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7.7.9.0. lpNF
Procedure from library freegb.lib (see freegb_lib).
- Usage:
- lpNF(p,G); f letterplace polynomial, ideal I
- Return:
- poly
- Purpose:
- computation of the normal form of p with respect to G
- Assume:
- p is a Letterplace polynomial, G is a set Letterplace polynomials,
being a Letterplace Groebner basis (no check for this will be done)
- Note:
- Strategy: take the smallest monomial wrt ordering for reduction
- For homogenous ideals the shift does not matter
- For non-homogenous ideals the first shift will be the smallest monomial
Example:
| | LIB "freegb.lib";
ring r = 0,(x,y,z),dp;
int d =5; // degree
def R = makeLetterplaceRing(d);
setring R;
ideal I = y(1)*x(2)*y(3) - z(1)*y(2)*z(3), x(1)*y(2)*x(3) - z(1)*x(2)*y(3), z(1)*x(2)*z(3) - y(1)*z(2)*x(3), x(1)*x(2)*x(3) + y(1)*y(2)*y(3) + z(1)*z(2)*z(3) + x(1)*y(2)*z(3);
ideal J = letplaceGBasis(I); // compute a Letterplace Groebner basis
poly p = y(1)*x(2)*y(3)*z(4)*y(5) - y(1)*z(2)*z(3)*y(4) + z(1)*y(2)*z(3);
poly q = z(1)*x(2)*z(3)*y(4)*z(5) - y(1)*z(2)*x(3)*y(4)*z(5);
lpNF(p,J);
==> z(1)*y(2)*z(3)*z(4)*y(5)-y(1)*z(2)*z(3)*y(4)+z(1)*y(2)*z(3)
lpNF(q,J);
==> 0
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