On Oct 7, 11:38 am, Paul Zimmermann <[EMAIL PROTECTED]> wrote: > Hi, > > a question of a colleague from my lab: > > can Sage solve linear systems A*x=b, where A is a matrix with positive > integer coefficients, b is a vector with positive integer coefficients, > and the unknown vector x is searched over the positive integers? > > I guess this is more or less equivalent to integer linear programming (ILP), > see http://en.wikipedia.org/wiki/Integer_linear_programming#Integer_unknowns.
This may be a silly question, but integer linear programming seems to be about maximizing some quantity relative to constraints given by a matrix equality (or inequality), where everything is happening over the integers. How does this relate to finding integer solutions to a matrix equation? I find myself wanting to do something similar: find *all* solutions to Ax = b, where A, x, and b have non-negative integer entries. I'm trying to figure out if the various responses here will help me. In the situation of interest to me, I know that there are only finitely many solutions, and I know one solution. John --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
