This is the part in sage, f1,f2,f3 are 3 polynomials and I have to reduce them by I, the ideal in the line 8. This ideal is a vanishing ideal of some points. R = GF(3)['x1,x2,x3,x4']; R.<x1,x2,x3> = PolynomialRing(GF(3), order='degrevlex') x1,x2,x3 = R.gens(); f1=-x1^3+x1^2*x3-x1^2+x1*x3-x1; f2=x1^3-x1^2*x3+x1^2-x1*x3+x1+1; f3=-x1^3-x1^2*x3-x1^2-x1*x3-x1+1; I=R.ideal([ x1+x2-1,x2*x3-x3^2+x2-x3,x2^2-x3^2+x2-x3,x1^3-x1 ,x2^3- x2 ,x3^3-x3 ]); gf=I.groebner_fan(); gf.weight_vectors();
This is the part in singular, this because I have to change the term order (in sage is not possible). LIB "decodegb.lib"; LIB "polymake.lib"; LIB "standard.lib"; ring rin=3,(x(1..3)),Wp(1,2,2); poly f1=-x(1)^3+x(1)^2*x(3)-x(1)^2+x(1)*x(3)-x(1); poly f2= x(1)^3-x(1)^2*x(3)+x(1)^2-x(1)*x(3)+x(1)+1; poly f3=-x(1)^3-x(1)^2*x(3)-x(1)^2-x(1)*x(3)-x(1)+1; ideal tot=ideal([x(1)+x(2)-1,x(2)*x(3)-x(3)^2+x(2)-x(3),x(2)^2- x(3)^2+x(2)-x(3),x(3)^3-x(3),x(1)^3-x(1),x(2)^3-x(2)]); reduce(f1,std(tot)); reduce(f2,std(tot)); reduce(f3,std(tot)); Thank you! Bye! On Apr 6, 2:18 pm, Marshall Hampton <hampto...@gmail.com> wrote: > Can you post the system you are working with? Or if its very large, > post a link to a file? I don't work over finite fields myself, so the > current implementation is probably very biased towards QQ. It would > help me to see a "real life" example. > > Thanks, > Marshall Hampton > > On Apr 6, 2:04 am, Andrea Gobbi <andreamat...@gmail.com> wrote: > > > Thank you for the answer...I have some question: > > -I have gf=I.groebner_fan(); where I is a 0-dimentional ideal. Now gf > > has the function gf.weight_vectors(); This returns the weight vectors > > corresponding to the reduced Groebner bases. I try to call > > polyedralfan() but it raises an error...maybe because I' in > > characteristic p prime? Anyway if i can associate the polyedralfan and > > i call rays I obtain the same of gf.weight_vectors()?. > > -now I' thinking that I'm working in finite fields...maybe I can't > > consider the Grobner fan...I have to study more about it.... > > > I will post news when i'm sure of what i'm doing.... > > Thanks!! > > > On Apr 1, 5:48 pm, Marshall Hampton <hampto...@gmail.com> wrote: > > > > Unfortunately I don't think this is easy to do right now. > > > > If you have a Groebnerfan object for your ideal - lets call it G - > > > then you can get the associated polyhedral fan: > > > > Gp = G.polyhedralfan() > > > > This object has a method Gp.rays() that will give you the weight > > > vectors of the faces of the Groebner fan. You'd like to use those to > > > define a term-order; unfortunately that isn't wrapped in a real > > > convenient way in Sage but it is possible. If you read the help in: > > > > sage.rings.polynomial.term_order? > > > > it tells you that you can pass a term-ordering directly to Singular. > > > For that you need the information at: > > > >http://www.singular.uni-kl.de/Manual/3-1-0/sing_31.htm > > > > ...I think you'd want: > > > Wp( intvec_expression ) > > > > but I am not sure. > > > > Right now the PolyhedralFan object doesn't know which of the lower- > > > dimensional faces of the Groebner fan correspond to distinct bases. > > > That information must be available from Gfan somehow but I don't know > > > offhand how to extract it. > > > > Thanks for writing in with this question - I am more interested in > > > working on the interface knowing that someone is actually trying to > > > use it! My apologies for its limitations. > > > > -Marshall Hampton > > > > On Apr 1, 2:10 am, Andrea Gobbi <andreamat...@gmail.com> wrote:> > > > Hi!!!!!!!!! > > > > How can I use > > > > the function grobnerfan(ideal)? > > > > I have to reduce a polynomial > > > > f(x_1,....,x_n) using all possible grobner basis in F_p. This is too > > > > long, and so i decided to look only the grobner fan. But I can go > > > > over...i have a list (of what???) given by grobnerfan, and also a list > > > > of weight...but i don't understand how i can reduce the polynomial. > > > > > I means, if i have a term order, degrvlex for exmaple, i calculate the > > > > grobner fan (the term order is not important). With the function > > > > grobnerfan i obtain a lot of possible generators of the ideal, > > > > depending for the term order...but if i want to reduce a polynomial > > > > seems that i'm using the base term order, in my case degrevlex...or > > > > not? > > > > > I hope I was clear ( I'm italian and my english is very bad!!!!)... > > > > Thanks!!! -- 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 To unsubscribe, reply using "remove me" as the subject.
