Singular Manual: CompDecomp

| ##### 7.5.1.0. CompDecomp Procedure from library `bimodules.lib` (see bimodules_lib). Usage: CompDecomp(p); p poly Note: This procedure only works if the basering is an enveloping algebra A^{env} of a (non-commutative) ring A. Thus also the polynomial in the argument has to be in A^{env}. Return: Returns an ideal I in A^{env}, where the sum of all terms of the argument with the same right side (of the tensor summands) are stored as a generator of I. Let b != c, then for p = (a (X) b) + (c (X) b) + (a (X) c) the ideal I := CompDecomp(p) is given by: I[1] = (a (X) b) + (c (X) b); I[2] = a (X) c. Purpose: By decomposing the polynomial we can easily check whether the given polynomial is a pure tensor. Example:
    LIB "bimodules.lib";
    ring r = 0,(x,s),dp;
    def R = nc_algebra(1,s); setring R; //1st shift algebra
    def Re = envelope(R); setring Re; //basering is now R^{env} = R (X) R^{opp}
    poly f = X*S*x^2+5*x*S*X+S*X; f;
    ==> x2SX+x2S+5xSX+SX
    ideal I = CompDecomp(f);
    print(matrix(I)); // what means that f = (x2+5x+1)*SX + x2*S
    ==> x2SX+5xSX+SX,x2S
    poly p = x*S+X^2*S+2*s+x*X^2*s+5*x*s; p;
    ==> xsX2+5xs+xS+2s+SX2+2SX+S
    ideal Q = CompDecomp(p);
    print(matrix(Q));
    ==> xsX2,5xs+2s,xS+S,SX2,2SX

User manual for Singular version 4.4.1, 2025, generated by texi2html.