Hi! On 3 Sep., 21:37, JamesHDavenport <[email protected]> wrote: > On Sep 3, 6:56 pm, Jason Bandlow <[email protected]> wrote:> For polynomial > equations, the following should work in general. > > > sage: R.<x,y> = CC['x','y'] > > sage: f = x-y > > sage: g = x^2 - y^2 > > sage: I = R.ideal([f]).radical() > > sage: g in I > > True > > > In general, to see if the equation g == 0 is implied by the equations > > f1==0, f2==0, ..., fn==0 you can do > > > I = R.ideal([f1, f2, ..., fn]).radical() > > g in I > > Assuming that you are working over the complexes (or more generally > any algebraically closed field, subject to changing CC appropriately), > yes. Ove rthe reals it is solved, but more difficult and I don't know > if SAGE has the tools.
What exactly is the problem? Given two sets p1, p2 of polynomials over a ring R: (1) Test whether all solutions of [q==0 for q in p1] in R are also solutions of [q==0 for q in p2]. or (2) Test whether the ideal generated by p2 is contained in the ideal generated by p1. ? If it is (2), the solution is to use Gröbner bases, which are of course available in Sage. If it is (1) then James is right that one has to know whether R is algebraically closed (if it is, one can use the radical of the ideal). And I don't know either if the solution over the reals is in Sage. If it is, then it is probably via Singular. So, I guess it'd be worth while to look into the Singular manual. Cheers, Simon -- 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
