Opened 2 years ago

Closed 2 years ago

#18279 closed enhancement (fixed)

implement rational preperiodic points for polynomials over number fields

Reported by: bhutz Owned by: bhutz
Priority: minor Milestone: sage-6.7
Component: algebraic geometry Keywords:
Cc: Merged in:
Authors: Ben Hutz Reviewers: Grayson Jorgenson
Report Upstream: N/A Work issues:
Branch: f4bd855 (Commits) Commit: f4bd8554f573f5557fcad138fb34ecf58c859b40
Dependencies: Stopgaps:

Description

Through the use of Weil restriction we can reduce the problem of rational points over number fields to QQ-rational points. Combining the Weil restriction functionality with the rational preperiodic point functionality, we can extend the latter to number fields.

Change History (10)

comment:1 Changed 2 years ago by bhutz

  • Branch set to u/bhutz/ticket/18279
  • Created changed from 04/22/15 14:22:22 to 04/22/15 14:22:22
  • Modified changed from 04/22/15 14:22:22 to 04/22/15 14:22:22

comment:2 Changed 2 years ago by bhutz

  • Commit set to ff79600f7aa59a301e6bb6ca560b6616de46039f
  • Status changed from new to needs_review
  • Summary changed from implemented rational preperiodic points for polynomials over number fields to implement rational preperiodic points for polynomials over number fields

New commits:

ff7960018279: rational preperiodic for number fields

comment:3 Changed 2 years ago by bhutz

  • Authors set to Ben Hutz

comment:4 Changed 2 years ago by gjorgenson

  • Status changed from needs_review to needs_work
  • the point at infinity will always be a totally ramified fixed point so no check is needed
  • Maps over QQbar seem get incorrect output:
    P.<x,y> = ProjectiveSpace(QQbar,1)
    H = End(P)
    f = H([x^2-y^2,y^2])
    print f.rational_preperiodic_points()
    

returns None

but

P.<x,y> = ProjectiveSpace(QQbar,1)
H = End(P)
f = H([x^2-y^2,y^2])
f = f._number_field_from_algebraics()
print f.rational_preperiodic_points()

returns [(1 : 1), (1 : 0), (-1 : 1), (0 : 1)]

comment:5 Changed 2 years ago by git

  • Commit changed from ff79600f7aa59a301e6bb6ca560b6616de46039f to 55312ac9603c6d67cc7c2a1157fd4c1ca1764016

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

55312ac18279: fix issues from review

comment:6 Changed 2 years ago by bhutz

  • Status changed from needs_work to needs_review

fixed issues. I also noticed that the 'inverted' polynomial case, i.e., where 0 is totally ramified and fixed was not actually working since the inverse of the weil restriction was not producing the correct points. I fixed this as well.

comment:7 Changed 2 years ago by gjorgenson

Everything looks good, but there is just a small typo (I think it was there before the commits though)

-in line 3110, Determined should be Determines

Also, it looks like the first lines of the documentation for rational_preperiodic_graph are the same as those of rational_preperiodic_points, but the function returns the graph of the preperiodic points

comment:8 Changed 2 years ago by git

  • Commit changed from 55312ac9603c6d67cc7c2a1157fd4c1ca1764016 to f4bd8554f573f5557fcad138fb34ecf58c859b40

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

f4bd85518279: fix typos in docs

comment:9 Changed 2 years ago by gjorgenson

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

comment:10 Changed 2 years ago by vbraun

  • Branch changed from u/bhutz/ticket/18279 to f4bd8554f573f5557fcad138fb34ecf58c859b40
  • Resolution set to fixed
  • Status changed from positive_review to closed
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