Create a Polymake pexpect interface

[simon-king-jena]

There is PyPolymake, to be added at #21170. But I think it wouldn't hurt to additionally have a pexpect interface to Polymake. And the purpose of this ticket is to create one.

Depends on #22501

CC: @videlec @jplab

Component: packages: optional

Keywords: Polymake, days84

Author: Simon King

Branch: 52a77ee

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/22452

[simon-king-jena]

Changed keywords from Polymake, days85 to Polymake, days84

[simon-king-jena]

Branch: u/SimonKing/create_a_polymake_pexpect_interface

[videlec]

Commit: c3add96

[videlec]

Last 10 new commits:

33b53f3	Add documentation to _get_primitive
d78b239	'Implement string representation by single underscore methods': Apply this mantra to interfaces
9a0bcca	Change string representation of invalid interface elements whose parent is None
6910107	Keep the tests that have been removed in the previous commits
cd97ff3	Parse error message of _check_valid() in order to cope with unpredictable future semantical changes
fdaeb2e	Include error message of validity check into string representation of invalid interface elements
cdb085b	Revert introduction of _get_custom_name
b5df135	Actually remove _get_custom_name, not only its applications
6b53229	Reverse addition of _get_primitive. Fix `__cmp__`, bool etc. and their documentation
c3add96	Initial wrapper: providing help, tab completion, accessing members, calling functions, nice(r) string representation

[simon-king-jena]

comment:4

Here I am showcasing some things that work already:

sage: from sage.interfaces.polymake import polymake
sage: polymake.help("objects/Cone/properties/Combinatorics/RAYS_IN_FACETS")
property RAYS_IN_FACETS : IncidenceMatrix<NonSymmetric>
 Ray-facet incidence matrix, with rows corresponding to facets and columns
 to rays. Rays and facets are numbered from 0 to N_RAYS-1 rsp.
 N_FACETS-1, according to their order in RAYS rsp. FACETS.

sage: polymake.help('rand_sphere')
functions/Producing a polytope from scratch/rand_sphere:
rand_sphere(d, n; Options) -> Polytope

 Produce a d-dimensional polytope with n random vertices
 uniformly distributed on the unit sphere.

Arguments:
  Int d the dimension
  Int n the number of random vertices

Options:
  seed => Int controls the outcome of the random number generator;
    fixing a seed number guarantees the same outcome. 

Returns Polytope 

So, there is access to Polymake' help system.

sage: P = polymake.rand<tab key>
                polymake.rand01                polymake.rand_knot              
                polymake.rand_aof              polymake.rand_metric            
                polymake.rand_box              polymake.rand_metric_int       >
                polymake.rand_cyclic           polymake.rand_perm              
                polymake.rand_inner_points     polymake.rand_seed 

So, tab completion of the interface itself works, it yields ALL function names, including those that are not part of the current Polymake application.

sage: P = polymake.rand_sphere(3,10,seed=5)

So, calling a function with parameters works

sage: P
Random spherical polytope of dimension 3; seed=5

So, string representation works, actually nicer than in Polymake (more examples below).

sage: P.known_properties()   # members computed so far
['BOUNDED', 'CONE_AMBIENT_DIM', 'FEASIBLE', 'POINTS']
sage: P.get_schedule('F_VECTOR')

precondition : BOUNDED ( lrs.convex_hull.count: N_FACETS : RAYS | INPUT_RAYS )
lrs.convex_hull.count: N_FACETS : RAYS | INPUT_RAYS
sensitivity check for VertexPerm
cdd.convex_hull.canon: POINTED, RAYS, LINEALITY_SPACE : INPUT_RAYS
CONE_DIM : RAYS | INPUT_RAYS
N_RAYS : RAYS
precondition : POINTED ( LINEALITY_DIM, LINEALITY_SPACE : )
LINEALITY_DIM, LINEALITY_SPACE :
COMBINATORIAL_DIM : CONE_DIM, LINEALITY_DIM
precondition : COMBINATORIAL_DIM ( F_VECTOR : N_FACETS, N_RAYS, COMBINATORIAL_DIM )
F_VECTOR : N_FACETS, N_RAYS, COMBINATORIAL_DIM

So, this shows how the f-vector would be computed for this polytope.

sage: V = P.VER<tab key>
                P.VERTEX_BARYCENTER        P.VERTICES                 
                P.VERTEX_LABELS            P.VERTICES_IN_FACETS       
                P.VERTEX_NORMALS           P.VERTICES_IN_INEQUALITIES 
                P.VERTEX_SIZES             P.VERY_AMPLE               

So, tab completion for Polymake elements works. It shows both members (including those that aren't computed yet) and functions (including those that won't be applicable to the object).

sage: set_verbose(3)
sage: V = P.VERTICES
sage: F = P.F_VECTOR
polymake: used package lrs
  Implementation of the reverse search algorithm of Avis and Fukuda.
  Copyright by David Avis.
  http://cgm.cs.mcgill.ca/~avis/lrs.html

So, when verbosity is set to a positive value, comments printed by Polymake will be printed by Sage.

sage: F
10 24 16
sage: V

1 -549467720344047/2251799813685248 -1666038093248221/2251799813685248 5646952731601237/9007199254740992
1 396443771972991/562949953421312 -3761317241461329/36028797018963968 6325385137097525/9007199254740992
1 8731416515056451/9007199254740992 8225904699783425/36028797018963968 6513541817898829/72057594037927936
1 -6649740931032245/9007199254740992 -316039202166671/562949953421312 -6735311418008155/18014398509481984
1 1027872253618593/1125899906842624 -4941443956760209/18014398509481984 -5443456128447233/18014398509481984
1 3237778007687205/4503599627370496 -3127563668227821/4503599627370496 8478171037802839/288230376151711744
1 4654944693569921/9007199254740992 -2595293938705027/4503599627370496 5702536786492105/9007199254740992
1 -4153090305917205/4503599627370496 2814681273371419/18014398509481984 -3186909849764487/9007199254740992
1 6185041161130579/9007199254740992 -2775723053730255/4503599627370496 -6944451127537363/18014398509481984
1 -6106052881221159/18014398509481984 -2063008243044317/18014398509481984 -8410984913482021/9007199254740992

So, string representation is (at least for the things that are currently wrapped) meaningful.

sage: F[2]
16
sage: V[3][3]
-6735311418008155/18014398509481984

So, attribute access works.

sage: V.foobar()
Traceback (most recent call last)
...
TypeError: polymake:  ERROR: Undefined subroutine &Polymake::User::foobar called at input line 1.
sage: polymake.eval('foobar(4)')
^CInterrupting Polymake...
Traceback (most recent call last)
...
KeyboardInterrupt: Ctrl-c pressed while running Polymake
sage: polymake.eval('foobar(4);')
Traceback (most recent call last)
...
PolymakeError: polymake:  ERROR: Undefined subroutine &Polymake::User::foobar called at input line 1.

So, error handling is implemented.

Meanwhile, more members are known:

sage: P.known_properties()

['AFFINE_HULL',
 'BOUNDED',
 'COMBINATORIAL_DIM',
 'CONE_AMBIENT_DIM',
 'CONE_DIM',
 'FAR_FACE',
 'FEASIBLE',
 'FULL_DIM',
 'F_VECTOR',
 'LINEALITY_DIM',
 'LINEALITY_SPACE',
 'N_FACETS',
 'N_POINTS',
 'N_VERTICES',
 'POINTED',
 'POINTS',
 'VERTICES']

Of course, some things won't work yet. For example, I am not catching warnings yet.

[sagetrac-git]

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

bfae486

Implement getting length of arrays and hashes

[sagetrac-git]

Changed commit from c3add96 to bfae486

[simon-king-jena]

comment:6

Example for the next commit:

sage: from sage.interfaces.polymake import polymake
sage: P = polymake.rand_sphere(3,10,seed=5)
sage: len(P)   # A polytope is in fact internally represented by an array
14
sage: V = P.VERTICES
sage: len(V)
10
sage: len(V[2])
4

---

New commits:

bfae486

Implement getting length of arrays and hashes

[simon-king-jena]

comment:8

Now I am totally puzzled. After doing some changes, many thinks didn't work. Thus, I reverted all changes. I even deleted my local git branch and downloaded the branch from here. But things still don't work (tab completion etc). Of course I did sage -br.

Do you have any idea what could cause such persisting problems?

[simon-king-jena]

comment:9

It seems that my Sage installation is totally broken. I did "make start" and it seems that it installs python3 without my asking for it.

[sagetrac-git]

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

c3e7d47

Fix reading from file. Fix KeyboardInterrupt for Polymake