generic latte_int interface to integrate

[mforets]

Provide a generic interface to integrate a polynomial over a polytope.

See also #18232.

Depends on #22497

CC: @videlec @mkoeppe @jplab

Component: packages: optional

Keywords: days84

Author: Marcelo Forets

Branch/Commit: 6a474f9

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/22522

[mforets]

Dependencies: #22497

[videlec]

Changed keywords from none to days84

[mforets]

Branch: u/mforets/22497

[mforets]

Commit: 96e4099

[mforets]

New commits:

d5ff154	22497: generic interface to LattE integrale count
96e4099	Integral of a polynomial over a polytope.

[sagetrac-git]

Changed commit from 96e4099 to d3c9589

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d3c9589

Add volume function to generic latte_int interface.

[videlec]

comment:6

Why your commit d3c9589 is here!? Shouldn't it belong to another ticket?

[sagetrac-git]

Changed commit from d3c9589 to 000bf8b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

000bf8b

Restructured the script, with an integrate function accepting different valuations.

[sagetrac-git]

Changed commit from 000bf8b to 5aa6695

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5aa6695

Added test for helper function _to_latte_polynomial.

[sagetrac-git]

Changed commit from 5aa6695 to 72d03a1

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

72d03a1

Minor changes to helper function and integrate.

[mkoeppe]

comment:10

Replying to @videlec:

Why your commit d3c9589 is here!? Shouldn't it belong to another ticket?

The branch is on top of the branch of #22497.

[mkoeppe]

Reviewer: Matthias Koeppe

[mkoeppe]

comment:11

Looks good to me.

Now follow-up tickets with corresponding methods of Polyhedron would be good.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

6a474f9

fixed a typo in the docstring

[sagetrac-git]

Changed commit from 72d03a1 to 6a474f9

[mkoeppe]

comment:13

What does

``[1,[2,2,2]]``

do in the doctest?

[mkoeppe]

comment:16

Learn about :: in the doc formatting. This will solve your problem.
Also build and verify the html doc.

[tscrim]

comment:17

There are also a number of doc issues with integrate in base.py. The doc should start with

    def integrate(self, polynomial, **kwds):
        r"""
        Return the integral of a polynomial over a polytope.

        INPUT:

        - ``polynomial`` -- a multivariate polynomial or a valid LattE description string
          for a polynomial

        - ``**kwds`` -- additional keyword arguments that are passed to the engine

        OUTPUT:

        The integral of the polynomial over the polytope.

        .. NOTE::

            The polytope triangulation algorithm is used. This function depends on
            LattE (i.e., the ``latte_int`` optional package).

The code in the EXAMPLES:: block also needs to be indented (as per comment:16).

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

91d885e	Fix the docstrings, and enhance integrate method.
507aea5	Add the new volume engine Polyhedron.

[sagetrac-git]

Changed commit from 17911f7 to 507aea5

[mforets]

comment:19

done! and thanks both for the help. from my side this ticket and #20887 are ok.

in the proposed solution, the new volume and integrate methods can also receive polyhedra in RDF, and each vertex is cast to QQ with an iterator over the vertices.

[videlec]

comment:20

Replying to @mforets:

done! and thanks both for the help. from my side this ticket and #20887 are ok.

Nice work!

in the proposed solution, the new volume and integrate methods can also receive polyhedra in RDF, and each vertex is cast to QQ with an iterator over the vertices.

Is the answer of .integrate() will be a RDF? Otherwise I think it is a bad idea.

[videlec]

comment:21

Replying to @sagetrac-git:

Branch pushed to git repo; I updated commit sha1. New commits:

91d885e	Fix the docstrings, and enhance integrate method.
507aea5	Add the new volume engine Polyhedron.

I don't understand why these commits are here... this ticket is about generic latte_int interface to integrate. If you change the purpose of the ticket you need to update the description.

[mforets]

comment:23

Replying to @videlec:

Replying to @mforets:

done! and thanks both for the help. from my side this ticket and #20887 are ok.

Nice work!

in the proposed solution, the new volume and integrate methods can also receive polyhedra in RDF, and each vertex is cast to QQ with an iterator over the vertices.

Is the answer of .integrate() will be a RDF? Otherwise I think it is a bad idea.

But why? It will be a QQ.

[videlec]

comment:24

Replying to @mforets:

Replying to @videlec:

Replying to @mforets:

done! and thanks both for the help. from my side this ticket and #20887 are ok.

Nice work!

in the proposed solution, the new volume and integrate methods can also receive polyhedra in RDF, and each vertex is cast to QQ with an iterator over the vertices.

Is the answer of .integrate() will be a RDF? Otherwise I think it is a bad idea.

But why? It will be a QQ.

It does not make any sense. If I have a Polyhedron defined over RDF (= non exact field) its volume can not defined as an element of QQ (= exact field).

[mforets]

comment:25

Hmm.. Matrices have a change_ring feature that comes very handy for conversion. Shall we add a similar one for Polyhedron?

And following your recommendation, make integrate and volume via latte raise a value error when instantiated with, say, P = 1.4142*polytopes.cube().

With the change ring, we could still integrate integrate a polynomial over P with the slightly more complicated P.change_ring().integrate(x<sup>2*y</sup>2*z^2), instead of the ugly

sage: P_QQ = Polyhedron(vertices = [[QQ(vi) for vi in v] for v in P.vertices_generator()])
sage: P_QQ.integrate(x^2*y^2*z^2)

If there are alternative recommended options, I'd really like to learn; but I can post it as a ask.sagemath one if i'm off-topic :)

[mkoeppe]

comment:26

Integration over an RDF polyhedron via QQ polyhedron (latte) could make sense as long as the method converts the answer back to RDF to indicate that the answer is inexact.

As to change_ring, this could be useful. I had related discussions with JP.

[mkoeppe]

comment:27

(In addition to change_ring, there could also be change_backend.)

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a563192

fix a bug in _volume_latte

[sagetrac-git]

Changed commit from 507aea5 to a563192

[mforets]

Changed branch from u/mforets/22497 to u/mforets/22522

[mforets]

Changed commit from a563192 to 6a474f9

[vbraun]

Changed branch from u/mforets/22522 to 6a474f9