Gast
2006-06-24, 15:24:08
Kann jemand mit einem CAS bitte eine Lösung folgenden polynomialen Gleichungssystems finden, sodass die Determinante von (aij) != 0 ist? Mir reicht schon eine einzige Lösung
(3*a12^2*a21^2*a22+4*a11*a12*a33*a32*a21+4*a11*a12*a33^2*a32*a31+4*a11*a12*a22*a 21+a11^2*a22-3*a31^2*a32-3*a11^2*a12*a33*a32-3*a11^2*a12*a22+4*a11*a12*a22*a33*a31+a11^2*a33*a32+2*a11*a13*a31*a22+4*a11*a13* a31*a33*a32+3*a12^2*a21^2*a33*a32+a13^2*a31^2*a22+3*a13^2*a31^2*a33*a32+2*a11*a1 3*a32*a21+3*a12^2*a33^2*a31^2*a22+3*a12^2*a33^3*a31^2*a32+6*a12^2*a21*a22*a33*a3 1+6*a12^2*a21*a33^2*a31*a32+4*a12*a21*a13*a31*a22+8*a12*a21*a13*a31*a33*a32+2*a1 2*a21^2*a13*a32+4*a12*a22*a13*a31^2*a33+6*a12*a33^2*a31^2*a13*a32+2*a13^2*a31*a3 2*a21-3*a11^2*a13*a32-6*a11*a12^2*a21*a22-6*a11*a12^2*a21*a33*a32-6*a11*a12*a21*a13*a32-6*a11*a12^2*a22*a33*a31-6*a11*a12*a22*a13*a31-6*a11*a12^2*a33^2*a31*a32-12*a11*a12*a33*a31*a13*a32-6*a11*a13^2*a31*a32-3*a12^3*a21^2*a22-3*a12^3*a21^2*a33*a32-3*a12^2*a21^2*a13*a32-6*a12^3*a21*a22*a33*a31-6*a12^2*a21*a22*a13*a31-6*a12^3*a21*a33^2*a31*a32-12*a12^2*a21*a33*a31*a13*a32-6*a12*a21*a13^2*a31*a32-3*a12*a22*a13^2*a31^2-3*a12^3*a22*a33^2*a31^2-6*a12^2*a22*a33*a31^2*a13-3*a12^3*a33^3*a31^2*a32-9*a12^2*a33^2*a31^2*a13*a32-9*a12*a33*a31^2*a13^2*a32-3*a13^3*a31^2*a32) = 0,
(-a12^3*a33^3*a32^3-a12^3*a22^3+a12^2*a33^3*a32^3+3*a12^2*a33^2*a32^2*a22+4*a12*a22*a13*a32^2*a33+2* a12*a22^2*a13*a32+a13^2*a32^3*a33-6*a12^2*a22*a33*a32^2*a13-a32^3-3*a12*a33*a32^3*a13^2-3*a12^3*a22^2*a33*a32+2*a12*a33^2*a32^3*a13-3*a12^2*a33^2*a32^3*a13+a13^2*a32^2*a22-3*a12^2*a22^2*a13*a32-3*a12*a22*a13^2*a32^2-a13^3*a32^3+3*a12^2*a22^2*a33*a32-3*a12^3*a22*a33^2*a32^2+a12^2*a22^3) = 0,
(-3*a12^3*a21*a22^2+2*a11*a12*a33^2*a32^2+4*a11*a12*a33*a32*a22+2*a11*a12*a22^2-3*a31*a32^2-3*a11*a12^2*a22^2-3*a11*a13^2*a32^2+3*a12^2*a22^2*a21+3*a12^2*a22^2*a33*a31+a13^2*a32^2*a21+3*a13^ 2*a32^2*a33*a31+2*a11*a13*a32*a22+2*a11*a13*a32^2*a33+3*a12^2*a33^2*a32^2*a21+3* a12^2*a33^3*a32^2*a31+6*a12^2*a21*a22*a33*a32+4*a12*a21*a13*a32*a22+4*a12*a21*a1 3*a32^2*a33+6*a12^2*a22*a33^2*a31*a32+2*a12*a22^2*a13*a31+8*a12*a22*a13*a31*a33* a32+6*a12*a33^2*a31*a13*a32^2+2*a13^2*a31*a32*a22-3*a11*a12^2*a33^2*a32^2-6*a11*a12^2*a22*a33*a32-6*a11*a12*a22*a13*a32-6*a11*a12*a33*a32^2*a13-3*a12*a21*a13^2*a32^2-3*a12^3*a21*a33^2*a32^2-6*a12^3*a21*a22*a33*a32-6*a12^2*a21*a22*a13*a32-6*a12^2*a21*a33*a32^2*a13-3*a12^3*a22^2*a33*a31-3*a12^2*a22^2*a13*a31-6*a12^3*a22*a33^2*a31*a32-12*a12^2*a22*a33*a31*a13*a32-6*a12*a22*a13^2*a31*a32-9*a12*a33*a31*a13^2*a32^2-3*a12^3*a33^3*a31*a32^2-9*a12^2*a33^2*a31*a32^2*a13-3*a13^3*a31*a32^2) = 0
(Lösen nach a11,a12,a13,a21,a22,a23,a31,a32,a33)
(3*a12^2*a21^2*a22+4*a11*a12*a33*a32*a21+4*a11*a12*a33^2*a32*a31+4*a11*a12*a22*a 21+a11^2*a22-3*a31^2*a32-3*a11^2*a12*a33*a32-3*a11^2*a12*a22+4*a11*a12*a22*a33*a31+a11^2*a33*a32+2*a11*a13*a31*a22+4*a11*a13* a31*a33*a32+3*a12^2*a21^2*a33*a32+a13^2*a31^2*a22+3*a13^2*a31^2*a33*a32+2*a11*a1 3*a32*a21+3*a12^2*a33^2*a31^2*a22+3*a12^2*a33^3*a31^2*a32+6*a12^2*a21*a22*a33*a3 1+6*a12^2*a21*a33^2*a31*a32+4*a12*a21*a13*a31*a22+8*a12*a21*a13*a31*a33*a32+2*a1 2*a21^2*a13*a32+4*a12*a22*a13*a31^2*a33+6*a12*a33^2*a31^2*a13*a32+2*a13^2*a31*a3 2*a21-3*a11^2*a13*a32-6*a11*a12^2*a21*a22-6*a11*a12^2*a21*a33*a32-6*a11*a12*a21*a13*a32-6*a11*a12^2*a22*a33*a31-6*a11*a12*a22*a13*a31-6*a11*a12^2*a33^2*a31*a32-12*a11*a12*a33*a31*a13*a32-6*a11*a13^2*a31*a32-3*a12^3*a21^2*a22-3*a12^3*a21^2*a33*a32-3*a12^2*a21^2*a13*a32-6*a12^3*a21*a22*a33*a31-6*a12^2*a21*a22*a13*a31-6*a12^3*a21*a33^2*a31*a32-12*a12^2*a21*a33*a31*a13*a32-6*a12*a21*a13^2*a31*a32-3*a12*a22*a13^2*a31^2-3*a12^3*a22*a33^2*a31^2-6*a12^2*a22*a33*a31^2*a13-3*a12^3*a33^3*a31^2*a32-9*a12^2*a33^2*a31^2*a13*a32-9*a12*a33*a31^2*a13^2*a32-3*a13^3*a31^2*a32) = 0,
(-a12^3*a33^3*a32^3-a12^3*a22^3+a12^2*a33^3*a32^3+3*a12^2*a33^2*a32^2*a22+4*a12*a22*a13*a32^2*a33+2* a12*a22^2*a13*a32+a13^2*a32^3*a33-6*a12^2*a22*a33*a32^2*a13-a32^3-3*a12*a33*a32^3*a13^2-3*a12^3*a22^2*a33*a32+2*a12*a33^2*a32^3*a13-3*a12^2*a33^2*a32^3*a13+a13^2*a32^2*a22-3*a12^2*a22^2*a13*a32-3*a12*a22*a13^2*a32^2-a13^3*a32^3+3*a12^2*a22^2*a33*a32-3*a12^3*a22*a33^2*a32^2+a12^2*a22^3) = 0,
(-3*a12^3*a21*a22^2+2*a11*a12*a33^2*a32^2+4*a11*a12*a33*a32*a22+2*a11*a12*a22^2-3*a31*a32^2-3*a11*a12^2*a22^2-3*a11*a13^2*a32^2+3*a12^2*a22^2*a21+3*a12^2*a22^2*a33*a31+a13^2*a32^2*a21+3*a13^ 2*a32^2*a33*a31+2*a11*a13*a32*a22+2*a11*a13*a32^2*a33+3*a12^2*a33^2*a32^2*a21+3* a12^2*a33^3*a32^2*a31+6*a12^2*a21*a22*a33*a32+4*a12*a21*a13*a32*a22+4*a12*a21*a1 3*a32^2*a33+6*a12^2*a22*a33^2*a31*a32+2*a12*a22^2*a13*a31+8*a12*a22*a13*a31*a33* a32+6*a12*a33^2*a31*a13*a32^2+2*a13^2*a31*a32*a22-3*a11*a12^2*a33^2*a32^2-6*a11*a12^2*a22*a33*a32-6*a11*a12*a22*a13*a32-6*a11*a12*a33*a32^2*a13-3*a12*a21*a13^2*a32^2-3*a12^3*a21*a33^2*a32^2-6*a12^3*a21*a22*a33*a32-6*a12^2*a21*a22*a13*a32-6*a12^2*a21*a33*a32^2*a13-3*a12^3*a22^2*a33*a31-3*a12^2*a22^2*a13*a31-6*a12^3*a22*a33^2*a31*a32-12*a12^2*a22*a33*a31*a13*a32-6*a12*a22*a13^2*a31*a32-9*a12*a33*a31*a13^2*a32^2-3*a12^3*a33^3*a31*a32^2-9*a12^2*a33^2*a31*a32^2*a13-3*a13^3*a31*a32^2) = 0
(Lösen nach a11,a12,a13,a21,a22,a23,a31,a32,a33)