Printing of p-adic extensions

[xcaruso]

We make the print representation of p-adic extensions shorter and clearer (in order to prepare #23218).

For example, the different outputs below from before this ticket:

sage: R.<a> = ZqCR(25, 40); R
Unramified Extension in a defined by x^2 + 4*x + 2
with capped relative precision 40 over 5-adic Ring

sage: R.<a> = ZqCA(25, 40); R
Unramified Extension in a defined by x^2 + 4*x + 2
with capped absolute precision 40 over 5-adic Ring

sage: R.<a> = ZqFM(25, 40); R
Unramified Extension in a defined by x^2 + 4*x + 2
of fixed modulus 5^40 over 5-adic Ring

sage: R.<a> = ZqFP(25, 40); R
Unramified Extension in a defined by x^2 + 4*x + 2
with floating precision 40 over 5-adic Ring

become the same shorter outpout after this ticket:

sage: R.<a> = ZqCR(25, 40); R
5-adic Unramified Extension Ring in a defined by x^2 + 4*x + 2

sage: R.<a> = ZqCA(25, 40); R
5-adic Unramified Extension Ring in a defined by x^2 + 4*x + 2

sage: R.<a> = ZqFM(25, 40); R
5-adic Unramified Extension Ring in a defined by x^2 + 4*x + 2

sage: R.<a> = ZqFP(25, 40); R
5-adic Unramified Extension Ring in a defined by x^2 + 4*x + 2

CC: @roed314 @slel

Component: padics

Keywords: printing, padicIMA

Author: Xavier Caruso

Branch/Commit: 648ea64

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/25908

[roed314]

Branch: u/roed/padic_printing

[roed314]

New commits:

debf1fc

Commit to make different from develop

[roed314]

Commit: debf1fc

[roed314]

Changed keywords from printing to printing, padicIMA

[xcaruso]

Changed branch from u/roed/padic_printing to u/caruso/padic_parent_printing

[sagetrac-git]

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

25c86a6

Change printing for p-adic extensions

[sagetrac-git]

Changed commit from debf1fc to 25c86a6

[sagetrac-git]

Changed commit from 25c86a6 to e74fe63

[sagetrac-git]

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

e74fe63

Doctest for the helper method _extension_type

[roed314]

comment:6

I get these failures:

sage -t src/sage/categories/pushout.py  # 1 doctest failed
sage -t src/sage/modular/overconvergent/genus0.py  # 4 doctests failed
sage -t src/sage/rings/padics/CA_template.pxi  # 6 doctests failed
sage -t src/sage/rings/padics/CR_template.pxi  # 6 doctests failed
sage -t src/sage/rings/padics/FM_template.pxi  # 6 doctests failed
sage -t src/sage/rings/padics/FP_template.pxi  # 6 doctests failed
sage -t src/sage/rings/polynomial/padics/polynomial_padic.py  # 2 doctests failed
sage -t src/sage/rings/polynomial/polynomial_element.pyx  # 1 doctest failed
sage -t src/sage/rings/finite_rings/finite_field_base.pyx  # 2 doctests failed
sage -t src/sage/rings/ring.pyx  # 1 doctest failed
sage -t src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py  # 1 doctest failed
sage -t src/sage/schemes/elliptic_curves/padic_lseries.py  # 1 doctest failed
sage -t src/sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field.py  # 1 doctest failed
sage -t src/sage/structure/parent.pyx  # 1 doctest failed

[sagetrac-git]

Changed commit from e74fe63 to 5c4e3a3

[sagetrac-git]

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

5c4e3a3

Fix doctest

[xcaruso]

comment:8

I've fixed the doctests.
The ticket is ready for review.

[sagetrac-git]

Changed commit from 5c4e3a3 to 7c5c68c

[sagetrac-git]

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

7c5c68c

Notion of absolute and relative degree / ramification index / inertia degree

[sagetrac-git]

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

c722955

Added/fixed doctests

[sagetrac-git]

Changed commit from 7c5c68c to c722955

[roed314]

Changed branch from u/caruso/padic_parent_printing to u/roed/padic_parent_printing

[roed314]

comment:12

Looks good to me.

---

New commits:

c722955

Added/fixed doctests

[roed314]

Changed branch from u/roed/padic_parent_printing to u/caruso/padic_parent_printing

[roed314]

Author: Xavier Caruso

[roed314]

Reviewer: David Roe

[roed314]

Changed branch from u/caruso/padic_parent_printing to u/roed/padic_parent_printing

[roed314]

Changed commit from c722955 to 8815d83

[roed314]

New commits:

8815d83

Fix typos

[xcaruso]

comment:15

Patchbot (on cygwin) complains. Let's try again.

[xcaruso]

Changed branch from u/roed/padic_parent_printing to u/caruso/padic_parent_printing

[roed314]

Changed commit from 8815d83 to 648ea64

[roed314]

comment:18

All tests pass for me. We can wait for the patchbot to see if there are plugin errors.

---

New commits:

648ea64

"base field" / "base ring"

[xcaruso]

comment:19

If you agree, I give a positive review and open a new ticket for the pyflakes issues found by the patchbot.

[vbraun]

Changed branch from u/caruso/padic_parent_printing to 648ea64