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

[mkoeppe]

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.

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

See also:

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

CC: @anneschilling @tscrim @nthiery @jdemeyer @tkluck @dimpase @novoselt @videlec @fchapoton @kcrisman @w-bruns @mo271 @jplab @mmasdeu @dkrenn @seblabbe @sagetrac-etzanaki @embray @sagetrac-tmonteil @mforets @braunmath @sophiasage

Component: geometry

Keywords: days84

Issue created by migration from https://trac.sagemath.org/ticket/20875

[mkoeppe]

Changed author from aschilling, tscrim, nthiery, jdemeyer, tkluck, dimpase to none

[jplab]

Changed keywords from none to days84