# Revision history [back]

It is easy to compute what you want in Sage if you have a specific ring and specific number of variables. The method you want is the vector_space_dimension method of the ideal I. Here is an example from the documentation for that method that involves the field QQ (rational numbers) and two generators u, v:

sage: R.<u,v> = PolynomialRing(QQ)
sage: g = u^4 + v^4 + u^3 + v^3
sage: I = ideal(g) + ideal(g.gradient())
sage: I
Ideal (u^4 + v^4 + u^3 + v^3, 4*u^3 + 3*u^2, 4*v^3 + 3*v^2) of Multivariate Polynomial Ring in u, v over Rational Field
sage: I.dimension()
0
sage: I.vector_space_dimension()
4

It is easy to compute what you want in Sage if you have a specific ring field k and specific number of variables. generators. The method you want is the vector_space_dimension method of the ideal I. Here is an example from the documentation for that method that involves the field QQ (rational numbers) and two generators u, v:

sage: R.<u,v> = PolynomialRing(QQ)
sage: g = u^4 + v^4 + u^3 + v^3
sage: I = ideal(g) + ideal(g.gradient())
sage: I
Ideal (u^4 + v^4 + u^3 + v^3, 4*u^3 + 3*u^2, 4*v^3 + 3*v^2) of Multivariate Polynomial Ring in u, v over Rational Field
sage: I.dimension()
0
sage: I.vector_space_dimension()
4