Laurent polynomials, Fitting ideals and characteristic varieties

[enriqueartal]

Recently in sagemath#36128 (already in develop) characteristic varieties of finitely presented fundamental groups were introduced. Its computation is based on Fitting ideals of Laurent polynomial matrices. In sagemath#36299, Fitting ideals were implemented for generic rings with some improvements for PID and polynomial rings.

There are two original goals in this PR: to improve the output of characteristic varieties and to use the cited implementation. In order to make computations faster, the implementation of Fitting ideals should apply to Laurent polynomial rings and for this goal, several changes should be applied to Laurent polynomials in Sagemath.

I am not sure if a deeper change should be made, since I applied only the changes I needed for the above goal:

• src/sage/groups/finitely_presented.py:
  • Changes in fitting_ideals.
• src/sage/matrix/matrix2.py: Style changes.
• src/sage/matrix/matrix_laurent_mpolynomial_dense.pyx: This is a new file to create the class Matrix_laurent_mpolynomial_dense.
  • A method laurent_matrix_reduction to obtain a matrix of polynomials where the variables are non common factors for neither the rows nor the columns.
  • A methord _fitting_ideal to use the same method for matrices of polynomials.
• src/sage/matrix/matrix__mpolynomial_dense.pyx: Style changes.

The main changes are for Laurent polynomials to avoid errors in the above implementations.

• src/sage/rings/polynomials/laurent_polynomial.pyx:
  • Style changes.
  • Create xgcd needed for inverse_mod.
  • Create inverse_mod.
  • Create divides, I copied the code for polynomials with minor changes.
• src/sage/rings/polynomials/laurent_polynomial_ideal.py:
  • Style changes.
  • Changes in hint keyword in __init__, the previous code create issues, e.g., impossible to sum ideals of univariate Laurent polynomial rings. They involve changes in doctests for hint
  • Changes in __contains__ since __reduce__ is different for univariate and multivaraite case.
  • Create gens_reduced.
  • Changes in polynomial_ideal to deal differently if uni- and multi-variate.
• src/sage/rings/polynomials/laurent_polynomial_mpair.py:
  • Style changes.
  • Create divides, I copied the code for polynomials with minor changes.
• src/sage/rings/polynomials/laurent_polynomial_ring.py:
  • Style changes.
  • Some TestSuite's applied to domains as base_rings; the corresponding TestSuite's for polynomials also failed if applied to polynomial rings.
• src/sage/rings/polynomials/laurent_polynomial_ring_base.py:
  • Style changes.
  • Implement is_noetherian.
• src/sage/rings/polynomials/polynomial_element.pyx: Style changes.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies