D.5.4.2 gmsnf

Procedure from library gaussman.lib (see gaussman_lib).

Usage:

gmsnf(p,K); poly p, int K

Assume:

basering returned by gmsring

Return:

list nf; ideal nf[1]; projection of p to <gmsbasis>C[[s]] mod s^(K+1) ideal nf[2]; p==nf[1]+nf[2]

Note:

computation can be continued by setting p=nf[2]

Example:

LIB "gaussman.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
def G=gmsring(t,"s");
setring(G);
list l0=gmsnf(gmspoly,0);
print(l0[1]);
→ -1/2y5
list l1=gmsnf(gmspoly,1);
print(l1[1]);
→ -1/2y5+1/2s
list l=gmsnf(l0[2],1);
print(l[1]);
→ 1/2s