D.4.15.2 modSat

Usage:

modSat(I, J, #); I, J ideals, # an optional list which is either empty (not entered) or consists of precisely one integer which is 0 or 1.

Assume:

The common basering of I and J is defined over the rationals.

Return:

A list consisting of an ideal [1] and an integer [2]:
[1] = saturation of of I by J
[2] = saturation exponent (= min( k | I:J^k = I:J^(k+1)))

Note:

[1] is given by a standard basis in the basering.
- The function proceeds by successively computing ideal quotients. The intermediate results will be checked for correctness if # is either empty (not entered)s or if #[1] = 1.
Without the checks, the function returns a final result which is correct with high probability.

LIB "modquotient.lib";
ring R = 0, (x,y,z), dp;
ideal I = x2+xyz, y2-z3y, z3+y5xz;
ideal J = maxideal(3);
list L = modSat(I, J);
L;
==> [1]:
==>    _[1]=yz+x
==>    _[2]=z3-y
==>    _[3]=xz2+y2
==>    _[4]=y3-x2z
==>    _[5]=x4z-1
==>    _[6]=x3y2+z
==>    _[7]=x4y-z2
==>    _[8]=x5+y
==> [2]:
==>    2