Singular Manual: ncRelations

7.5.20.0. ncRelations

Procedure from library nctools.lib (see nctools_lib).

Usage:: ncRelations(r); r a ring
Return:: list L with two elements, both elements are of type matrix:
L[1] = matrix of coefficients C,
L[2] = matrix of polynomials D
Purpose:: recover the noncommutative relations via matrices C and D from a noncommutative ring

Example:

LIB "nctools.lib";
ring r = 0,(x,y,z),dp;
matrix C[3][3]=0,1,2,0,0,-1,0,0,0;
print(C);
==> 0,1,2, 
==> 0,0,-1,
==> 0,0,0  
matrix D[3][3]=0,1,2y,0,0,-2x+y+1;
print(D);
==> 0,1,2y,     
==> 0,0,-2x+y+1,
==> 0,0,0       
def S=nc_algebra(C,D);setring S; S;
==> // coefficients: QQ considered as a field
==> // number of vars : 3
==> //        block   1 : ordering dp
==> //                  : names    x y z
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    yx=xy+1
==> //    zx=2xz+2y
==> //    zy=-yz-2x+y+1
def l=ncRelations(S);
print (l[1]);
==> 0,1,2, 
==> 0,0,-1,
==> 0,0,0  
print (l[2]);
==> 0,1,2y,     
==> 0,0,-2x+y+1,
==> 0,0,0