msolveSaturate -- compute a Groebner basis for the saturation of an ideal by a single polynomial in GRevLex order

Synopsis

Usage:

msolveSaturate(I)
Inputs:
- I, an ideal, in a polynomial ring with GRevLex order and coefficients over ZZ/p in characteristic more than $2^16$ and less than $2^{31}$
- f, a ring element, a polynomial in the same ring as I.
Optional inputs:
- Threads => an integer, default value 5, number of processor threads to use;
- Verbosity => an integer, default value 0, level of verbosity between 0, 1, and 2;
Outputs:
- GB, a matrix, whose columns form a Groebner basis for the ideal $I:f^\infty$, in the GRevLex order

Description

This functions uses the F4SAT algorithm implemented in the msolve library to compute a Groebner basis, in GRevLex order, of $I:f^\infty$, that is of the saturation of the ideal $I$ by the principal ideal generated by the polynomial $f$.

i1 : R=ZZ/1073741827[z_1..z_3]

o1 = R

o1 : PolynomialRing

i2 : I=ideal(z_1*(z_2^2-17*z_1-z_3^3),z_1*z_2)

                 3      2      2
o2 = ideal (- z z  + z z  - 17z , z z )
               1 3    1 2      1   1 2

o2 : Ideal of R

i3 : satMsolve=ideal msolveSaturate(I,z_1)

                 3
o3 = ideal (z , z  + 17z )
             2   3      1

o3 : Ideal of R

i4 : satM2=saturate(I,z_1)

                 3
o4 = ideal (z , z  + 17z )
             2   3      1

o4 : Ideal of R

Note that the ring must be a polynomial ring over a finite field.

Caveat

Currently the F4SAT algorithm is only implemented over prime fields in characteristic between $2^{16}$ and $2^{31}$.

Ways to use msolveSaturate:

msolveSaturate(Ideal,RingElement)

For the programmer

The object msolveSaturate is a method function with options.