Opened 3 years ago

Closed 3 years ago

#28200 closed enhancement (fixed)

reduce base field for scheme morphisms

Reported by: bhutz Owned by:
Priority: major Milestone: sage-8.9
Component: algebraic geometry Keywords: SI2019
Cc: Merged in:
Authors: Ben Hutz Reviewers: Meghan Grip, Emily Rachfal, Henry Talbott
Report Upstream: N/A Work issues:
Branch: a0e7824 (Commits, GitHub, GitLab) Commit: a0e7824d1b09faa5b59f55833b3ba51fef2d6456
Dependencies: #28161, #28174 Stopgaps:

Status badges

Description

It is possible that the field defined by the coefficients is strictly contained in base field of the morphism. This can be happen in a number of situations, especially from conjugations or computing normal forms. There should be a general function to reduce to the field of definition of the coefficients.

Change History (11)

comment:1 Changed 3 years ago by bhutz

  • Branch set to u/bhutz/28200_reduce_base_field
  • Commit set to 222c9aa779e787ccee188349e87b653e2ab54758

Here is an initial implementation that could use some more testing.

This just implements the function and does not have any of the 'client' functions utilize this; like conjugate or normal form. I'm not sure those additional modifications should be part of this ticket.


New commits:

6c9c01f28161: from_algebraics return ds
b33de7728161 returns ds
5a75f00Merge branch 8.9.beta2 into t/28161/master
f9db11028161: update docs
c7b03d728200: implement reduce_base_field for schememorphisms
4f462a028174: Fix dehomogenization error for non-endomorphisms
222c9aaMerge commit '4f462a0255fef1590a6979d4b95fee204f55b432' of git://trac.sagemath.org/sage into reduce_base

comment:2 Changed 3 years ago by bhutz

  • Dependencies changed from 28161, 28174 to #28161, #28174

comment:3 Changed 3 years ago by bhutz

  • Status changed from new to needs_review

comment:4 Changed 3 years ago by gh-HTalbott

  • Status changed from needs_review to needs_work

On line 1684 of src/sage/schemes/projective/projective_morphism.py, the method finds the max of the the degrees of the coefficients. This should find the LCM rather than the max. For instance, the following code currently gives the minimal field as GF(5 to 3), when it should give GF(5 to 6), as below:

sage: K.<t>=GF(5^6)
sage: A.<x>=AffineSpace(K,1)
sage: H=End(A)
sage: f=H([x^2+x*(t^3 + 2*t^2 + 4*t)+(t^5 + 3*t^4 + t^2 + 4*t)])
sage: f.reduce_base_field()
Scheme endomorphism of Affine Space of dimension 1 over Finite Field in t of size 5^6
  Defn: Defined on coordinates by sending (x) to
        (x^2 + (t^3 + 2*t^2 - t)*x + (t^5 - 2*t^4 + t^2 - t))

comment:5 Changed 3 years ago by git

  • Commit changed from 222c9aa779e787ccee188349e87b653e2ab54758 to e9fc3faa1c8acef91cfc1d03f987352bfedab7df

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

1ad13aeMerge branch 8.9.beta4 into t/28200/28200_reduce_base_field
e9fc3fa28200: fix to lcm and add example

comment:6 Changed 3 years ago by bhutz

  • Status changed from needs_work to needs_review

comment:7 Changed 3 years ago by gh-meggrip

  • Reviewers set to Meghan Grip, Emily Rachfal, Henry Talbott

comment:8 Changed 3 years ago by gh-HTalbott

  • Branch changed from u/bhutz/28200_reduce_base_field to u/gh-HTalbott/28200_reduce_base_field

comment:9 Changed 3 years ago by git

  • Commit changed from e9fc3faa1c8acef91cfc1d03f987352bfedab7df to a0e7824d1b09faa5b59f55833b3ba51fef2d6456

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

a0e782428200: fixed example formatting

comment:10 Changed 3 years ago by gh-HTalbott

  • Status changed from needs_review to positive_review

Fixed small documentations errors. Everything else looks good!


New commits:

482ed83Merge branch 'u/bhutz/28200_reduce_base_field' of git://trac.sagemath.org/sage into test
a0e782428200: fixed example formatting

comment:11 Changed 3 years ago by vbraun

  • Branch changed from u/gh-HTalbott/28200_reduce_base_field to a0e7824d1b09faa5b59f55833b3ba51fef2d6456
  • Resolution set to fixed
  • Status changed from positive_review to closed
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