linear programming enhancements

[jasongrout]

I've been using the linear programming for class, and love it! Thanks! I noticed a few areas that would make it more user-friendly:

• it would be great if p.get_variables() returned the values of all of the variables by default, instead of insisting that you ask for a specific variable
• Maybe a p.show_solution() method could be added that would print out the optimal objective function value and the values of all variables, if the problem was solved.
• it would be cool if we wrapped the sensitivity analysis of various solvers. Like http://en.wikibooks.org/wiki/GLPK/Solution_information#Sensitivity_analysis_report for GLPK.
• the maximization=False parameter is a little awkward. Perhaps that parameter could be renamed to type="maximize" or type="minimize". Or perhaps we could also have a minimize=None parameter, and if maximize and minimize are both None, the default is maximize (for compatibility), but if either is set, that is the problem, and if both are set to True, then we throw an error.

CC: @nathanncohen @mforets

Component: linear programming

Issue created by migration from https://trac.sagemath.org/ticket/15356

[novoselt]

comment:3

Note also that #14288 is positively reviewed!