Opened 4 years ago

Closed 4 years ago

Last modified 4 years ago

#16838 closed enhancement (fixed)

make affine and projective dehomogenize and homogenize work together

Reported by: bhutz Owned by: bhutz
Priority: minor Milestone: sage-6.4
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 4 years ago by bhutz

  • 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 4 years ago by git

  • Commit set to c3d007ffa7a1ed25e9c9b1982f756d595ce29a62

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

c3d007f16838: fixes for algebraic subschemes

comment:3 Changed 4 years ago by git

  • Commit changed from c3d007ffa7a1ed25e9c9b1982f756d595ce29a62 to 30e8fde4ac43f796f4dbdfcdd01aa1ade1e71754

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

30e8fde16838: fix issues with homogenize morphism

comment:4 Changed 4 years ago by git

  • Commit changed from 30e8fde4ac43f796f4dbdfcdd01aa1ade1e71754 to 16efbbedf4a34b277028958c6ae3128916cf2164

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

16efbbe16838: slight correction to homogenize

comment:5 Changed 4 years ago by bhutz

  • Authors set to Ben Hutz
  • Status changed from new to needs_review

comment:6 Changed 4 years ago by jdefaria

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 4 years ago by jdefaria

  • Reviewers set to Joao de Faria

comment:8 Changed 4 years ago by git

  • Commit changed from 16efbbedf4a34b277028958c6ae3128916cf2164 to 88158554bf0a8613fa59b108b498744f9b0eeffe

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

881585516838: fixed some typos

comment:9 Changed 4 years ago by jdefaria

  • Status changed from needs_review to positive_review

Everything looks good.

comment:10 Changed 4 years ago by vbraun

  • Branch changed from u/bhutz/ticket/16838 to 88158554bf0a8613fa59b108b498744f9b0eeffe
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:11 Changed 4 years ago by kcrisman

  • Commit 88158554bf0a8613fa59b108b498744f9b0eeffe deleted
  • Reviewers changed from Joao de Faria to Joao Alberto de Faria
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