Opened 5 years ago
Closed 5 years ago
#17067 closed enhancement (fixed)
Canonical height over number fields for projective morphisms
Reported by:  bhutz  Owned by:  bhutz 

Priority:  minor  Milestone:  sage6.4 
Component:  algebraic geometry  Keywords:  canonical height 
Cc:  paulfili  Merged in:  
Authors:  Ben Hutz  Reviewers:  Paul Fili 
Report Upstream:  N/A  Work issues:  
Branch:  f71d707 (Commits)  Commit:  f71d7072c901c379d8f7ead2f8edd2ba2e0c4cea 
Dependencies:  Stopgaps: 
Description
Enable compute canonical height over number fields for points and morphisms defined over number fields. The method will be to extend the local height computations (green's functions) to include number field places.
Change History (18)
comment:1 Changed 5 years ago by
 Branch set to u/bhutz/ticket/17067
 Created changed from 09/29/14 16:01:24 to 09/29/14 16:01:24
 Modified changed from 09/29/14 16:01:24 to 09/29/14 16:01:24
comment:2 Changed 5 years ago by
 Commit set to bc111997c874e67e09dfbfe29e71118924fe4f9b
comment:3 Changed 5 years ago by
 Commit changed from bc111997c874e67e09dfbfe29e71118924fe4f9b to fa40d41412f940b81cbdef0e94d6f33be1913c4e
Branch pushed to git repo; I updated commit sha1. New commits:
fa40d41  errors bounds and local heights

comment:4 Changed 5 years ago by
Here is a first attempt at the generalized error bounds. It needed the implementation of local heights for morphisms, so I did that and for points as well.
I need to do some serious testing still, but the original set of doc tests were still basically correct. With the new error bound computation the values were slightly different, but within the specified tolerance.
comment:5 Changed 5 years ago by
 Commit changed from fa40d41412f940b81cbdef0e94d6f33be1913c4e to 59af0821faaa86dd385cfd8f20715852bc8d04ff
Branch pushed to git repo; I updated commit sha1. New commits:
59af082  added local_heights to use in error_bounds

comment:6 Changed 5 years ago by
 Commit changed from 59af0821faaa86dd385cfd8f20715852bc8d04ff to c5363e3cabdfb6515f9fc011662b6850eab0947a
Branch pushed to git repo; I updated commit sha1. New commits:
c5363e3  added todo block

comment:7 Changed 5 years ago by
 Status changed from new to needs_review
comment:8 Changed 5 years ago by
 Commit changed from c5363e3cabdfb6515f9fc011662b6850eab0947a to c0894eae89838a5078cddfca5707f1b4449977ec
Branch pushed to git repo; I updated commit sha1. New commits:
c0894ea  17067: fixed doc typos

comment:9 Changed 5 years ago by
comment:10 Changed 5 years ago by
 Status changed from needs_review to positive_review
comment:11 Changed 5 years ago by
 Reviewers set to Paul Fili
comment:12 Changed 5 years ago by
 Status changed from positive_review to needs_work
Conflicts, probably with #17517
comment:13 Changed 5 years ago by
It's not #17517 as it doesn't touch any of the same files. I just downloaded the latest beta5 and had no issues with merge, and it is still listed as green for automerge on trac. Do I need to wait until a new beta comes out or is there a way to see what happened here?
comment:14 Changed 5 years ago by
 Commit changed from c0894eae89838a5078cddfca5707f1b4449977ec to 3cd6d3e8a270d1ba08730c4768d22caab2c8d71d
Branch pushed to git repo; I updated commit sha1. New commits:
3cd6d3e  17067: fix merge issues into 6.5.beta6

comment:15 Changed 5 years ago by
 Commit changed from 3cd6d3e8a270d1ba08730c4768d22caab2c8d71d to f71d7072c901c379d8f7ead2f8edd2ba2e0c4cea
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
f71d707  Merge branch 'master' into ticket/17067

comment:16 Changed 5 years ago by
 Status changed from needs_work to needs_review
Merge issues fixed. Note that the commit 3cd6d3e was rolled back and the conflict resolution redone.
comment:17 Changed 5 years ago by
 Status changed from needs_review to positive_review
Passes doctests on my 6.5beta6 build, looks good to me.
comment:18 Changed 5 years ago by
 Branch changed from u/bhutz/ticket/17067 to f71d7072c901c379d8f7ead2f8edd2ba2e0c4cea
 Resolution set to fixed
 Status changed from positive_review to closed
ok. I've now taken the original code from Adam Towsley and Paul Fili from sagedays 55 and made it mesh with the current functionality in Sage. It should be noted that I left QQ using RR and Qp so that the flip trick works better. However, over number fields, the size of the point is growing quite quickly so N cannot be too large. I didn't see a way to get a good use of the residue field (with precision) as with QQ.
Please take a look and see what you think. I've run many more examples there are in the docs where I pullback rational points to a number field and haven't run into any issues there. Another way to get valid tests would be nice.
I'm also considering adding the error bound computation for dimension >1 to this ticket as well, but I've haven't yet looked into how complicated that will be.
New commits:
implement canonical heights over number fields