Meta-ticket: Polytopes, lattice (integer) point counting / enumeration, and their applications

[Matthias Köppe]

In this meta-ticket, I'm collecting tickets regarding lattice point counting and enumeration, relevant library interfaces, and its applications.

Not promising to do any work on it! Discussions on this ticket are very welcome in the comments section.

• #18029: speed up integral point enumeration
• #21037: Polyhedron.integral_points() fails for non-rational polytopes
• #21041: Polyhedron.integral_points(): Generalize Smith form based enumeration to semi-rational polytopes
• #18957: ehrhart_polynomial should be made available for polytopes defined over QQ
• #18190: bindings to Latte
• #18232: Support other LattE features: Ehrhart series, multivariate generating functions, integration, volume computation
• #13117: lrs_volume does not work with long numbers
• #18199: sage.geometry.polyhedron should have an lrs (lrslib) backend
• #20886: Upgrade lrslib to version 6.2 and build a shared library
• #15872: Let cddlib build a shared lib on Cygwin.
• #15871: Improve cddlib build system (especially split out non-upstream stuff).
• #21952: Update cddlib's autotooling
• #18195: Use cdd as a backend for polyhedra
• #20885: Normaliz interface
• #17920: Reimplement IntegerLists using Polyhedron.integral_points()
• #20905: fixing frobby package
• #10669: Implement MacMahon?'s partition analysis Omega operator (#22066 implements MacMahon?'s Omega operator)
• #17264: Polyhedron function broken with floats in sage-6.3 (worked in sage-6.2)
• #18220: Bug when creating a polyhedron with coefficients in RR
• #19803: difference of behavior in polyhedra with different backends
• #18214: Bug in volume computation of polyhedron
• #21270: Polyhedron RDF plotting bug
• #21143: new style package for qhull
• #12352: Add some tests for the qhull optional package
• #17197: document Polyhedron defined over number field
• #21217: Point lattices (free Z-modules) generated by algebraic real vectors
• #20278: Compute fundamental domain for symmetry groups of polyhedra
• #12957: Categories for finite (enumerated) sets
• #10544: LLL reduced kernel bases are not always correct
• #12388: add a function to solve CVP
• #17215: Bounding hyperplanes for polyhedra
• #17339: Polyhedron class mistreats empty inputs
• #21950: Add pulling_triangulation method to polyhedron class and point configuration
• #22067: generating function of integer-valued polyhedra
• #22111: generating function of integral points of polyhedra: option algorithm (naive, lattE)
• #22181: Implement Minkowski decomposition of polytopes
• #22469: Deprecate/remove sage/geometry/polytope.py
• #21937: Library of polytopes should allow specifying backend=...
• #22562: Lattice point count with preprocessing
• #23547: Add isl and barvinok packages

See also:

• #22420: Meta-ticket: Polyhedron: new features and known bugs
• #20302 Meta-ticket: Improvements to MixedIntegerLinearProgram, its backends, and InteractiveLinearProgram
• #20877 Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions
• #22710: Meta-ticket: polymake
• #22827: Meta-ticket: expose all normaliz features