problems with command 'division'

[seelisch]

(This trac ticket is based on two emails from markus.lange.hegermann@… received Sept 23, 2009.) unexpected zero entries in U (see attachment); unexpected mismatching matrix dimensions (see attachment)

[seelisch]

example with polynomial entries: ========================================= ring RR = 0,(x,y,z),ds;

matrix M[5][6]=[0,x*y-x^3*y,0,x4-x^6,x3*y-x^5*y,x3*z-x^{5*z, 0,y*z-x}2*y*z,0,x^3*z-x5*z,x^2*y*z-x4*y*z,x^2*z2-x^4*z2, 0,z-x^2*z,x2-x^2*y+x*y2-x^4-x*y3+x^4*y,-x2*y*z,x^2*y*z-x*y2*z+x*y^3*z-x4*y*z,-x*y*z^{2, 0,0,-x*y+x*y}2-y^3+x3*y+y^4-x3*y^2,x2*z+x*y^2*z-x4*z,x*y*z-x*y^2*z+y3*z-x^3*y*z-y4*z+x^3*y2*z,x*z^2+y2*z^2-x3*z^{2, 0,0,0,0,0,0 ];}

matrix N[5][5]=[0,x*y,0,x^4,x3*y,x^{3*z, 0,y*z,0,x}3*z,x^2*y*z,x2*z^{2, -x*y,z,x}2-x^2*y+x*y2,-x^2*y*z,x2*y*z-x*y^2*z,-x*y*z2, y^2,0,-x*y+x*y2-y^3,x2*z+x*y^{2*z,x*y*z-x*y}2*z+y^3*z,x*z2+y^2*z2, 1-x^2,0,-y2+x^2*y,-x3*z,y^2*z-x2*y*z,-x^2*z2 ];

list l=division(M,N);

matrix T=l[1]; matrix R=l[2]; matrix U=l[3];

U should be a diagonal matrix of units print(U);

but the first column of M is zero print(M);

=========================================== example with number entries: =========================================== ring RR = 0,(x),ds;

matrix M[2][2]=[1,0,0,0];

matrix NN[2][1]=[1,0]; module N=std(NN);

list l=division(M,N);

matrix T=l[1]; matrix R=l[2]; matrix U=l[3];

print("matrix(M)*U"); print(matrix(M)*U); print("matrix(N)*T+matrix(R)"); print(matrix(N)*T+matrix(R));

print("M"); print(M); print("N"); print(N); print("T"); print(T); R should have the same dimension as M print("R"); print(R); here again a zero is given instead of a unit print("U"); print(U);

matrix R2=reduce(M,N); R2 should have the same dimension as M print("R2"); print(R2);

[hannes]

2 problems: - size of result matrices in reduce and division: fixed

• shall U be filled with 1 in unused places ? yes (according to the manual)