#17855 closed enhancement (fixed)
create is_preperiodic function for points of projective space
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:  476cf36 (Commits, GitHub, GitLab)  Commit:  
Dependencies:  Stopgaps: 
Description
The function will take a point and map as input and return a boolean of whether or not the point is preperiodic for the map. Perhaps there should be an option to also return the period if the point is preperiodic
Change History (12)
comment:1 Changed 6 years ago by
 Branch set to u/bhutz/ticket/17855
 Created changed from 02/25/15 17:32:59 to 02/25/15 17:32:59
 Modified changed from 02/25/15 17:32:59 to 02/25/15 17:32:59
comment:2 Changed 6 years ago by
 Commit set to f2f641403f8e05e7345a2ffb132b6cfcb8695b9b
comment:3 Changed 6 years ago by
 Status changed from new to needs_review
This incorporated a few additional changes
 there was an error in the error_bound canonical height computations which is now corrected
 heights and canonical heights are now computable for QQbar points
 methods to change QQbar points and maps to number field points and maps
 change_ring now accepts an embedding for points and maps
comment:4 Changed 6 years ago by
 Status changed from needs_review to needs_work
These examples don't seem to work:
P.<x,y,z> = ProjectiveSpace(QQbar,2) H = Hom(P,P) f = H([x^2,y^2,z^2]) Q = P([1,1,1]) Q.is_preperiodic(f)
P.<x,y,z> = ProjectiveSpace(QQbar,2) H = Hom(P,P) f = H([x^2,y^2,z^2]) Q = P([QQbar(I),1,0]) Q.is_preperiodic(f)
comment:5 Changed 6 years ago by
 Commit changed from f2f641403f8e05e7345a2ffb132b6cfcb8695b9b to 06f4c355c940be11eef57bccfbd474de7a8952f3
Branch pushed to git repo; I updated commit sha1. New commits:
06f4c35  17855: fix issues from review

comment:6 Changed 6 years ago by
 Status changed from needs_work to needs_review
Yes, there were a couple issues with getting the right compositum base field. These should be fixed now.
comment:7 Changed 6 years ago by
From the review, for is_preperiodic need:
 check that map is a morphism
 check that given point is in the domain of the map
 check that if over a number field, it is an absolute number field
comment:8 Changed 6 years ago by
 Commit changed from 06f4c355c940be11eef57bccfbd474de7a8952f3 to 476cf364e6b2f8df396df10141b96763e5a38f16
Branch pushed to git repo; I updated commit sha1. New commits:
476cf36  17855: fix additional input cases

comment:9 Changed 6 years ago by
 Status changed from needs_review to positive_review
Everything seems to be working well and the changes fixed all of the issues from the reviews.
comment:10 Changed 6 years ago by
 Reviewers set to Grayson Jorgenson
comment:11 Changed 6 years ago by
 Branch changed from u/bhutz/ticket/17855 to 476cf364e6b2f8df396df10141b96763e5a38f16
 Resolution set to fixed
 Status changed from positive_review to closed
comment:12 Changed 6 years ago by
 Commit 476cf364e6b2f8df396df10141b96763e5a38f16 deleted
 Milestone changed from sage6.6 to sage6.7
Branch pushed to git repo; I updated commit sha1. New commits:
Merge branch 'master' into ticket/17855