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7.7.9.0. 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, that is when p1 * (A/<LM(G)>) * p2 != 0 for all p1, p2 in (A/<LM(G)> - {0}).
- Assume:
- - basering is a Letterplace ring
- G is a Groebner basis
- Theory:
- 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 = makeLetterplaceRing(5);
setring R;
ideal G = x(1)*x(2), y(1)*y(2); // K<x,y>/<xx,yy> is prime
lpIsPrime(G);
==> 1
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