Thank you very much for your kind help. On 25 April 2010 17:00, Simon King <simon.k...@nuigalway.ie> wrote:
> On 25 Apr., 12:50, Santanu Sarkar <sarkar.santanu....@gmail.com> > wrote: > > Sorry again. Dependency needs over integer. > > Probably there is a better way of doing it, but the following works: > > Transform the problem into a matrix: One row for each polynomial, one > column for each monomial that occurs in one of the polynomials, and > the entries given by the coefficient of a monomial in a polynomial. > > Hence: > sage: R.<x1,x2,x3>=ZZ[] > sage: f1=1+x1+x2+x1*x2 > sage: f2=1+x1+x3+x1*x3 > sage: P = [f1, f2, f1*f2, x1*f2, x2*f2] # the list of polynomials > sage: V = list(set(sum([p.monomials() for p in P],[]))) # the list of > all occuring monomials > sage: V > [1, x1*x2*x3, x1*x3, x1*x2, x1, x1^2, x3, x2, x1^2*x2, x1^2*x3, x2*x3, > x1^2*x2*x3] > sage: p_to_dict = lambda p: dict([(x[1],x[0]) for x in list(p)]) # an > auxiliary function > sage: D = [p_to_dict(p) for p in P] # list of dictionaries providing > the coefficients > sage: M = Matrix(ZZ, [[d.get(m,0) for m in V] for d in D]) > sage: M > [1 0 0 1 1 0 0 1 0 0 0 0] > [1 0 1 0 1 0 1 0 0 0 0 0] > [1 2 2 2 2 1 1 1 1 1 1 1] > [0 0 1 0 1 1 0 0 0 1 0 0] > [0 1 0 1 0 0 0 1 0 0 1 0] > sage: M.kernel() > Free module of degree 5 and rank 0 over Integer Ring > Echelon basis matrix: > [] > > So, no linear dependency. > > But, as I said, I would expect that it can be done better, and I even > don't know if the above transformations are efficiently done. > > 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<sage-support%2bunsubscr...@googlegroups.com> > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- 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
