Singular Manual: lpIsSemiPrime

| ##### 7.7.9.0. lpIsSemiPrime Procedure from library `fpaprops.lib` (see fpaprops_lib). Usage: lpIsSemiPrime(G); G an ideal in a Letterplace ring Return: boolean Purpose: Check whether A/<LM(G)> is semi prime, that is when p * (A/<LM(G)>) * p != 0 for all p in (A/<LM(G)> - {0}). Assume: - basering is a Letterplace ring - G is a Groebner basis Theory: lpIsSemiPrime works with the monomial algebra A/<LM(G)>. A positive answer holds for both A/<LM(G)> and A/<G>, while a negative answer applies only to A/<LM(G)> and not necessarily to A/<G>. Example:
    LIB "fpaprops.lib";
    ring r = 0,(x1,x2),dp;
    def R = makeLetterplaceRing(5);
    setring R;
    ideal G = x1(1)*x2(2), x2(1)*x1(2); // K<x1,x2>/<x1*x2,x2*x1> is semi prime
    lpIsSemiPrime(G);
    ==> 1

User manual for Singular version 4-1-1p3, 2018, generated by texi2html.