Improvements for p-adic polynomials

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Improvements for p-adic polynomials #23508

Open 2190d0ee-e4da-4602-8835-8ea53fc1c317 opened 7 years ago

2190d0ee-e4da-4602-8835-8ea53fc1c317 commented 7 years ago

Add various methods to polynomial_padic.py for invariant computations and Monge reduction and update factor() to use OMTree from #12561 for factoring polynomials over p-adic extensions.

In all, this makes large changes to factor() and adds methods:

is_eisenstein
normalized (For use in factoring)
omtree
ramification_polynomial
ramification_polygon
ramification_polygon_with_colinear_points (used for residual polynomials)
hasse_herbrand (Evaluate n times Hasse-Herbrand at integers)
residual_polynomials (of the ramification polygon)
residual_polynomial_of_component (Monge's S_m)
has_residual_polynomial_class (Test whether another polynomial is in the same invariant class)
monge_reduce

Depends on #12561 Depends on #23471 Depends on #23510

CC: @pjbruin

Component: padics

Keywords: sd87

Author: Sebastian Pauli, Brian Sinclair

Branch/Commit: u/roed/ticket/23508 @ ed86978

Issue created by migration from https://trac.sagemath.org/ticket/23508

2190d0ee-e4da-4602-8835-8ea53fc1c317 commented 7 years ago

Changed dependencies from #12561, #23471 to #12561, #23471, #23510

2190d0ee-e4da-4602-8835-8ea53fc1c317 commented 7 years ago

Branch: u/bsinclai/ticket/23508

2190d0ee-e4da-4602-8835-8ea53fc1c317 commented 7 years ago

Commit: d4bfddb

2190d0ee-e4da-4602-8835-8ea53fc1c317 commented 7 years ago

comment:2

Factoring over unramified extension does not work currently (See #23510). The following doctest shows this.

We run into R.fraction_field() is self occurring in _coerce_map_from_(self, R) in padic_extension_generic.pyc when we attempt to change_ring() our polynomial in _factor_non_monic() to increase precision cap.

R.<c> = Zq(125, prec = 500)
Rz.<z>=R[]
g = 25*z^15 + 5
Fg = g.factor()

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

`7926b41`	`Moving code for fraction_field and integer_ring, and enabling fraction fields for fixed-mod`
`7d74ce5`	`Merge branch 'u/roed/fixed_mod_frac_field' of git://trac.sagemath.org/sage into develop`
`9cfb828`	`Fixed monge_reduce()`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from d4bfddb to 9cfb828

roed314 commented 7 years ago

Changed branch from u/bsinclai/ticket/23508 to u/roed/ticket/23508

pjbruin commented 6 years ago

Changed commit from 9cfb828 to ed86978

pjbruin commented 6 years ago

New commits:

`c8a3261`	`Merge branch 'u/bsinclai/ticket/12561' of git://trac.sagemath.org/sage into t/12561/om_tree`
`ed86978`	`Merge branch 'u/bsinclai/ticket/23508' of git://trac.sagemath.org/sage into t/23508/padic_polynomial_improvements`