faster conversions from number field to interval field

[videlec]

The conversion of number field elements to real interval field is slow (that was actually the main reason for the slowness constated in #23388). We implement a function cdef void nf_elem_get_mpfi(mpfi_t x, NumberFieldElement a, mp_prec_t prec) that provides an interval approximation of a number field element. We then refactorize the methods floor() and _richcmp_() and provide a straightforward implementation of _real_mpfi_().

This improves the overall performance of any method of number field element using approximation.

Depends on #23402

Component: number fields

Author: Vincent Delecroix

Branch/Commit: u/vdelecroix/23447 @ 4a40fbe

Issue created by migration from https://trac.sagemath.org/ticket/23447

[videlec]

Commit: 4a40fbe

[videlec]

Author: Vincent Delecroix

[videlec]

Branch: u/vdelecroix/23447

[videlec]

New commits:

0146c86	23388: faster floor for nf element
8124ba5	23402: faster hash for nf elements
4a40fbe	23447: faster conversion nf -> rif

[videlec]

comment:5

doctest failures...

sage -t --long --warn-long 37.3 src/sage/modular/modform_hecketriangle/hecke_triangle_group_element.py  # 3 doctests failed
sage -t --long --warn-long 37.3 src/sage/schemes/projective/projective_morphism.py  # 4 doctests failed
sage -t --long --warn-long 37.3 src/sage/groups/matrix_gps/finitely_generated.py  # 1 doctest failed
sage -t --long --warn-long 37.3 src/sage/schemes/curves/curve.py  # 1 doctest failed

[videlec]

comment:6

Replying to @videlec:

doctest failures...

Most are because of #23402... so they are fixed there.