1*X3^2*Y2*x0^2 - 2*X1*X3^2*Y2*y0^2 + X1*X3^2*Y4*x0^2 - X1*X3^2*Y4*y0^2 + X1*X3^2*x0^2*y0 + X1*X3^2*y0^3 - 2*X1*X3*X4^2*Y2*x0 + 2*X1*X3*X4^2*x0*y0 + 2*X1*X3*Y2^2*Y4*x0 - 2*X1*X3*Y2^2*x0*y0 - 2*X1*X3*Y2*Y4^2*x0 + 2*X1*X3*Y2*x0^3 + 2*X1*X3*Y2*x0*y0^2 + 2*X1*X3*Y4^2*x0*y0 - 2*X1*X3*Y4*x0^3 - 2*X1*X3*Y4*x0*y0^2 + X1*X4^2*Y2^2*Y3 - X1*X4^2*Y2^2*y0 - 2*X1*X4^2*Y2*Y3*y0 + 2*X1*X4^2*Y2*x0^2 + 2*X1*X4^2*Y2*y0^2 - X1*X4^2*Y3*x0^2 + X1*X4^2*Y3*y0^2 - X1*X4^2*x0^2*y0 - X1*X4^2*y0^3 - 2*X1*X4*Y2^2*Y3*x0 + 2*X1*X4*Y2^2*x0*y0 + 2*X1*X4*Y2*Y3^2*x0 - 2*X1*X4*Y2*x0^3 - 2*X1*X4*Y2*x0*y0^2 - 2*X1*X4*Y3^2*x0*y0 + 2*X1*X4*Y3*x0^3 + 2*X1*X4*Y3*x0*y0^2 - X1*Y2^2*Y3^2*Y4 + X1*Y2^2*Y3^2*y0 + X1*Y2^2*Y3*Y4^2 + X1*Y2^2*Y3*x0^2 - X1*Y2^2*Y3*y0^2 - X1*Y2^2*Y4^2*y0 - X1*Y2^2*Y4*x0^2 + X1*Y2^2*Y4*y0^2 + 2*X1*Y2*Y3^2*Y4*y0 - 2*X1*Y2*Y3^2*x0^2 - 2*X1*Y2*Y3^2*y0^2 - 2*X1*Y2*Y3*Y4^2*y0 + 2*X1*Y2*Y3*x0^2*y0 + 2*X1*Y2*Y3*y0^3 + 2*X1*Y2*Y4^2*x0^2 + 2*X1*Y2*Y4^2*y0^2 - 2*X1*Y2*Y4*x0^2*y0 - 2*X1*Y2*Y4*y0^3 + X1*Y3^2*Y4*x0^2 - X1*Y3^2*Y4*y0^2 + X1*Y3^2*x0^2*y0 + X1*Y3^2*y0^3 - X1*Y3*Y4^2*x0^2 + X1*Y3*Y4^2*y0^2 - X1*Y3*x0^4 - 2*X1*Y3*x0^2*y0^2 - X1*Y3*y0^4 - X1*Y4^2*x0^2*y0 - X1*Y4^2*y0^3 + X1*Y4*x0^4 + 2*X1*Y4*x0^2*y0^2 + X1*Y4*y0^4 + X2^2*X3^2*X4*Y1 - X2^2*X3^2*X4*y0 - X2^2*X3^2*Y1*x0 + X2^2*X3^2*Y4*x0 - X2^2*X3*X4^2*Y1 + X2^2*X3*X4^2*y0 - X2^2*X3*Y1*Y4^2 + 2*X2^2*X3*Y1*Y4*y0 + X2^2*X3*Y1*x0^2 - X2^2*X3*Y1*y0^2 + X2^2*X3*Y4^2*y0 - 2*X2^2*X3*Y4*x0^2 - 2*X2^2*X3*Y4*y0^2 + X2^2*X3*x0^2*y0 + X2^2*X3*y0^3 + X2^2*X4^2*Y1*x0 - X2^2*X4^2*Y3*x0 + X2^2*X4*Y1*Y3^2 - 2*X2^2*X4*Y1*Y3*y0 - X2^2*X4*Y1*x0^2 + X2^2*X4*Y1*y0^2 - X2^2*X4*Y3^2*y0 + 2*X2^2*X4*Y3*x0^2 + 2*X2^2*X4*Y3*y0^2 - X2^2*X4*x0^2*y0 - X2^2*X4*y0^3 - X2^2*Y1*Y3^2*x0 + 2*X2^2*Y1*Y3*x0*y0 + X2^2*Y1*Y4^2*x0 - 2*X2^2*Y1*Y4*x0*y0 + X2^2*Y3^2*Y4*x0 - X2^2*Y3*Y4^2*x0 - X2^2*Y3*x0^3 - X2^2*Y3*x0*y0^2 + X2^2*Y4*x0^3 + X2^2*Y4*x0*y0^2 - 2*X2*X3^2*X4*Y1*x0 + 2*X2*X3^2*X4*x0*y0 + X2*X3^2*Y1^2*Y4 - X2*X3^2*Y1^2*y0 - 2*X2*X3^2*Y1*Y4*y0 + 2*X2*X3^2*Y1*x0^2 + 2*X2*X3^2*Y1*y0^2 - X2*X3^2*Y4*x0^2 + X2*X3^2*Y4*y0^2 - X2*X3^2*x0^2*y0 - X2*X3^2*y0^3 + 2*X2*X3*X4^2*Y1*x0 - 2*X2*X3*X4^2*x0*y0 - 2*X2*X3*Y1^2*Y4*x0 + 2*X2*X3*Y1^2*x0*y0 + 2*X2*X3*Y1*Y4^2*x0 - 2*X2*X3*Y1*x0^3 - 2*X2*X3*Y1*x0*y0^2 - 2*X2*X3*Y4^2*x0*y0 + 2*X2*X3*Y4*x0^3 + 2*X2*X3*Y4*x0*y0^2 - X2*X4^2*Y1^2*Y3 + X2*X4^2*Y1^2*y0 + 2*X2*X4^2*Y1*Y3*y0 - 2*X2*X4^2*Y1*x0^2 - 2*X2*X4^2*Y1*y0^2 + X2*X4^2*Y3*x0^2 - X2*X4^2*Y3*y0^2 + X2*X4^2*x0^2*y0 + X2*X4^2*y0^3 + 2*X2*X4*Y1^2*Y3*x0 - 2*X2*X4*Y1^2*x0*y0 - 2*X2*X4*Y1*Y3^2*x0 + 2*X2*X4*Y1*x0^3 + 2*X2*X4*Y1*x0*y0^2 + 2*X2*X4*Y3^2*x0*y0 - 2*X2*X4*Y3*x0^3 - 2*X2*X4*Y3*x0*y0^2 + X2*Y1^2*Y3^2*Y4 - X2*Y1^2*Y3^2*y0 - X2*Y1^2*Y3*Y4^2 - X2*Y1^2*Y3*x0^2 + X2*Y1^2*Y3*y0^2 + X2*Y1^2*Y4^2*y0 + X2*Y1^2*Y4*x0^2 - X2*Y1^2*Y4*y0^2 - 2*X2*Y1*Y3^2*Y4*y0 + 2*X2*Y1*Y3^2*x0^2 + 2*X2*Y1*Y3^2*y0^2 + 2*X2*Y1*Y3*Y4^2*y0 - 2*X2*Y1*Y3*x0^2*y0 - 2*X2*Y1*Y3*y0^3 - 2*X2*Y1*Y4^2*x0^2 - 2*X2*Y1*Y4^2*y0^2 + 2*X2*Y1*Y4*x0^2*y0 + 2*X2*Y1*Y4*y0^3 - X2*Y3^2*Y4*x0^2 + X2*Y3^2*Y4*y0^2 - X2*Y3^2*x0^2*y0 - X2*Y3^2*y0^3 + X2*Y3*Y4^2*x0^2 - X2*Y3*Y4^2*y0^2 + X2*Y3*x0^4 + 2*X2*Y3*x0^2*y0^2 + X2*Y3*y0^4 + X2*Y4^2*x0^2*y0 + X2*Y4^2*y0^3 - X2*Y4*x0^4 - 2*X2*Y4*x0^2*y0^2 - X2*Y4*y0^4 - X3^2*X4*Y1^2*Y2 + X3^2*X4*Y1^2*y0 + X3^2*X4*Y1*Y2^2 + X3^2*X4*Y1*x0^2 - X3^2*X4*Y1*y0^2 - X3^2*X4*Y2^2*y0 - X3^2*X4*Y2*x0^2 + X3^2*X4*Y2*y0^2 + X3^2*Y1^2*Y2*x0 - X3^2*Y1^2*Y4*x0 - X3^2*Y1*Y2^2*x0 + 2*X3^2*Y1*Y4*x0*y0 - X3^2*Y1*x0^3 - X3^2*Y1*x0*y0^2 + X3^2*Y2^2*Y4*x0 - 2*X3^2*Y2*Y4*x0*y0 + X3^2*Y2*x0^3 + X3^2*Y2*x0*y0^2 + X3*X4^2*Y1^2*Y2 - X3*X4^2*Y1^2*y0 - X3*X4^2*Y1*Y2^2 - X3*X4^2*Y1*x0^2 + X3*X4^2*Y1*y0^2 + X3*X4^2*Y2^2*y0 + X3*X4^2*Y2*x0^2 - X3*X4^2*Y2*y0^2 + X3*Y1^2*Y2*Y4^2 - 2*X3*Y1^2*Y2*Y4*y0 - X3*Y1^2*Y2*x0^2 + X3*Y1^2*Y2*y0^2 - X3*Y1^2*Y4^2*y0 + 2*X3*Y1^2*Y4*x0^2 + 2*X3*Y1^2*Y4*y0^2 - X3*Y1^2*x0^2*y0 - X3*Y1^2*y0^3 - X3*Y1*Y2^2*Y4^2 + 2*X3*Y1*Y2^2*Y4*y0 + X3*Y1*Y2^2*x0^2 - X3*Y1*Y2^2*y0^2 - X3*Y1*Y4^2*x0^2 + X3*Y1*Y4^2*y0^2 - 2*X3*Y1*Y4*x0^2*y0 - 2*X3*Y1*Y4*y0^3 + X3*Y1*x0^4 + 2*X3*Y1*x0^2*y0^2 + X3*Y1*y0^4 + X3*Y2^2*Y4^2*y0 - 2*X3*Y2^2*Y4*x0^2 - 2*X3*Y2^2*Y4*y0^2 + X3*Y2^2*x0^2*y0 + X3*Y2^2*y0^3 + X3*Y2*Y4^2*x0^2 - X3*Y2*Y4^2*y0^2 + 2*X3*Y2*Y4*x0^2*y0 + 2*X3*Y2*Y4*y0^3 - X3*Y2*x0^4 - 2*X3*Y2*x0^2*y0^2 - X3*Y2*y0^4 - X4^2*Y1^2*Y2*x0 + X4^2*Y1^2*Y3*x0 + X4^2*Y1*Y2^2*x0 - 2*X4^2*Y1*Y3*x0*y0 + X4^2*Y1*x0^3 + X4^2*Y1*x0*y0^2 - X4^2*Y2^2*Y3*x0 + 2*X4^2*Y2*Y3*x0*y0 - X4^2*Y2*x0^3 - X4^2*Y2*x0*y0^2 - X4*Y1^2*Y2*Y3^2 + 2*X4*Y1^2*Y2*Y3*y0 + X4*Y1^2*Y2*x0^2 - X4*Y1^2*Y2*y0^2 + X4*Y1^2*Y3^2*y0 - 2*X4*Y1^2*Y3*x0^2 - 2*X4*Y1^2*Y3*y0^2 + X4*Y1^2*x0^2*y0 + X4*Y1^2*y0^3 + X4*Y1*Y2^2*Y3^2 - 2*X4*Y1*Y2^2*Y3*y0 - X4*Y1*Y2^2*x0^2 + X4*Y1*Y2^2*y0^2 + X4*Y1*Y3^2*x0^2 - X4*Y1*Y3^2*y0^2 + 2*X4*Y1*Y3*x0^2*y0 + 2*X4*Y1*Y3*y0^3 - X4*Y1*x0^4 - 2*X4*Y1*x0^2*y0^2 - X4*Y1*y0^4 - X4*Y2^2*Y3^2*y0 + 2*X4*Y2^2*Y3*x0^2 + 2*X4*Y2^2*Y3*y0^2 - X4*Y2^2*x0^2*y0 - X4*Y2^2*y0^3 - X4*Y2*Y3^2*x0^2 + X4*Y2*Y3^2*y0^2 - 2*X4*Y2*Y3*x0^2*y0 - 2*X4*Y2*Y3*y0^3 + X4*Y2*x0^4 + 2*X4*Y2*x0^2*y0^2 + X4*Y2*y0^4 + Y1^2*Y2*Y3^2*x0 - 2*Y1^2*Y2*Y3*x0*y0 - Y1^2*Y2*Y4^2*x0 + 2*Y1^2*Y2*Y4*x0*y0 - Y1^2*Y3^2*Y4*x0 + Y1^2*Y3*Y4^2*x0 + Y1^2*Y3*x0^3 + Y1^2*Y3*x0*y0^2 - Y1^2*Y4*x0^3 - Y1^2*Y4*x0*y0^2 - Y1*Y2^2*Y3^2*x0 + 2*Y1*Y2^2*Y3*x0*y0 + Y1*Y2^2*Y4^2*x0 - 2*Y1*Y2^2*Y4*x0*y0 + 2*Y1*Y3^2*Y4*x0*y0 - Y1*Y3^2*x0^3 - Y1*Y3^2*x0*y0^2 - 2*Y1*Y3*Y4^2*x0*y0 + Y1*Y4^2*x0^3 + Y1*Y4^2*x0*y0^2 + Y2^2*Y3^2*Y4*x0 - Y2^2*Y3*Y4^2*x0 - Y2^2*Y3*x0^3 - Y2^2*Y3*x0*y0^2 + Y2^2*Y4*x0^3 + Y2^2*Y4*x0*y0^2 - 2*Y2*Y3^2*Y4*x0*y0 + Y2*Y3^2*x0^3 + Y2*Y3^2*x0*y0^2 + 2*Y2*Y3*Y4^2*x0*y0 - Y2*Y4^2*x0^3 - Y2*Y4^2*x0*y0^2 ans = 0
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