Fraction field of fixed modulus p-adic rings should have floating point type

[sagetrac-bsinclai]

Fraction field of fixed modulus p-adic rings should have floating point type.

Currently the change() method requires that the type be specified, in this case, but instances such as the check R.fraction_field() is self occurring in coerce_map_from(self, R) in padic_extension_generic.pyc.

Depends on #14825
Depends on #13591

CC: @roed314

Component: padics

Keywords: sd87

Author: David Roe

Branch/Commit: 189ac2b

Reviewer: Adele Bourgeois, Julian Rüth

Issue created by migration from https://trac.sagemath.org/ticket/23510

[roed314]

Branch: u/roed/fixed_mod_frac_field

[roed314]

Dependencies: #20310

[roed314]

Author: David Roe

[roed314]

Commit: 7926b41

[roed314]

Last 10 new commits:

921af5e	Changing modulus and defining_polynomial to use an exact keyword
39043f1	Merge branch 't/23331/allow_exact_defining_polynomials_for_p_adic_extensions' into t/20310/change_precision
77779ea	minor docstring changes
6e2495f	Merge branch 't/23331/allow_exact_defining_polynomials_for_p_adic_extensions' into t/20310/change_precision
7428353	minor docstring fixes
bd15d71	add exact keyword
99dccf6	Merge branch 't/23331/allow_exact_defining_polynomials_for_p_adic_extensions' into t/20310/change_precision
ef4ed33	Fix SEEALSO:
1754b44	Fix exact=True errors in the right branch
7926b41	Moving code for fraction_field and integer_ring, and enabling fraction fields for fixed-mod

[roed314]

Changed keywords from none to sd87

[sagetrac-abourgeois]

Reviewer: Adele Bourgeois

[sagetrac-abourgeois]

comment:3

All tests pass!

[saraedum]

comment:4

sage: R.<u> = ZqFM(125, 500)
sage: R.fraction_field().coerce_map_from(R)
UnboundLocalError: local variable 'coerce_map' referenced before assignment

[saraedum]

Changed branch from u/roed/fixed_mod_frac_field to u/saraedum/fixed_mod_frac_field

[xcaruso]

Changed commit from 7926b41 to 16fb79b

[xcaruso]

comment:6

By the way, I would be in favour of implementing a p-adic field with fixed modulus precision (in which each p-adic number is truncated at the same precision encapsulated in the parent). I think it makes perfectly sense. Do you have any objections?

---

New commits:

16fb79b

Check that fraction_field() works as expected

[roed314]

comment:7

Replying to @xcaruso:

By the way, I would be in favour of implementing a p-adic field with fixed modulus precision (in which each p-adic number is truncated at the same precision encapsulated in the parent). I think it makes perfectly sense. Do you have any objections?

So, the amount of information stored in an element is unbounded. This seems problematic since computations can blow up. Why do you want to have this precision type?

[xcaruso]

comment:8

Replying to @roed314:

So, the amount of information stored in an element is unbounded. This seems problematic since computations can blow up.

Indeed. But is it really an issue?
I noticed that similarly QpCA does not exist and that the fraction field of ZpCA is QpCR and I assume that this is for the same reason, isn't it?

Why do you want to have this precision type?

I will maybe need it for implementing precision lattices for which I imagine an absolute cap (having a relative cap is certainly also interesting but does not solve the issue of unbounded elements in the framework of lattice precision since the precision may be spread out over several elements which have quite different valuations).

However, besides this, I think that QpCA and QpFM make sense perfectly and should be the integer ring of ZpCA and ZpFM respectively. I don't think that it is a good idea to switch automatically between absolute and relative precision, it should be the choice of the user.
For instance, for now, we have the following behaviour

    sage: R = ZpCA(5)
    sage: R.fraction_field().integer_ring()
    5-adic Ring with capped relative precision 20
    sage: R.fraction_field().integer_ring() is R
    False

which is, I think, a bit annoying.

[sagetrac-git]

Changed commit from 16fb79b to 8814d31

[sagetrac-git]

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

8814d31

Merge branch 'develop' into t/23510/fixed_mod_frac_field

[roed314]

Changed branch from u/saraedum/fixed_mod_frac_field to u/roed/fixed_mod_frac_field

[roed314]

Changed commit from 8814d31 to 7e62f70

[roed314]

comment:11

Depend on #14825 to include fixes for sections that are internal to coercion system. Tests pass.

As for the discussion about adding QpFM and QpCA, I don't have a strong objection, but it will be very difficult to implement with the current framework in Sage. In particular, it would require two new templates, since the CR_template and FP_template don't have the correct precision behavior, while the CA_template and FM_template don't have the right data representation (they can't store elements with negative valuation). I don't think this is going to happen anytime soon.

---

Last 10 new commits:

7f87069	Fix segfault
b9c2fe4	Fix pickling of sections for p-adic coercions
6ba62dd	Fix SEEALSO again
e9c4c39	Merge branch 'u/roed/allow_exact_defining_polynomials_for_p_adic_extensions' of git://trac.sagemath.org/sage into t/23331/allow_exact_defining_polynomials_for_p_adic_extensions
561f5ac	Fix doctest errors
3142701	Merge branch 'u/roed/change_precision' of git://trac.sagemath.org/sage into t/20310/change_precision
138d939	Fix string representation doctest from #22103
1eeb367	Merge branch 't/20310/change_precision' into t/14825/polynomial_representation_of_a_padic_number
bc95b69	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/23510/fixed_mod_frac_field
7e62f70	Fixing errors in the coercion to the fraction field for fixed-mod p-adics

[roed314]

Changed dependencies from #20310 to #14825

[saraedum]

Changed reviewer from Adele Bourgeois to Adele Bourgeois, Julian Rüth

[vbraun]

comment:20

See patchbot

[roed314]

Changed branch from u/saraedum/fixed_mod_frac_field to u/roed/fixed_mod_frac_field

[roed314]

comment:22

Thanks. Setting back to needs review for tests...

---

New commits:

b81b722	Remove use of depraceted list()
04a1579	Fix NOTES blocks
6764ea2	Merge branch 'develop' into t/14825/polynomial_representation_of_a_padic_number
dad02c7	Merge branch 'u/saraedum/fixed_mod_frac_field' of git://trac.sagemath.org/sage into t/23510/fixed_mod_frac_field
189ac2b	Add _test_fraction_field to the coercion tutorial

[roed314]

Changed commit from 3292259 to 189ac2b

[roed314]

comment:23

The test failures don't seem to be related to this ticket....

[saraedum]

comment:25

This does not fix the following problem:

sage: R=ZpFM(3)
sage: K=R.fraction_field()
sage: K.coerce_map_from(R).is_injective()
NotImplementedError

[saraedum]

comment:26

Let's make this a new issue, #23965.

[vbraun]

Changed branch from u/roed/fixed_mod_frac_field to 189ac2b