Ramified extensions of general p-adic rings and fields

roed314 commented 7 years ago

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.

Depends on #23221 Depends on #23228 Depends on #23471 Depends on #25908 Depends on #21994

CC: @saraedum @sagetrac-swewers @xcaruso

Component: padics

Keywords: sd87, padicIMA

Author: David Roe, Julian Rüth, Xavier Caruso

Branch/Commit: 319f6d4

Reviewer: Julian Rüth, Xavier Caruso, David Roe

Issue created by migration from https://trac.sagemath.org/ticket/23218

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

Changed commit from d037d15 to a6b4361

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

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`

roed314 commented 7 years ago

Diff against #23471

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

Changed commit from a6b4361 to e201321

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

comment:33

Attachment: 23218_over_23471.diff.gz

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

e201321 Make conversion from residue field work for two step extensions

roed314 commented 7 years ago

comment:34

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

roed314 commented 7 years ago

Changed dependencies from #23221, #23228, #20310, #14825, #23471 to #23221, #23228, #23471

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

Changed commit from e201321 to 392a5b6

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

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`

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

Changed commit from 392a5b6 to 9633e88

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

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`

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

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`

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

Changed commit from 9633e88 to ef0f2d9

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

Changed commit from ef0f2d9 to 493625a

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

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`

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

Changed commit from 493625a to 8939981

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

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`

742ccff4-512f-43e4-bdd0-5df91c799a52 commented 6 years ago

comment:40

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)

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

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`

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

Changed commit from 8939981 to f4ce9aa

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

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`

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

Changed commit from f4ce9aa to e3a1c86

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

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`

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

Changed commit from e3a1c86 to 65f2853

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

Changed commit from 65f2853 to e3a1c86

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

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`

roed314 commented 6 years ago

comment:45

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.

xcaruso commented 6 years ago

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

roed314 commented 6 years ago

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

xcaruso commented 6 years ago

comment:48

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`

xcaruso commented 6 years ago

Changed commit from e3a1c86 to 3404208

roed314 commented 6 years ago

Changed keywords from sd87 to sd87, padicIMA

365a0c67-81c0-4123-b354-fa6cea4e9402 commented 6 years ago

comment:50

_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.)

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

Changed commit from 3404208 to 740ff4f

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

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`

365a0c67-81c0-4123-b354-fa6cea4e9402 commented 6 years ago

comment:52

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

xcaruso commented 6 years ago

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

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

Changed commit from 740ff4f to 17322fa

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

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`

xcaruso commented 6 years ago

Changed dependencies from #23221, #23228, #23471 to #23221, #23228, #23471, #25908

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

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

8882d03 Fix expansion

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

Changed commit from 17322fa to 8882d03

xcaruso commented 6 years ago

comment:57

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

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

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

3654af8 Some fixes in the sqrt function

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

Changed commit from 8882d03 to 3654af8

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

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

5553da8 Remove a unwanted print statement

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

Changed commit from 3654af8 to 5553da8

roed314 commented 6 years ago

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

xcaruso commented 6 years ago

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

roed314 commented 6 years ago

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

sagemath / sage

Ramified extensions of general p-adic rings and fields #23218