On 13 Okt., 12:21, Simon King <[email protected]> wrote: > I am not sure if the methods "dimension" and "vector_space_dimension" > would automatically compute the Gröbner basis. The corresponding > commands in Singular won't.
I just checked: Yes, the GB is computed internally if the Krull or vector space dimensions are requested. Hence, the computation can be slightly simplified doing sage: P.<x,y,z> = QQ[] sage: I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) sage: IR = I.radical(); IR # at this point, the GB isn't computed... Ideal (x + y + z - 3, y^2 + y*z + z^2 - 3*y - 3*z + 2, 3*z^3 - 9*z^2 + 6*z + 2) of Multivariate Polynomial Ring in x, y, z over Rational Field sage: IR.dimension() # ... but here it is, internally 0 sage: IR.vector_space_dimension() 6 or in one line sage: I.radical().vector_space_dimension() 6 which would raise a TypeError if the ideal was not zero dimensional. Cheers, Simon -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
