f_res.matrixdecomp

f_res.matrixdecomp( Dpoly, UC, Vars )

:: Dixon polynomial を行列に分解する.

return

リスト

Dpoly

多項式

UC

配列

Vars

リスト

• dixonpolynomial Dpoly を行が UC の monomial, 列が Vars の monomial で添字付けられる行列に分解する.
• 戻り値は, [ (UC の monomial の配列),(行列),(Vars の monomial の配列) ] という形で,それぞれsigma_P = V D_P W の V, D_P, W を表す.

[0] F0 = a1*x + a2*y + a3$
[1] F1 = b1*x + b2*y + b3$
[2] F2 = c1*x^2 + c2*y^2 + c3 + c4*x*y + c5*x + c6*y$
[3] D = f_res.dixonpolynomial( [F0,F1,F2], [x,y] )$
[4] M = f_res.matrixdecomp( D[0], D[1], [x,y] );
[[ 1 _1 _0 ],[ c1*b3*a2-c1*b2*a3 -c2*b3*a1+c4*b3*a2+(c2*b1-c4*b2)*a3 (c3*b2-c6*
b3)*a1+(-c3*b1+c5*b3)*a2+(c6*b1-c5*b2)*a3 ]
[ 0 -c2*b2*a1+c2*b1*a2 -c2*b3*a1+c2*b1*a3 ]
[ -c1*b2*a1+c1*b1*a2 -c4*b2*a1+c4*b1*a2 -c4*b3*a1+c1*b3*a2+(c4*b1-c1*b2)*a3 ],[
 x y 1 ]]
[5] V = M[0]*M[1]$
[6] D[0] == V[0]*M[2][0]+V[1]*M[2][1]+V[2]*M[2][2];
1

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