sage.geometry.polyhedron should have an lrs (lrslib) backend

[mkoeppe]

Sage already has lrs as an optional package (#18127 renames it lrslib).

For higher-dimensional polytopes, computing vertices by lrs is often much faster than the implementations of the double description method in cddlib and ppl. lrslib 6.2 (#20886) has two modes of parallel computation, plrs and mplrs, see ​​http://cgm.cs.mcgill.ca/~avis/C/lrs.html

lrs also has very fast and convenient code for removing redundant inequalities ("redund"). See ​https://groups.google.com/forum/#!topic/sage-support/WRpS5OgFMm8

Sage should have a backend_lrs.py to make use of the existing lrs package.

Links to older discussions regarding lrs: ​https://groups.google.com/forum/#!topic/sage-support/AZRzY7JyG_Y ​https://groups.google.com/forum/#!topic/sage-devel/oH6Jrjs-HUY

As has been said in these discussions, lrs also has a key benefit that it can generate the vertices as a stream, with very little memory use. This feature could be exposed using Python generators, using the Polyhedron methods Vrep_generator(), vertex_generator(), ray_generator(), line_generator().

See also: polymake (#20892) has an interface to at least some features of lrs

[ncohen]

I may have time to work on this in a couple of weeks.