Ramified extensions of general p-adic rings and fields

[roed]

We should have support for relative extensions of p-adic rings and fields. This is particularly useful for totally ramified extensions of unramified extensions of Qp, which will represent a general absolute extension of Qp.

[saraedum]

New commits:

​bcdc069

Initial files to work on for 23218

[git]

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

​1e4b2b4

Working on relative ramified extensions

[git]

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

​17a2ae0

Changes to make things build

[git]

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

​6470a1a	__init__ method on relative ramified FM parents
​4b56533	Add coercion to fraction field for floating point rings
​18f9d37	Merge branch 't/23220/coercion_from_floating_point_unramified_rings_to_their_fractionf_fields' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​77850fb	Fixing some problems with floating point in pushouts, adding type casts for celements in libs/linkages/padics/Polynomial*.pxi to allow access to __coeffs

[git]

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

​f815759	replace prec_cap with ram_prec_cap in many template.pxi files
​eafeefe	Use Polynomial_generic_dense_inexact in relative_ramified_FM

[git]

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

​fd3ee0f

Clarify calls of __init__ in cconstruct

[git]

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

​0204e7f

Make series printing work for two-step p-adic extension elements

[git]

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

​b51ab48

Implemented missing p-adic conversions

[git]

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

​a4c3bf5

Fix missing cases in conversion

[git]

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

​42a65ab	Working on series printing for two-step p-adics
​0204e7f	Make series printing work for two-step p-adic extension elements
​c7f71c1	Fixing terse printing
​0674979	Merge branch 'u/saraedum/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23217/ramified_extensions_of_general_p_adic_rings_and_fields
​4d4c973	cleanup and implementations in ramified linkage
​651e31f	Caching methods in pow computer

[git]

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

​19115e6

fix shifting

[git]

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

​1f89001	fix ccmp
​39534c3	initialize temporary variables
​b3e1001	explain why a conversion was not found
​25888bc	fix typo
​883b789	coercions and conversions from rationals into relative extensions
​9a65ead	Move _coerce_map_from_ to the affected parents

[git]

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

​497db77

Fixing pickling, adding relative extensions to factory, fixing bug in comparison

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​b7a0bff	Fix orders
​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
​a29bf7a	Merge branch 't/20310/change_precision' into t/23471/padic_ext_conversion
​2f3e44c	Merge branch 't/23471/padic_ext_conversion' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

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

​f985aa0	Add ability to call with arguments
​9763d7a	Fix implementation of _call_with_args
​21a476e	Merge branch 't/23471/padic_ext_conversion' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​e5d46b6	Move _shift_seed to PowComputer_relative_eis
​3b52f2c	Fix bug from args being a tuple, not a list
​e74a87f	Merge branch 't/23471/padic_ext_conversion' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

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

​3cddbdd	Fix doctests
​8586517	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​5c0aa4e	Fix sign error in PowComputer_relative

[git]

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

​1cb5597

Base change exact polynomial when creating PowComputer

[git]

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

​4eeb18b

Injections from the base ring for relative p-adic extensions

[git]

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

​1944974	Add morphisms to and from residue field (still need doctests)
​d037d15	Merge branch 't/8240/residue_coercion' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

Branch pushed to git repo; I updated commit sha1. 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
​1d1ad89	Merge branch 'u/roed/padic_ext_conversion' of git://trac.sagemath.org/sage into t/23471/padic_ext_conversion
​a6b4361	Merge branch 'u/roed/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[roed]

Diff against #23471

[git]

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

​e201321

Make conversion from residue field work for two step extensions

[roed]

Update dependency chain: #23471 depends on #14825, which depends on #20310.

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​0b7fd02	default docstring layout
​def3897	replace p with pi and clarify meaning of expansion
​99c40d6	add unit test for expansion
​6732d38	coefficients might be lists in the maximal unramified subextension
​acc606a	Merge branch 'u/saraedum/polynomial_representation_of_a_padic_number' of git://trac.sagemath.org/sage into t/14825/polynomial_representation_of_a_padic_number
​40737f6	Fix some of the errors in _test_expansion
​6efed0b	Merge branch 'u/roed/polynomial_representation_of_a_padic_number' of git://trac.sagemath.org/sage into t/14825/polynomial_representation_of_a_padic_number
​2b93c3c	Merge branch 'develop' into t/23471/padic_ext_conversion
​3fc818a	Merge branch 'u/roed/padic_ext_conversion' of git://trac.sagemath.org/sage into t/23471/padic_ext_conversion
​392a5b6	Merge branch 'u/roed/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​d7d5fb6	Fixing documentation
​8f34757	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/23471/padic_ext_conversion
​46f9cae	Merge branch 'develop' into t/14825/polynomial_representation_of_a_padic_number
​e51c0f5	Merge branch 'u/roed/polynomial_representation_of_a_padic_number' of git://trac.sagemath.org/sage into t/14825/polynomial_representation_of_a_padic_number
​b6457b1	Moving SEEALSO to the end of the docstring
​b81b722	Remove use of depraceted list()
​04a1579	Fix NOTES blocks
​6764ea2	Merge branch 'develop' into t/14825/polynomial_representation_of_a_padic_number
​0c58970	Merge branch 't/14825/polynomial_representation_of_a_padic_number' into t/23471/padic_ext_conversion
​9633e88	Merge branch 'u/roed/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

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

​1ad1dba	Removing commented code in relative_ramified_FM.pyx
​ef0f2d9	Merge commit '1ad1dba6a2' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​6311b85	cimport fraction field element types
​16f53ec	Remove sig_on from around cshift, since this can call python code in two step extensions
​10cdb0c	Fix sign errors in calling cshift
​6b995a4	Switch from clist to cexpansion_next and cexpansion_getitem
​a5f4606	Undo debugging change
​617f85b	Use conditional compilation to simplify code for relative ramified extensions
​7aecc2f	switch from % operator to add_bigoh in reduction
​0303c7b	Use integral coefficients for the internal polynomials representing two-step extension elements
​690ba7d	Compute inertia degee in whole tower when printing two-step p-adic extension elements
​493625a	Add coercion maps to fraction field for two-step extensions

[git]

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

​501577b	Add modulus and defining polynomials for Qp and Zp for consistency
​ce61f64	Improve base ring injections for relative extensions of p-adic fields
​16477d3	Make conversion from residue field work for two-step extensions of p-adics
​1c7cc71	Fix typo in section method for base ring injection in p-adic two-step extensions
​8be1504	Fix bugs in creduce and ccoefficients for two-step p-adic extensions
​d53df12	Add coerce_list back in to the _populate_coercion_lists_ call in pAdicExtensionGeneric.__init__
​e68beee	Fix some p-adic doctests
​635021a	Change _poly_rep to always return the polynomial representing the element, not the unit
​67c1f14	Change the internal base ring for two-step extensions to not show precision when printing, fix bug in base ring coercion
​8939981	Fix problems in expansion code

[lubicz]

It seems that I have found a problem with this ticket. Here is my example:

sage: R=Zq(2^10)
sage: P.<alpha>=R[]
sage: R1.<t>=R.ext(alpha^2+2*alpha+2)
sage: M1=matrix(R1, 2, 2)
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​e64d891	added square for unramified 2-adic fields
​f4ce9aa	Merge branch 'u/lubicz/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23344/sqrt_2

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​ce61f64	Improve base ring injections for relative extensions of p-adic fields
​16477d3	Make conversion from residue field work for two-step extensions of p-adics
​1c7cc71	Fix typo in section method for base ring injection in p-adic two-step extensions
​8be1504	Fix bugs in creduce and ccoefficients for two-step p-adic extensions
​d53df12	Add coerce_list back in to the _populate_coercion_lists_ call in pAdicExtensionGeneric.__init__
​e68beee	Fix some p-adic doctests
​635021a	Change _poly_rep to always return the polynomial representing the element, not the unit
​67c1f14	Change the internal base ring for two-step extensions to not show precision when printing, fix bug in base ring coercion
​8939981	Fix problems in expansion code
​e3a1c86	Merge commit '8939981e4b02ac12b86f943d93a8baef25e9af51' of git://trac.sagemath.org/sage into t/23218/general_extensions

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​e64d891	added square for unramified 2-adic fields
​65f2853	Merge commit 'e64d891c19b4b5bb1b2b8d666f16f02ad405c67e' of git://trac.sagemath.org/sage into t/23344/sqrt_2

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​ce61f64	Improve base ring injections for relative extensions of p-adic fields
​16477d3	Make conversion from residue field work for two-step extensions of p-adics
​1c7cc71	Fix typo in section method for base ring injection in p-adic two-step extensions
​8be1504	Fix bugs in creduce and ccoefficients for two-step p-adic extensions
​d53df12	Add coerce_list back in to the _populate_coercion_lists_ call in pAdicExtensionGeneric.__init__
​e68beee	Fix some p-adic doctests
​635021a	Change _poly_rep to always return the polynomial representing the element, not the unit
​67c1f14	Change the internal base ring for two-step extensions to not show precision when printing, fix bug in base ring coercion
​8939981	Fix problems in expansion code
​e3a1c86	Merge commit '8939981e4b02ac12b86f943d93a8baef25e9af51' of git://trac.sagemath.org/sage into t/23218/general_extensions

[roed]

Sorry for the weird force pushes. Things got confused with #23344. It should be okay now, and a fast-forward of the branch from an hour ago.

[caruso]

Here are a series of bugs/remarks (see also discussion on Zulip):

• the printing of the parent is not optimal
• there is an issue with precision with the computation of x^p
• the methods zero and one (of the parent) are not implemented
• the method expansion is broken
• coercion from QQ to a p-adic field does not always work (might be related to the previous item)
• the method polynomial is broken

---

New commits:

​d77b226	Ensure that coefficient lists are copied in the p-adic Polynomial linkage files
​aa1c48b	Fix error in category for _convert_map_for_ in p-adic extension rings
​73040f3	Handle base ring correctly in __init__ method for p-adic template elements
​96e977b	Fix a few bugs and add some tests
​f686d75	Merge branch 'develop' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​3404208	Merge branch 'u/caruso/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[varul]

_test_add, _test_elements, _test_log, _test_sub failed when running TestSuite? on the following 5-adic Eisenstein field.

sage: K.<a> = Qq(125)
sage: R.<x> = K[]
sage: W.<w> = K.extension(x^3 + 25*x^2 - 5*a*x + 5*(1+a^2))
sage: TestSuite(W).run()

For _test_add, the line

tester.assertTrue(y.is_equal_to(z-x,zprec))

fails. Even though the expressions z-(x+y) and x+y-z were fine, the expression z-x-y is not. (In my particular failure, they all had relative precision 60, x and z had absolute precision 60, y had absolute precision 63.)

[git]

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

​82c4ca0	Merge branch 'u/roed/ramified_extensions_of_general_p_adic_rings_and_fields' of git://trac.sagemath.org/sage into t/23218/general_extensions
​740ff4f	Fix in_field for pow_comptuers of relative p-adic extensions

[varul]

random_element fails because multiplying by an element in the base field with negative valuation throws a "ValueError?: negative valuation"

sage: K.<a> = Qq(125)
sage: R.<t> = K[]
sage: W.<w> = K.extension(t^3 + 5*(5*t^2 + (13*a-a^2)*t + a))
sage: K(1/5)*w
ValueError: negative valuation

[git]

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

​debf1fc	Commit to make different from develop
​25c86a6	Change printing for p-adic extensions
​e74fe63	Doctest for the helper method _extension_type
​17322fa	Merge branch 't/25908/padic_printing' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[git]

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

​8882d03

Fix expansion

[caruso]

Here is another bug:

sage: K.<a> = Qq(2^10, 10)
sage: S.<X> = K[]
sage: L.<pi> = K.extension(X^2 - 16*X + 2)
sage: L(2,absprec=3)
<repr(<sage.rings.padics.relative_ramified_CR.RelativeRamifiedCappedRelativeElement at 0x7febfb11d4d0>) failed: RuntimeError: repr_spec called on zero>

---

New commits:

​8882d03

Fix expansion

[git]

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

​3654af8

Some fixes in the sqrt function

[git]

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

​5553da8

Remove a unwanted print statement

[git]

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

​899d9f6

Extra doctests in morphism.pyx

[git]

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

​8d06440

Fix sphinx problem

[roed]

All tests pass on our machines. Sending it to the patchbots.

[caruso]

There's still a bug with shifting:

sage: W.<a> = Zq(2^10,3)
sage: S.<x> = W[]
sage: OL.<pi> = W.extension(x^2 - 2*a*x + 2)
sage: OL(1) >> 1
a + pi + pi^3 + a*pi^4 + O(pi^5)

The last answer should be 0, I guess.

In any case, results are not coherent:

sage: (OL(1) >> 1) >> 1
(a^2 + 1) + a*pi + pi^2 + O(pi^4)
sage: OL(1) >> 2
O(pi^4)

[git]

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

​5ffb263

replace creduce by normalize

[git]

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

​7e842e3

Avoid to call two times cremove

[git]

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

​8654e79	Make several methods work (or raise a NotImplementedError) for extensions
​e156f7f	Write a test suite for the shifting operator

[git]

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

​b979df8

Remove a sig_on/sig_off

[caruso]

I've found--and fixed--some bugs.

I'm not satisfied with this ticket. Positive review for me when patchbot is happy.

---

Last 10 new commits:

​9340a8a	Fix a corner case
​4d6623d	Merge branch 't/21994/quo_rem_revision' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​2975633	Add _quo_rem to lattice precision
​cabb63e	Merge branch 'u/caruso/quo_rem_revision' of git://trac.sagemath.org/sage into t/21994/quo_rem_revision
​4fed21f	Merge branch 't/21994/quo_rem_revision' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​aacb4c2	Merge branch 'u/roed/ramified_extensions_of_general_p_adic_rings_and_fields' of trac.sagemath.org:sage into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields
​0ea13c0	Fix two bugs: one in expansion, one in cshift
​22840e5	Prevent _test_log to compute log(0)
​87f4c43	Always creduce after cremove
​b1a3236	Remove unwanted print statements

[git]

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

​ecf1155

Fix _get_unit in CA_template.pxi

[git]

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

​b2d0d73

Fixing doctests

[git]

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

​ab5aab4

Fixing doctests and typos

[git]

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

​8576c59

Change construction functors for p-adics, making pushouts work in towers

[git]

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

​fda2c7d

Adding documentation and fixing minor issues

[git]

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

​46744d6	Make _quo_rem more easily accessible to the user
​c0da7de	Update documentation
​c8ae6a7	Move the generic implementation of _quo_rem back from 23218
​9662550	Merge branch 'u/roed/quo_rem_revision' of git://trac.sagemath.org/sage into t/21994/quo_rem_revision
​162b44d	Fixing doctests, bad argument in floordiv
​dc2df56	Merge branch 't/21994/quo_rem_revision' into t/23218/ramified_extensions_of_general_p_adic_rings_and_fields

[caruso]

All tests pass! (But several plugins failed.)

We're almost done!

---

New commits:

​e7a5b08	Reduce further after remove
​e639fae	Add keyword reduce_relative in cremove

[roed]

I think we're planning on ignoring the pyflakes plugin; that's a task for another ticket.

We did leave in the _unit debugging method for relative_ramified_FP.pyx. That should either get removed or documented.

I can finish this off in the next few days if you don't get a chance before your flight.

[git]

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

​319f6d4

Remove the debugging method _unit

[caruso]

I removed the method _unit.

The plugin startup_module says:

startup_modules Failed
startup_modules -- 3 seconds

but I don't understand what's the problem.

---

New commits:

​319f6d4

Remove the debugging method _unit

[caruso]

The latest patchbot report reports failures, but I think that they are not related to this ticket. Do you agree?

[roed]

I agree. And the startup_module is just checking that new modules aren't unintentionally added to Sage when they shouldn't be. Since we're intending to, it's no problem.

I think we're all set!