I am not an expert on LP, but as an author of alternative (not merged, see http://trac.sagemath.org/ticket/14288 ) LP functionality let me add a couple rubbles nevertheless.
My implementation does not assume any bounds on variables when you construct an LPProblem, but you can add non-negativity or non-positivity explicitly and when constructing LPProblemStandardForm everything is forced to be non-negative. >From what I know of simplex method (after teaching it to a few hundred students ;-)), sign restrictions on variables are quite different from other constraints and, in fact, it is very natural to reduce a system of equality and inequality constraints to a system of equations plus sign restrictions, i.e. leave only the simplest inequalities possible: homogeneous and in a single variable each. I imagine that non-homogeneous inequalities in a single variable also can be handled much more efficiently than generic ones and it is very natural to do it for binary variables. Let me also without any modesty suggest yet another solution: merge my module without any extra assumptions for use by students and perhaps leave "the real LP functionality" that is used by experts close to actual solvers. I also completely support getting rid of get/set methods for bounds - specify them when defining a variable! Thank you, Andrey -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
