In mathematics, the Grothendieck ring of varieties is an algebraic ring. It is defined as the quotient of the free abelian group on the set of isomorphism classes of varieties over a field k​, by relations of the form [X] = [X - Z] + [Z], where Z is a closed subvariety of X. Multiplication is distributively induced by [X] ∙ [Y] = [ (X × Y)_red ].

This repository contains (Python) code to compute classes of complex varieties, in terms of the class of the affine line q = [ A¹_C ]. As an example, the class of the variety X = { (x, y) in C² : xy = 1 and x ≠ 3 } would be computed using the following code.

import sympy as sp

x, y = sp.symbols('x, y')

system = System([ x, y ], [ x*y - 1 ], [ x - 3 ])

solver = Solver()
solver.compute_grothendieck_class(system)

The output will be q - 2, as expected.