#16838 closed enhancement (fixed)
make affine and projective dehomogenize and homogenize work together
Reported by:  bhutz  Owned by:  bhutz 

Priority:  minor  Milestone:  sage6.4 
Component:  algebraic geometry  Keywords:  
Cc:  Merged in:  
Authors:  Ben Hutz  Reviewers:  Joao Alberto de Faria 
Report Upstream:  N/A  Work issues:  
Branch:  8815855 (Commits)  Commit:  
Dependencies:  Stopgaps: 
Description
There are a number of issues currently with the homogenization
and dehomogenization
functionality. Essentially, what I'd like to see is that dehomogenizing and then homogenizing returns basically the same object. Currently dehomogenization is using AffinePatch
, but homogenization is creating a new projective space every time. This causes a number of funny behaviors so should instead be using projective embedding. I'd like to see tests of the following form return True
:
P.<x,y,z>=ProjectiveSpace(QQ,2) H=End(P) f=H([x*y,y^2,z^2]) n=1 f.dehomogenize(n).homogenize(n)==f
A.<x,y>=AffineSpace(QQ,2) H=End(A) f=H([x*y,y^2]) n=0 f.homogenize(n).dehomogenize(n)==f
This also requires having the affine_patch
and projective_embedding
play nicely together. Fixing this would also allow objects homogenized or dehomogenized from the same space to then live in the same new space. The same for points and currently there is no homogenization function at all for affine points.
I've started working on this and just need to fix a couple more things.
Change History (11)
comment:1 Changed 5 years ago by
 Branch set to u/bhutz/ticket/16838
 Created changed from 08/16/14 16:11:12 to 08/16/14 16:11:12
 Modified changed from 08/16/14 16:11:12 to 08/16/14 16:11:12
comment:2 Changed 5 years ago by
 Commit set to c3d007ffa7a1ed25e9c9b1982f756d595ce29a62
comment:3 Changed 5 years ago by
 Commit changed from c3d007ffa7a1ed25e9c9b1982f756d595ce29a62 to 30e8fde4ac43f796f4dbdfcdd01aa1ade1e71754
Branch pushed to git repo; I updated commit sha1. New commits:
30e8fde  16838: fix issues with homogenize morphism

comment:4 Changed 5 years ago by
 Commit changed from 30e8fde4ac43f796f4dbdfcdd01aa1ade1e71754 to 16efbbedf4a34b277028958c6ae3128916cf2164
Branch pushed to git repo; I updated commit sha1. New commits:
16efbbe  16838: slight correction to homogenize

comment:5 Changed 5 years ago by
 Status changed from new to needs_review
comment:6 Changed 5 years ago by
Outside of a couple of small typos with spacing around equality signs, everything else looks good, ran the long test and confirmed that all tests passed.
comment:7 Changed 5 years ago by
 Reviewers set to Joao de Faria
comment:8 Changed 5 years ago by
 Commit changed from 16efbbedf4a34b277028958c6ae3128916cf2164 to 88158554bf0a8613fa59b108b498744f9b0eeffe
Branch pushed to git repo; I updated commit sha1. New commits:
8815855  16838: fixed some typos

comment:9 Changed 5 years ago by
 Status changed from needs_review to positive_review
Everything looks good.
comment:10 Changed 5 years ago by
 Branch changed from u/bhutz/ticket/16838 to 88158554bf0a8613fa59b108b498744f9b0eeffe
 Resolution set to fixed
 Status changed from positive_review to closed
comment:11 Changed 5 years ago by
 Commit 88158554bf0a8613fa59b108b498744f9b0eeffe deleted
 Reviewers changed from Joao de Faria to Joao Alberto de Faria
Branch pushed to git repo; I updated commit sha1. New commits:
16838: fixes for algebraic subschemes