Hello everybody !

It is getting late here, and I am just out of a patch that took me
quite some time and energy.

It is a complete rewrite of the interface between Sage and the LP
solvers it supports (GLPK, Coin, CPLEX). It means that we now have
some abstract Cython interface to deal with all of them, and not these
ugly python calls from before which prevented us from using any
interesting solver-specific method (for example with Gurobi...). The
code is cleaner, more efficient, easier to change, and we can already
do more things with it.

For example, constraint generation. I do not even know of any way to
dynamically generate constraints and variables when working on LP
without actually writing C code, and it is now possible directly in
Python. Or in Cython, if you want it to be faster. This means that
some new things are possible in Sage, which leads to more efficient
algorithms for Feedback Edge set #9923 or to a new one to compute the
fractional chromatic index of a graph #10044. Many others will follow,
it will just be too easy to obtain impressive speedups using it :-)

This patch is now to be reviewed on ticket #10043, and I expect this
will take some time. It passes all tests with any solver available on
my computer, and I of course tried to think of everything, but
considering the time it is quite likely I missed a lot.... so if
anybody here is willing to help, I'll be quite glad to discuss/fix any
part of the code as soon as something odd appears... starting tomorrow
!

... and I hope this will prove useful :-)

Have fuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuun !!!

Nathann

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