# The number of solutions of a polynomial system using a Gröbner basis

The following extract from this Wikipedia page explains that we can easily deduce the number of solutions of a polynomial system using Gröbner basis:

Given the Gröbner basis G of an ideal I, it has only a finite number of zeros, if and only if, for each variable x, G contains a polynomial with a leading monomial that is a power of x (without any other variable appearing in the leading term). If it is the case

the number of zeros, counted with multiplicity, is equal to the number of monomials that are not multiple of any leading monomial of G. This number is called the degree of the ideal.

*Question*: Is there a function in Sage computing this number of zeros from a given Gröbner basis?