#18232: Support other LattE features: Ehrhart series, multivariate generating
functions, integration, volume computation
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Reporter: mkoeppe | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-6.7
Component: geometry | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #18211, #18475, #18812 | Stopgaps:
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Changes (by mkoeppe):
* type: enhancement => task
Old description:
> #18211 added support for computing Ehrhart polynomials of lattice
> polytopes.
>
> LattE integrale has many more features that should be exposed in Sage:
>
> counting integer points in rational polytopes (#18812),
> computing Ehrhart series of rational polytopes,
> computing multivariate generating functions of integer points in
> polyhedra,
> integration (of polynomials over polytopes),
> volume computation (for polytopes).
>
> (See manual at
> https://www.math.ucdavis.edu/~latte/software/packages/latte_current/manual_v1.7.2.pdf)
>
> (The manual reveals that LattE has some other features that, however,
> require Maple as a subroutine; I omitted them in the list above.)
>
> All of these features are available from the command-line, so this is
> independent of #18190 (library bindings to LattE).
> The command-line interfacing can be adapted from #18211
> sage.geometry.polyhedron.Polyhedron_ZZ::ehrhart_polynomial
> (after that has been cleaned up in #18475 to use LattE's exit codes for
> more robust error handling)
New description:
#18211 added support for computing Ehrhart polynomials of lattice
polytopes.
LattE integrale has many more features that should be exposed in Sage:
counting integer points in rational polytopes (#18812),
computing Ehrhart series of rational polytopes,
computing multivariate generating functions of integer points in
polyhedra,
integration (of polynomials over polytopes),
volume computation (for polytopes).
(See manual at
https://www.math.ucdavis.edu/~latte/software/packages/latte_current/manual_v1.7.2.pdf)
(The manual reveals that LattE has some other features that, however,
require Maple as a subroutine; I omitted them in the list above.)
All of these features are available from the command-line, so this is
independent of #18190 (library bindings to LattE).
The command-line interfacing can be adapted from #18211
sage.geometry.polyhedron.Polyhedron_ZZ::ehrhart_polynomial
(after that has been cleaned up in #18475 to use LattE's exit codes for
more robust error handling)
Tickets:
- #20887: Integration of polynomials over polytopes with LattE
--
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Ticket URL: <https://trac.sagemath.org/ticket/18232#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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