grobx

grobx computes reduced Gröbner bases of polynomial ideals over prime fields GF(p), p a prime below 2^64, and over the rationals ℚ. This is its Python module. It takes the ideal's generators as text and returns the basis as text.

The package is a wheel for Linux on x86-64 and CPython 3.12 and later.

Install

pip install grobx

Example

import grobx

r = grobx.groebner("x,y\n7\nx^2+y,\nx*y-1\n")
r.basis    # '[y^2+x,\nx*y+6,\nx^2+y]:\n'

The input is msolve's format: the variables on line 1, separated by commas, the largest first; the characteristic on line 2, a prime below 2^64 for GF(p) or 0 for ℚ; then the generators, separated by commas. Over ℚ:

r = grobx.groebner("x,y,z\n0\nx+y+z,\nx*y+y*z+z*x,\nx*y*z-1\n")
print(r.basis)
# [x+y+z,
# y^2+y*z+z^2,
# z^3-1]:

The call

grobx.groebner(text, *, order="grevlex", threads=0, seed=None, deadline=None, cancel=None,
               memory=None, checker=None, cofactors=False, report=False)

The call releases the GIL while it computes. It returns a grobx.Result:

An instance or a parameter the call cannot take raises grobx.Error, a subclass of ValueError.

Documentation

The manual describes the formats, the bounds, the checker, and the engine. grobx.com has the benchmarks and the instance corpus, and GitHub the source.

License

GPL-3.0-only. Copyright Code1 GmbH.

Code1 GmbH also offers grobx under a commercial license.