Update Zariski-van Kampen functions

[enriqueartal]

📚 Description

This PR has been cleaned and I think it is ready for review. The main goal of this PR is to update, create and make faster some functions in zariski_vankampen.py. I describe here the functions created or modified and the reasons:

• discrim: It applies now to a list or tuple of polynomials instead of a polynomial. Since only the zeroes of $\textrm{disc}_y f$ are needed, we compute (using @parallel) the discriminant of each polynomial and the pairwise resultants. Moreover the computations are not done in QQbar but in the number field of definition (only the roots are in QQbar). Some other functions are only changed to be applied to tuples or lists as roots_interval, roots_interval_cached, populate_roots_interval_cache, braid_in_segment.
• orient_circuit: If we know that the circuit is convex a much faster and precise method is used.
• voronoi_cells: It is a new function whose input is a corrected Voronoi diagram; the output is the graph of the diagram, the counterclock-wise boundary, a base point in the boundary, and the dual graph. It has been isolated for clarity.
• fieldI: It is a new function whose function is the ground field F (a subfield of QQbar) and the output is the smallest subfield of QQbar containing F and I. Since the vertices of the Voronoi diagrams are Gauss rationals, it allows to express everything in a subfield of QQbar where computations are much faster than in QQbar.
• populate_roots_interval_cache: We add a hack (inspired by the original braid_monodromy function to avoid some random fails when parallelizing.
• braid_in_segment: We replace the complex numbers of the input by Gauss rational and we add as input a dictionnary precision to be recurrently used in order to increase the precision of the interval computations and avoid hangs of the original function.
• geometric_basis: This function produces a geometric basis of the free group $\pi_1(\mathbb{C}\setminus\Delta;p)$ where $\Delta$ is the set of discriminant points; the elements of the basis are meridians around each point such that its product is the counterclockwise boundary of a big disk. The input is basically the output of voronoi_cells; there is a new method to produce such a basis since the previous one gave an error for some diagrams.
• strand_components: This function adds a new feature. It applies to lists or tuples of polynomials and assign each strand of the braids to the index of the polynomial associated with this strand. It is not a hard computation and adds usefuel information that can be long (or impossible) to be retrieved once the braid monodromy is computed
• braid_monodromy: The core of this function remains unchanged. The output includes now a dictionnary associating each strand to an element of an optional tuple of polynomials in the input.
• conjugate_positive_form is an auxiliary function which processes the special braids appearing in the braid monodromy to make faster he computation of the fundamental group since the mapping class group action of the braid group on the free group can be very slow.
• braid2rels: this is a separate function to return a minimal set of relations produced by the action of a braid on a free group.
• fundamental_group_from_braid_mon. This function computes the fundamental group from braid monodromy
• fundamental_group: This function admits the optional argument puiseux (braid2rels is used to get a smaller set of relations).
• fundamental_group_arrangement. The input is a list of polynomials and, besides the fundamental group a dictionnary is given, associating to each factor some meridians of these components.
  The methods fundamental_group and braid_monodromy for affine curves have been adapted. A new class of arrangements of curves should be created to take advantage of the new features.
  Actually, in another branch I created a method fundamental_group for hyperplane arrangements which take care of the meridian of each hyperplane. I encountered some problems since the class of hyperplane arrangements ordered in a rigid way the meridians and I plan to create a class of ordered hyperplane arrangements to avoid this problem.
  What it is called a Puiseux presentation of the $\pi_1$ of the complement of an affine curve has the same homotopy type as this complement (as proved by Libgober).
  Tests and documentation have been updated (probably not enough).

Fixes #34415.

📝 Checklist

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

⌛ Dependencies

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Documentation preview for this PR (built with commit fa2c771; changes) is ready! 🎉