Hi Roland, On 21 Jul., 06:33, Rolandb <rola...@planet.nl> wrote: > Hi, > How to simplify an expression if you have some known relations > (equalities)? Example: > > relation: 0 = a*x1^2 + b*x2^2 > expression = (a*x1^2 + b*x2^2)*y1+b*y2^3
Are all your relations polynomial? Then the standard solution is to use Gröbner bases and reduction. For example: sage: R.<x,y,z> = QQ[] sage: I = [x*y+z,y*z+x]*R So, the ideal I contains some relations, namely x*y+z=0 and y*z+x=0, and all of its consequences. It is easy to see that x^2-z^2 is a consequence of the relations. Indeed: sage: G = I.groebner_basis() sage: G [x^2 - z^2, x*y + z, y*z + x] sage: f = x^2 + x*y*z + x*z sage: f.reduce(G) x*z Of course, it is essential that one uses a Gröbner basis in the reduction: The original generating set of I is not appropriate: sage: (x^2-z^2).reduce(I) x^2 - z^2 sage: (x^2-z^2).reduce(G) 0 Cheers, 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
