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:  sage8.9 
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: 
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
 Branch set to u/bhutz/28200_reduce_base_field
 Commit set to 222c9aa779e787ccee188349e87b653e2ab54758
comment:2 Changed 3 years ago by
 Dependencies changed from 28161, 28174 to #28161, #28174
comment:3 Changed 3 years ago by
 Status changed from new to needs_review
comment:4 Changed 3 years ago by
 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
 Commit changed from 222c9aa779e787ccee188349e87b653e2ab54758 to e9fc3faa1c8acef91cfc1d03f987352bfedab7df
comment:6 Changed 3 years ago by
 Status changed from needs_work to needs_review
comment:7 Changed 3 years ago by
 Reviewers set to Meghan Grip, Emily Rachfal, Henry Talbott
comment:8 Changed 3 years ago by
 Branch changed from u/bhutz/28200_reduce_base_field to u/ghHTalbott/28200_reduce_base_field
comment:9 Changed 3 years ago by
 Commit changed from e9fc3faa1c8acef91cfc1d03f987352bfedab7df to a0e7824d1b09faa5b59f55833b3ba51fef2d6456
Branch pushed to git repo; I updated commit sha1. New commits:
a0e7824  28200: fixed example formatting

comment:10 Changed 3 years ago by
 Status changed from needs_review to positive_review
comment:11 Changed 3 years ago by
 Branch changed from u/ghHTalbott/28200_reduce_base_field to a0e7824d1b09faa5b59f55833b3ba51fef2d6456
 Resolution set to fixed
 Status changed from positive_review to closed
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:
28161: from_algebraics return ds
28161 returns ds
Merge branch 8.9.beta2 into t/28161/master
28161: update docs
28200: implement reduce_base_field for schememorphisms
28174: Fix dehomogenization error for nonendomorphisms
Merge commit '4f462a0255fef1590a6979d4b95fee204f55b432' of git://trac.sagemath.org/sage into reduce_base