7.10.3.3 lpIsPrime

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>.

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