Hi Andrew! On 12 Okt., 11:34, andrew ewart <aewartma...@googlemail.com> wrote: > If I is Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) and X=V(I), where > V(I) is the variety of I > and I have the following code > Code: > P.<x,y,z> = PolynomialRing(CC,order='lex') > I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) > ans=I.groebner_basis()
First of all, it is better to use QQ as coefficients, not CC. Even if you eventually want to compute complex solutions, a Gröbner basis computation in QQ would suffice - and have *theoretically* the same result as over CC. *Practically*, a computation over CC may give you a wrong result, because Gröbner basis computations are rather fragile if rounding errors occur. > how do I use this lex grobner basis to produce code that would output > the size of the set X What do you mean by "size"? Vector space dimension, if the Krull dimension is zero? Then you can proceed like this: sage: P.<x,y,z> = QQ[] # polynomial ring with exact coefficients sage: I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) sage: G = I.groebner_basis() sage: type(G) <class 'sage.structure.sequence.Sequence'> In order to compute dimension etc, you need to have an ideal, not a sequence. Hence: sage: IG = P*G # another syntax for creating an ideal sage: type(IG) <class 'sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal'> sage: IG.dimension? # if you like to learn what it does sage: IG.dimension() # this is the Krull dimension 0 By the way, here is a way to learn about the existence of methods. If you are interested into the vector space dimension, then a reasonable guess is that the method name starts with "ve". So, you may do sage: IG.ve<hit TAB-key> # this shows you all possible name extensions IG.vector_space_dimension IG.version sage: IG.vector_space_dimension() # this is (I guess) your expected result 6 By the way, it would not work over CC: sage: PC = PolynomialRing(CC,['x','y','z']) sage: IC = I.gens()*PC sage: GC = IC.groebner_basis() sage: IGC = GC*PC sage: IGC.dimension() 0 sage: IGC.vector_space_dimension() Traceback (most recent call last): ... TypeError: Cannot call Singular function 'vdim' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain'>' I guess this is in order to avoid nonsensical results over inexact fields. Cheers Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
