D.4.7.8 sat_with_exp

Usage:

sat(id,j); id=ideal/module, j=ideal

Return:

list of an ideal/module [1] and an integer [2]:
[1] = saturation of id with respect to j (= union_(k=1...) of id:j^k) [2] = saturation exponent (= min( k | id:j^k = id:j^(k+1) ))

Note:

[1] is a standard basis in the basering

LIB "elim.lib";
ring r     = 2,(x,y,z),dp;
poly F     = x5+y5+(x-y)^2*xyz;
ideal j    = jacob(F);
sat(j,maxideal(1));
==> _[1]=x3+x2y+xy2+y3
==> _[2]=y4+x2yz+y3z
==> _[3]=x2y2+y4
sat(j,maxideal(2));
==> _[1]=x3+x2y+xy2+y3
==> _[2]=y4+x2yz+y3z
==> _[3]=x2y2+y4