Suppose I form the row matrix: M = [ (p_1*p_2, .., p_i*p_j) ] and then try looking for a column vector x satifying M*x = q where the elements of x are integers, hopefully 1 or -1. If I tried this approach how would I get sage to only consider integer vectors x as solutions.
On Sep 8, 6:20 am, john_perry_usm <[email protected]> wrote: > Are you asking whether q=p_1*p_2+...+p_5*p_6? If so, you can simply > construct q and the p_i, then test for equality: > > sage: q == p_1*p_2 + ... + p_5*p_6 > > >> True (or False, depending) > > (you would fill in the ellipsis with the form you want, which is not > obvious to me from what you've written). > > If instead you want to know if q is *some* linear combination of > p_1*p_2, ..., p_5*p_6 then you could use either linear algebra (I > think) or some slightly more sophisticated commutative algebra (e.g., > a Groebner basis, but that might be more than you need for this > specific case). > > regards > john perry > > On Sep 8, 1:57 am, Cary Cherng <[email protected]> wrote: > > > > > I am not familiar with algebraic geometry or its terminology and new > > to sage. > > > p_1,...p_n and q are elements of Z[x_1,...,x_n]. In my context I have > > some evidence that q can be written as something like q = p_1*p_2 > > + ... + p_5*p_6. In other words q is a degree 2 polynomial in the > > p_i's. Can Sage find out if q can be written in terms of the p_i's? -- 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
