> The last element of that Groebner basis is a univariate polynomial in > x2, so it is relatively easy to analyze its solutions. There is one > triple root at x2=0, and then four others which are presumably the > four you are thinking of. Once you have a value for x2, you can > substitute it into the other Groebner basis equations to find x1.
Indeed, you're right, my preferred solution is in there! I looked to see if the first element was in one variable and when it wasn't, I didn't think to look at the others. doh! Now, I can copy and paste the appropriate basis element to turn it into something I can pass to solve(), but there must be a better (more programmatic) way to coerce it: sage: B[2] x2^7 + 4*x2^6 - 6*x2^5 - 20*x2^4 + 5*x2^3 sage: type(B[2]) <type 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'> sage: foo = x2^7 + 4*x2^6 - 6*x2^5 - 20*x2^4 + 5*x2^3 ; foo x2^7 + 4*x2^6 - 6*x2^5 - 20*x2^4 + 5*x2^3 sage: type(foo) <type 'sage.symbolic.expression.Expression'> > ... phcpack ... My equations are actually first order condtions of the Lagrangian from a constrained optimization problem. I've been trying to solve them symbolically so I know I've found all the solutions (not just the one closest to my starting value). That is, up til now I've been loath to apply numerical optimization methods to the problem directly. But using phcpack on the FOC's seems to find all the solutions so that might be a numerical method that's OK in this case. Thanks! Doug --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
