If phcpack does not report any 'failure' solutions in classified_solution_dicts(), then it should have found all the roots. But the groebner methods are preferable if you are interested in exact solutions.
-Marshall On Jul 16, 11:29 am, Doug <mcke...@gmail.com> wrote: > > 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 -~----------~----~----~----~------~----~------~--~---
