ParamPunPam.jl computes Groebner bases in
ParamPunPam.jl is primarily designed to work in cases when the coefficients of the basis are sparse and of low degree.
You can install ParamPunPam.jl with the following command in Julia:
import Pkg; Pkg.add("ParamPunPam")ParamPunPam.jl provides a single function: paramgb.
This function works in combination with polynomials from Nemo.jl.
See the following example:
using ParamPunPam, Nemo
# Create polynomial rings
R_param, (a, b) = QQ["a", "b"]
R, (x, y, z) = fraction_field(R_param)["x", "y", "z"]
# Polynomial system
F = [
x^2 + x + (a + 1),
x*y + b*y*z + 1//(a*b),
x*z + z + b
]
paramgb(F)
# Returns
3-element Vector{AbstractAlgebra.Generic.MPoly{AbstractAlgebra.Generic.FracFieldElem{fmpq_mpoly}}}:
z^2 + b//(a + 1)*z + b^2//(a + 1)
y + (-a - 1)//(a^2*b^2 + a*b^4 + a*b^2)*z - 1//(a^2*b + a*b^3 + a*b)
x + (-a - 1)//b*z