This is a follow-up from #28175 (Move optional sage optimization backends (COIN, CPLEX, Gurobi) to separate Cython packages to remove OptionalExtension problems).

In fact, sage.numerical.backends depends on very little from Sage. We could move the entire backend machinery to a separate packages - for broadening the developer base and/or within the context of #26511.

Some notes regarding this:

• get_solver uses base_ring - needs some mild refactoring to avoid dependency on the sagelib parent/element framework
• GLPKBackend depends on sage.libs.glpk, which should also become a separate Cython package. See also Meta-ticket: Use Python optimization interfaces: CVXPY, SCIP, or-tools, PuLP, Pyomo, cylp... #26511 for alternatives.

See also:

• Meta-ticket: Use Python optimization interfaces: CVXPY, SCIP, or-tools, PuLP, Pyomo, cylp... #26511 - Meta-ticket: Use Python optimization interfaces: PuLP, Pyomo, cylp...

CC: @isuruf @saraedum @kiwifb @dimpase @sagetrac-tmonteil @videlec

Component: numerical

Issue created by migration from https://trac.sagemath.org/ticket/28920