Hi! On 25 Apr., 11:41, Santanu Sarkar <sarkar.santanu....@gmail.com> wrote: > Suppose f1, f2,....,f10 are polynomials over 20 variables over integers. > How one can check weather they are linearly independent or not in Sage?
When you talk about linear indepence of polynomials, you probably assume that they are all homogeneous of the same degree, do you? If this is the case, you could use "interreduction" for obtaining a basis of the vector space that is spanned by your polynomials - and comparing the size of that basis with the number of the given polynomials, you can conclude whether the input is linearly independent or not. Here is a small example, that should easily scale to 10 polynomials over 20 variables: We create 3 homogeneous polynomials of degree 2 on 3 variables: sage: R.<x,y,z> = ZZ[] sage: p = x^2+y^2 sage: q = y^2-x*y+z^2 sage: r = x^2+x*y-z^2 We consider the ideal they generate: sage: I = [p,q,r]*R Since the polynomials are homogeneous of the same degree, the following is a basis for the vector space spanned by p,q,r: sage: I.interreduced_basis() [x^2 + y^2, -x*y + y^2 + z^2] Since len(I.interreduced_basis() is smaller than I.ngens(), the generators of I are (linearly) dependent. Best regards, 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
