functions for conversion from sage-flatsurf/pyflatsurf

[videlec]

We add functions to convert objects from pyflatsurf and sage-flatsurf.

Fixes #45

Dependencies

• Upgrade to 10.3 conda-forge/sage-feedstock#97
• normaliz v3.10.2 conda-forge/normaliz-feedstock#53
• pynormaliz v2.19 conda-forge/pynormaliz-feedstock#11

[videlec]

@saraedum The rank2 orbit closures from [EMMW] can be built with the following code

def rank2_quadrilateral_orbit_closure(angles, lengths):
    from flatsurf import similarity_surfaces, Polygon, GL2ROrbitClosure
    p = Polygon(angles=angles, lengths=lengths)
    S = similarity_surfaces.billiard(p).minimal_cover('translation').erase_marked_points().l_infinity_delaunay_triangulation()
    orbit_closure = GL2ROrbitClosure(S)
    for d in orbit_closure.decompositions(2):
        orbit_closure.update_tangent_space_from_flow_decomposition(d)
        if orbit_closure.dimension() == 4:
            break
    assert orbit_closure.dimension() == orbit_closure.absolute_dimension() == 4
    return orbit_closure
    
O0 = rank2_quadrilateral_orbit_closure((1, 1, 1, 7), (3, 2))
O1 = rank2_quadrilateral_orbit_closure((1, 1, 1, 9), (3, 2))
O2 = rank2_quadrilateral_orbit_closure((1, 1, 2, 8), (1, 1))
O3 = rank2_quadrilateral_orbit_closure((1, 1, 2, 12), (1, 1))
O4 = rank2_quadrilateral_orbit_closure((1, 2, 2, 11), (1, 1))
O5 = rank2_quadrilateral_orbit_closure((1, 2, 2, 15), (1, 1))
O = [O0, O1, O2, O3, O4, O5]

Then the added functions allow to create VeeringTriangulationLinearFamily from them and then

from veerer.flatsurf_conversion import sage_flatsurf_orbit_closure_to_veerer_linear_family
F = [sage_flatsurf_orbit_closure_to_veerer_linear_family(orbit_closure) for orbit_closure in O]
assert all(linear_family.is_geometric() for linear_family in F)
A = [f.geometric_automaton(run=False) for f in F]

and the code that takes forever and SEGFAULT because of Normaliz is

A[0].run()
A[1].run()
A[2].run()
A[3].run()
A[4].run()
A[5].run()

[saraedum]

I think we need a version of SageMath that works with FLINT 3 for this. Or rebuild the whole stack for FLINT 2.

[videlec]

I think we need a version of SageMath that works with FLINT 3 for this. Or rebuild the whole stack for FLINT 2.

We do now have a SageMath versions including flint3 (namely 10.3 and 10.4). Do you know if normaliz and pynormaliz work with flint3?

[saraedum]

The release from March 1st support FLINT 3, i.e., 3.10.2. It's waiting for me to package it here: conda-forge/normaliz-feedstock#53, conda-forge/pynormaliz-feedstock#11