Opened 3 years ago

Closed 3 years ago

#18281 closed enhancement (fixed)

implement critical point functionality including is_pcf for projective morphisms

Reported by: bhutz Owned by: bhutz
Priority: major Milestone: sage-6.8
Component: algebraic geometry Keywords:
Cc: Merged in:
Authors: Ben Hutz Reviewers: Grayson Jorgenson
Report Upstream: N/A Work issues:
Branch: f904d5d (Commits) Commit: f904d5df326f0874a531b288d5303a285442e5e1
Dependencies: Stopgaps:

Description

Implement computing the critical point locus for a morphism of projective space and checking if that morphism is post-critically finite (all critical points are preperiodic). We can also construction to critical point portrait.

Change History (10)

comment:1 Changed 3 years ago by bhutz

  • Branch set to u/bhutz/ticket/18281
  • Created changed from 04/22/15 15:30:20 to 04/22/15 15:30:20
  • Modified changed from 04/22/15 15:30:20 to 04/22/15 15:30:20

comment:2 Changed 3 years ago by bhutz

  • Authors set to Ben Hutz
  • Commit set to 83242df1ca8b49344cc0cbc58c4b197d36a2c41b
  • Status changed from new to needs_review

New commits:

83242df18281: critical point functionality for projective morphisms

comment:3 Changed 3 years ago by gjorgenson

  • Reviewers set to Grayson Jorgenson
  • Status changed from needs_review to needs_work

change_ring (for both SchemeMorphism_polynomial and SchemeMorphism_point):

  • Before creating an embedding into QQbar, need check that the map is defined over a number field, change_ring breaks otherwise:
    P.<x,y> = ProjectiveSpace(ZZ,1)
    H = End(P)
    f = H([3*x^2,y^2])
    f.change_ring(QQbar)
    
  • There is also an issue when trying to change_ring from QQbar to QQbar:
    P.<x,y> = ProjectiveSpace(QQbar,1)
    H = End(P)
    f = H([3*x^2,y^2])
    f.change_ring(QQbar)
    

_preperiodic_points_to_cyclegraph:

  • maybe add more comments explaining how equal points with different representations are dealt with

wronskian_ideal:

  • in line 2497, change format of NotImplementedError? to the standard format
  • change "== false" checks to "not" for faster performance

critical_points:

  • rational_points should return a list, so the list conversion in the return statement is not needed

is_postcritically_finite

  • remove extra lines in documentation, lines 2560 and 2595
  • subscheme check not needed since the check is present in critical_points
  • perhaps restrict to only maps defined over number fields

critical_point_portrait:

  • copying crit_points list not needed, instead could loop over crit_points by index, stopping when the index is the original length of the crit_points list
  • subscheme and endomorphism checks not needed since they are present in critical_points

critical_height:

  • maybe include a note that the keywords are optional
  • subscheme and endomorphism checks are already done in critical_points

comment:4 Changed 3 years ago by git

  • Commit changed from 83242df1ca8b49344cc0cbc58c4b197d36a2c41b to 5a9f9356ef6459e8a42d2f0bbdb39961d81da980

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

5a9f93518281: changes from review

comment:5 Changed 3 years ago by bhutz

  • Status changed from needs_work to needs_review

I made the changes. I changed the descriptions of the kwds for heights in a number of places.

I also decided that critical heights over number field orders was ok and moved the function to the 'rings' section.

comment:6 Changed 3 years ago by gjorgenson

I tested is_postcritically_finite and critical_point_portrait on examples of pcf maps.

Everything looks good, but there is one instance of whitespace in line 2184 of projective_morphism

Last edited 3 years ago by gjorgenson (previous) (diff)

comment:7 Changed 3 years ago by git

  • Commit changed from 5a9f9356ef6459e8a42d2f0bbdb39961d81da980 to f904d5df326f0874a531b288d5303a285442e5e1

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

f904d5d18281 removing trailing white space

comment:8 Changed 3 years ago by bhutz

  • Milestone changed from sage-6.7 to sage-6.8

comment:9 Changed 3 years ago by gjorgenson

  • Status changed from needs_review to positive_review

comment:10 Changed 3 years ago by vbraun

  • Branch changed from u/bhutz/ticket/18281 to f904d5df326f0874a531b288d5303a285442e5e1
  • Resolution set to fixed
  • Status changed from positive_review to closed
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