Singular

D.2.4.4 pnormalf

Usage:

pnormalf(poly f,ideal E,ideal N);
f: the polynomial in Q[a][x] (a=parameters,
x=variables) to be reduced modulo V(E) \ V(N)
of a segment in Q[a].
E: the null conditions ideal in Q[a]
N: the non-null conditions in Q[a]

Return:

a reduced polynomial g of f, whose coefficients are
reduced modulo E and having no factor in N.

Note:

Should be called from ring Q[a][x]. Ideals E and N must be given by polynomials in Q[a].

LIB "grobcov.lib";
if(defined(R)){kill R;}
ring R=(0,a,b,c),(x,y),dp;
short=0;
// parametric polynom
poly f=(b^2-1)*x^3*y+(c^2-1)*x*y^2+(c^2*b-b)*x+(a-bc)*y;
// ideals defining V(p)\V(q)
ideal p=c-1;
ideal q=a-b;
// pnormaform of f on V(p) \ V(q)
pnormalf(f,p,q);
==> (b^2-1)*x^3*y+(a-b)*y