Singular Manual: lpNF

| ##### 7.7.8.0. lpNF Procedure from library `freegb.lib` (see freegb_lib). Usage: lpNF(p,G); f letterplace polynomial, ideal I Return: poly Purpose: computation of the normalform 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

User manual for Singular version 4-0-3p3, 2016, generated by texi2html.