Use libsingular for polynomial rings over function fields

[simon-king-jena]

Singular has polynomial rings over function fields. However, Sage makes no use of it:

sage: P.<a> = QQ[]
sage: F = P.fraction_field()
sage: type(F['x','y'])
<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>
sage: F = FunctionField(QQ,'a')
sage: type(F['x','y'])
<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>

Update:

This works now:

sage: F = PolynomialRing(QQ,'a').fraction_field()
sage: R.<x,y> = F[]
sage: F.inject_variables()
Defining a
sage: I = R.ideal([a*x+5*y^2, (1+a)/(1-a)*x^3-3*y*x])
sage: I.groebner_basis()
[x^3 + (3*a - 3)/(a + 1)*x*y, y^2 + (a)/5*x]

}}}

CC: @malb @miguelmarco @simon-king-jena @dimpase @sagetrac-sbulygin @bhutz @Torrencem @tscrim @jdemeyer @jpflori @embray @EnderWannabe

Component: commutative algebra

Keywords: function field, libsingular

Author: Miguel Marco

Branch/Commit: 6ce2bed

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/16567

[simon-king-jena]

Changed keywords from none to function field, libsingular

[simon-king-jena]

comment:2

It is not a big deal to create the MPolynomialRing_libsingular with parameters. However, I need to find out how to create a Singular number with parameters. Martin, can you give me a pointer to a relevant file of the Singular sources?

[malb]

comment:3

Looks like you want kernel/longtrans.h:

/*
* ABSTRACT:   numbers in transcendental field extensions,
              i.e., in rational function fields
*/

[simon-king-jena]

comment:4

Replying to @malb:

Looks like you want kernel/longtrans.h:

/*
* ABSTRACT:   numbers in transcendental field extensions,
              i.e., in rational function fields
*/

Thank you, Martin!

So far, I only found number (*nPar)(int i). If I understand correctly, it returns the i-th parameter as a number. But this would probably be cumbersome to use for transforming an element of a Sage function field resp. of a Sage quotient field of polynomial ring.

[simon-king-jena]

comment:5

Seems like one actually needs to construct a number by starting with nPar(i) (which is a function pointer to ntPar, IIUC) and conversion of integers, and then add, multiply and divide. Or is there a way to directly convert a polynomial in variables a,b,c into a number in parameters a,b,c? After all, there is this globally accessible ring nacRing hosting numerator and denominator of a function field element.

[malb]

comment:6

I'd assume there should be a way to convert a polynomial to a number as these numbers are polynomials internally as far as I know. Maybe ask on libsingular-devel?

[simon-king-jena]

Branch: u/SimonKing/use_libsingular_for_polynomial_rings_over_function_fields

[simon-king-jena]

comment:8

Miguel asked me to push the basic steps that I did for this ticket.

All what works is to set up polynomial rings over "fraction fields of polynomial rings" as libsingular polynomial rings with parameters. What is missing is everything else. In particular: the element constructor must be modified so that elements of quotient fields of polynomial rings are converted into libsingular numbers.

---

New commits:

d15c0cc

Use libsingular for polynomial ring with parameters.

[simon-king-jena]

Commit: d15c0cc

[miguelmarco]

Changed branch from u/SimonKing/use_libsingular_for_polynomial_rings_over_function_fields to u/mmarco/use_libsingular_for_polynomial_rings_over_function_fields

[miguelmarco]

Changed branch from u/mmarco/use_libsingular_for_polynomial_rings_over_function_fields to u/SimonKing/use_libsingular_for_polynomial_rings_over_function_fields

[miguelmarco]

comment:11

Ping!

I am trying (once again) to work on this. I also got to the point of creating the ring, and am stuck in the point of translating the coefficients.

I have started with conversion from sage coefficients to singular ones (the sa2si function in singular.pyx; but for some reason i don't understand, the generated .c code does not import the definitions from transext.h.

[miguelmarco]

comment:12

Also, i am not sure if i am dealing with the pointers correctly. It could use some review freom someone with more c/cython experience.

[nbruin]

Changed branch from u/SimonKing/use_libsingular_for_polynomial_rings_over_function_fields to /u/mmarco/use_libsingular_for_polynomial_rings_over_function_fields

[nbruin]

comment:13

It's a little easier if the branch you're talking about is actually attached.

The cython docs for "cimport extern" is here:

https://cython.readthedocs.io/en/latest/src/userguide/external_C_code.html#referencing-c-header-files

It actually does say there that the extern declaration should let cython generate an #include "singular/polys/ext_fields/transext.h". However, cython with take it on blind fate that the cython declarations given in the block itself somehow correspond to something that makes sense in C, because cython will not generate any declarations to define the types you specify: the "extern" promises that this is somehow resolved (by the given include or something else). So you should probably check that the generated C file indeed has an #include included. Otherwise, if you made a subtle typo compared with what's in C, the error would only arise in the C compiler, so you should probably carefully read the error that the C compiler generates and check that your spelling of everything matches up. Hope this helps?

[nbruin]

Changed commit from d15c0cc to 6978419

[miguelmarco]

comment:14

Thanks for the answer!

I did check that: the generated .cpp file has this line

#include "singular/polys/ext_fields/transext.h"

and the file SAGE_LOCAL/local/include/singular/polys/ext_fields/transext.h has the following declarations:

struct fractionObject
{
  poly numerator;
  poly denominator;
  int complexity;
};

typedef struct fractionObject * fraction;

So I still have no idea about what could be going on.

One possible guess is that the generated file is a .cpp, that is, no pure C, but C++. Maybe some problem with scopes?

[miguelmarco]

comment:15

I think I finally got it. This branch seems to work.

Still needs some polishing (documentation, cleanup, and check that we are handling memory correctly... which means lots of testing).

So please be welcome to take a look and stress-test it.

[miguelmarco]

Changed commit from 6978419 to 136a89a

[miguelmarco]

New commits:

3de10e6	Hacky solution for sa2si (coefficients that fit in int size only)
2d89757	Use mpz to create coefficients
64f4f57	Working implementation. Still needs cleanup, documentation, and checking for memory leaks
3d3419f	Fixed case with just one parameter
136a89a	Fix problem with several parameters introduced by previous fix

[miguelmarco]

comment:36

Linter complains about an unused variable in a method for matrix groups, which is rewriten to use this interface in #19391.

Anyways, in the current implementation, that assignation is necesary to create the corresponding singular ring, even if the python variable is not used later. The linter is just not smart enough in this case.

[tscrim]

comment:37

There are some failures reported by the patchbot:

sage -t --long --random-seed=65607106580737169923545380617831998347 src/sage/dynamics/arithmetic_dynamics/projective_ds.py  # 1 doctest failed
sage -t --long --random-seed=65607106580737169923545380617831998347 src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py  # 1 doctest failed
sage -t --long --random-seed=65607106580737169923545380617831998347 src/sage/interfaces/expect.py  # 2 doctests failed

[miguelmarco]

comment:38

I can't reproduce the error in pexpect or projective_ds.py (I suspect somehow the file i am testing is different from the one in the patchbot).

About the error in macdonald polynomials, I found that it is due to one function creating polynomials in x0, x1... and the other on x1, x2 ... Will look into it.

[miguelmarco]

comment:39

By rebasing to the newest develop version, I can reproduce the error in src/sage/dynamics/arithmetic_dynamics/projective_ds.py. It has to do with code added in #31994.

I am trying to debug it, but it is quite complicated. Adding the people involved in that ticket to cc for help.

[EnderWannabe]

comment:40

I've traced the error to the affine_patch function in src/sage/schemes/projective/projective_subscheme.py. The error is caused by code equivalent to the following

sage: T.<c,d> = QQ[]
sage: F = FractionField(T)
sage: R.<x,y,z> = F[]
sage: Q = F['x', 'z']
sage: f = R(d*z^2 + c*y*z^2)
sage: f((Q.gens()[0], 1, Q.gens()[1]))
TypeError

My usual workaround here is to create a dictionary and attempt f.subs(), however,

f.subs({x: Q.gens()[0], y: 1, z:Q.gens()[1]})

crashes Sage.

[sagetrac-git]

Changed commit from 9424a24 to d412c77

[sagetrac-git]

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

1a94d13	Merge branch 'develop' into plural
2704119	Fix creating polynomial from strings in the case of field with several generators
84a04d1	Fix variable indices in doctest
d412c77	Fix crash in .subs()

[miguelmarco]

comment:42

Thanks for the hint. I could pinpoint the origin of both problems. This should solve it.

I still can't reproduce the error in expect.py. Can somebody confirm it happens?

[miguelmarco]

comment:44

One of the patchbot passes all tests, and complains only abut the unused variable (that is actually needed to prevent gargage collection). The other patchbots have what seem to be unrelated problems.

Is it ok to merge this in this state? or should I do some dummy operation with the variable to make pyflakes happy?

[tscrim]

comment:45

Then it is a spurious error. I wouldn't worry about the pyflakes error. Thank you.

[vbraun]

comment:46

On 32-bit:

**********************************************************************
File "src/sage/rings/polynomial/polydict.pyx", line 1628, in sage.rings.polynomial.polydict.ETuple.eadd
Failed example:
    y^(2^32)
Expected:
    Traceback (most recent call last):
    ...
    OverflowError: exponent overflow (...)
Got:
    <BLANKLINE>
    Traceback (most recent call last):
      File "/var/lib/buildbot/slave/sage_git/build/local/var/lib/sage/venv-python3.9.7/lib/python3.9/site-packages/sage/doctest/forker.py", line 694, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/var/lib/buildbot/slave/sage_git/build/local/var/lib/sage/venv-python3.9.7/lib/python3.9/site-packages/sage/doctest/forker.py", line 1088, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.rings.polynomial.polydict.ETuple.eadd[6]>", line 1, in <module>
        y**(Integer(2)**Integer(32))
      File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 2467, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:23166)
        singular_polynomial_pow(&_p, self._poly, exp, _ring)
    OverflowError: Python int too large to convert to C unsigned long
**********************************************************************
1 item had failures:
   1 of   8 in sage.rings.polynomial.polydict.ETuple.eadd
    [276 tests, 1 failure, 0.26 s]
----------------------------------------------------------------------
sage -t --long --random-seed=307417638528231788267817062701073757912 src/sage/rings/polynomial/polydict.pyx  # 1 doctest failed
----------------------------------------------------------------------

[sagetrac-git]

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

6ce2bed

Adapt overflow doctest to 32 bits

[sagetrac-git]

Changed commit from d412c77 to 6ce2bed

[tscrim]

comment:48

LGTM.

[vbraun]

Changed branch from u/mmarco/use_libsingular_for_polynomial_rings_over_function_fields to 6ce2bed