Comparison of number field elements dependent of real embedding #17830

videlec · 2015-02-22T18:03:40Z

Comparison of embedded number field elements should be identical to the comparison of the embedding. In other words, we should have:

sage: x = polygen(ZZ)
sage: K.<cbrt2> = NumberField(x^3 - 2, embedding=AA.polynomial_root(x^3-2, RIF(0,3)))
sage: 6064/4813 < cbrt2 < 90325/71691
True

This has been done in #13213 for quadratic number fields. This ticket aims to implement this for all number fields by storing into the parent a list of interval approximations of the generator.

This concerns only real embeddings.

To go further, one should consider:

having a fast evaluation of integer polynomial with real intervals (mpfi elements) input
make better interaction with QQbar (see also cleanup number fields coerce embeddings #18103 and Number fields with complex embeddings #18104)

CC: @sagetrac-tmonteil @jjermann @staroste @gagern @mkoeppe

Component: number fields

Keywords: sd66

Author: Vincent Delecroix, Štěpán Starosta

Branch/Commit: d63b7ac

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/17830

The text was updated successfully, but these errors were encountered:

videlec · 2015-02-22T22:08:18Z

Commit: 5f7f57b

videlec · 2015-02-22T22:08:18Z

Branch: u/vdelecroix/17830

videlec · 2015-02-22T22:08:18Z

comment:1

Working implementation (i.e. all tests pass in sage.rings.number_fields). Needs some speedup and bullet proofs!

New commits:

`1fd916f`	`trac #17830: ordering for real embedded number fields`
`316dd8e`	`trac #17830: floor/ceil`
`5f7f57b`	`trac #17830: cleaner import in number_field.py`

videlec · 2015-03-30T11:38:41Z

Changed keywords from none to sd66

staroste · 2015-04-01T11:59:53Z

Changed commit from 5f7f57b to 82f6d09

staroste · 2015-04-01T11:59:53Z

Changed branch from u/vdelecroix/17830 to u/sstarosta/17830

staroste · 2015-04-01T11:59:53Z

comment:5

I have done some testing and committed a few tweaks done on Sage days 66 + doc improvement.

videlec · 2015-04-01T15:28:11Z

comment:6

I am not sure it is because of your commit, but

sage -t continued_fraction.py  # 1 doctest failed
sage -t polynomial/polynomial_rational_flint.pyx  # 1 doctest failed

videlec · 2015-04-01T22:32:38Z

Changed branch from u/sstarosta/17830 to u/vdelecroix/17830

videlec · 2015-04-01T22:32:38Z

comment:7

The two failing doctests come from the introduction of the method _real_mpfi_. I just propose to get rid of it in this ticket. The main reason is that there are a lot of duplication between:

AA and QQbar
RLF and CLF
what is implemented in this ticket for number fields

I propose to clean it up in ticket #18103 and add the _real_mpfi_ feature there.

Vincent

New commits:

`d0f6f7b`	`Trac 17830: simpler initialization + TODO`
`96ac61e`	`Trac 17830: revert the introduction of _real_mpfi_`

videlec · 2015-04-01T22:32:38Z

Changed commit from 82f6d09 to 96ac61e

videlec · 2015-04-01T22:32:38Z

Changed author from Vincent Delecroix to Vincent Delecroix, Štěpán Starosta

sagetrac-git · 2015-04-29T22:39:16Z

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

`90b4acc`	`trac #17830: ordering for real embedded number fields`
`ee5a198`	`trac #17830: floor/ceil`
`ec50d4d`	`trac #17830: cleaner import in number_field.py`
`f07dc08`	`trac #17830: doc improvements and small tweaks`
`b7ba83a`	`Trac 17830: simpler initialization + TODO`

sagetrac-git · 2015-04-29T22:39:16Z

Changed commit from 96ac61e to b7ba83a

videlec · 2015-04-29T22:39:36Z

comment:10

rebase on sage-6.7.beta3

sagetrac-git · 2015-06-29T21:17:18Z

Changed commit from b7ba83a to a8c294b

sagetrac-git · 2015-06-29T21:17:18Z

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

`95f3ada`	`trac #17830: ordering for real embedded number fields`
`7d0d0c0`	`trac #17830: floor/ceil`
`2d49517`	`trac #17830: cleaner import in number_field.py`
`e1efbd6`	`trac #17830: doc improvements and small tweaks`
`875f756`	`Trac 17830: simpler initialization + TODO`
`a8c294b`	`Trac #17830: rich_to_bool is no longer a method`

videlec · 2015-06-29T21:17:46Z

comment:13

rebased on 6.8.beta6

sagetrac-git · 2015-07-01T13:52:53Z

Changed commit from a8c294b to eb50b94

sagetrac-git · 2015-07-01T13:52:53Z

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

`575b264`	`Trac #18159: add a ._test_cardinality in Sets category`
`cc87bd5`	`Trac #18159: remove a duplicated test`
`32c403d`	`Trac #18159: fix cardinality/is_finite in sets/set.py`
`937ebf4`	`Trac #18159: fix some tests related to TestSuite`
`eb50b94`	`Trac #18159: fix two parents`

sagetrac-git · 2015-07-01T13:54:59Z

Changed commit from eb50b94 to a8c294b

sagetrac-git · 2015-07-01T13:54:59Z

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

`95f3ada`	`trac #17830: ordering for real embedded number fields`
`7d0d0c0`	`trac #17830: floor/ceil`
`2d49517`	`trac #17830: cleaner import in number_field.py`
`e1efbd6`	`trac #17830: doc improvements and small tweaks`
`875f756`	`Trac 17830: simpler initialization + TODO`
`a8c294b`	`Trac #17830: rich_to_bool is no longer a method`

videlec · 2015-08-09T19:00:52Z

comment:18

Replying to @fchapoton:

+Decreased doctests rings/number_field/number_field_base.pyx from 11 / 11 = 100% to 12 / 13 = 92%

Then what? There is no way to test _init_embedding_approx that initialize private attributes. For sure we can duplicate doctests from _get_embedding_approx or even write

TESTS::

    sage: 1 + 1 # indirect doctest
    2

if it makes you happier. But I am not happy with that. If you have any constructive suggestion I would be happy to hear it.

General note: asking for review (= waiting from other people comments) is different from merging into Sage. Patchbot green light concerns the latter.

sagetrac-git · 2015-12-07T17:58:37Z

Changed commit from a8c294b to 9313849

sagetrac-git · 2015-12-07T17:58:37Z

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

`5b7e757`	`trac #17830: ordering for real embedded number fields`
`bd7eef0`	`trac #17830: floor/ceil`
`94b22b6`	`trac #17830: cleaner import in number_field.py`
`138957a`	`trac #17830: doc improvements and small tweaks`
`9313849`	`Trac 17830: simpler initialization + TODO`

videlec · 2015-12-07T17:58:55Z

New commits:

`5b7e757`	`trac #17830: ordering for real embedded number fields`
`bd7eef0`	`trac #17830: floor/ceil`
`94b22b6`	`trac #17830: cleaner import in number_field.py`
`138957a`	`trac #17830: doc improvements and small tweaks`
`9313849`	`Trac 17830: simpler initialization + TODO`

sagetrac-git · 2015-12-07T18:00:47Z

Changed commit from 9313849 to c7a50e7

sagetrac-git · 2015-12-07T18:00:47Z

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

`c7a50e7`	`Trac #17830: add a useless doctest`

vbraun · 2015-12-28T21:23:39Z

comment:22

Lgtm but merge conflict...

sagetrac-git · 2015-12-28T23:01:07Z

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

`ff13d1f`	`trac #17830: ordering for real embedded number fields`
`c52229d`	`trac #17830: floor/ceil`
`8543255`	`trac #17830: cleaner import in number_field.py`
`c098dc7`	`trac #17830: doc improvements and small tweaks`
`8bb1031`	`Trac #17830: simpler initialization + TODO`
`d63b7ac`	`Trac #17830: add a useless doctest`

sagetrac-git · 2015-12-28T23:01:07Z

Changed commit from c7a50e7 to d63b7ac

videlec · 2015-12-28T23:01:49Z

comment:24

Thanks for having a look! Rebased on 7.0.beta1.

Vincent

vbraun · 2015-12-28T23:06:08Z

Reviewer: Volker Braun

vbraun · 2015-12-29T17:52:15Z

Changed branch from u/vdelecroix/17830 to d63b7ac

videlec added this to the sage-6.6 milestone Feb 22, 2015

videlec added c: number fields labels Feb 22, 2015

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videlec changed the title ~~Comparison of number field elements dependent of embedding~~ Comparison of number field elements dependent of real embedding Feb 22, 2015

videlec added the s: needs review label Apr 1, 2015

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videlec modified the milestones: sage-6.6, sage-6.10 Dec 7, 2015

videlec added s: needs review and removed s: needs work labels Dec 7, 2015

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vbraun added s: positive review and removed s: needs review labels Dec 28, 2015

vbraun removed the s: positive review label Dec 29, 2015

vbraun closed this as completed in 464e76b Dec 29, 2015

sagetrac-mbell mannequin mentioned this issue Dec 29, 2022

document Polyhedron defined over number field #17197

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Comparison of number field elements dependent of real embedding #17830

Comparison of number field elements dependent of real embedding #17830

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