Singular Manual: lpIsPrime

| #### 7.10.3.3 lpIsPrime Procedure from library `fpaprops.lib` (see fpaprops_lib). Usage: lpIsPrime(G); G an ideal in a Letterplace ring Return: boolean Purpose: Check whether A/<LM(G)> is prime ring, alternatively whether <LM(G)> is a prime ideal in A. Assume: - basering is a Letterplace ring - G is a Groebner basis Theory: A (two-sided) ideal I in the ring A is prime, if for any a,b in A one has aAb subseteq I implies a in I or b in I. Note: lpIsPrime 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,(x,y),dp;
    def R = freeAlgebra(r, 5);
    setring R;
    ideal G = x*x, y*y; // K<x,y>/<xx,yy> is prime
    lpIsPrime(G);
    ==> 1

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