Opened 4 years ago
Closed 4 years ago
#18279 closed enhancement (fixed)
implement rational preperiodic points for polynomials over number fields
Reported by:  bhutz  Owned by:  bhutz 

Priority:  minor  Milestone:  sage6.7 
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 QQrational 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 4 years ago by
 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 4 years ago by
 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
comment:3 Changed 4 years ago by
comment:4 Changed 4 years ago by
 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^2y^2,y^2]) print f.rational_preperiodic_points()
returns None
but
P.<x,y> = ProjectiveSpace(QQbar,1) H = End(P) f = H([x^2y^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 4 years ago by
 Commit changed from ff79600f7aa59a301e6bb6ca560b6616de46039f to 55312ac9603c6d67cc7c2a1157fd4c1ca1764016
Branch pushed to git repo; I updated commit sha1. New commits:
55312ac  18279: fix issues from review

comment:6 Changed 4 years ago by
 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 4 years ago by
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 4 years ago by
 Commit changed from 55312ac9603c6d67cc7c2a1157fd4c1ca1764016 to f4bd8554f573f5557fcad138fb34ecf58c859b40
Branch pushed to git repo; I updated commit sha1. New commits:
f4bd855  18279: fix typos in docs

comment:9 Changed 4 years ago by
 Reviewers set to Grayson Jorgenson
 Status changed from needs_review to positive_review
comment:10 Changed 4 years ago by
 Branch changed from u/bhutz/ticket/18279 to f4bd8554f573f5557fcad138fb34ecf58c859b40
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
18279: rational preperiodic for number fields