
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 (twosided) 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

