Opened 3 years ago

Closed 3 years ago

#17067 closed enhancement (fixed)

Canonical height over number fields for projective morphisms

Reported by: bhutz Owned by: bhutz
Priority: minor Milestone: sage-6.4
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 3 years ago by bhutz

  • 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 3 years ago by bhutz

  • Commit set to bc111997c874e67e09dfbfe29e71118924fe4f9b

ok. I've now taken the original code from Adam Towsley and Paul Fili from sage-days 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:

bc11199implement canonical heights over number fields

comment:3 Changed 3 years ago by git

  • Commit changed from bc111997c874e67e09dfbfe29e71118924fe4f9b to fa40d41412f940b81cbdef0e94d6f33be1913c4e

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

fa40d41errors bounds and local heights

comment:4 Changed 3 years ago by bhutz

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 3 years ago by git

  • Commit changed from fa40d41412f940b81cbdef0e94d6f33be1913c4e to 59af0821faaa86dd385cfd8f20715852bc8d04ff

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

59af082added local_heights to use in error_bounds

comment:6 Changed 3 years ago by git

  • Commit changed from 59af0821faaa86dd385cfd8f20715852bc8d04ff to c5363e3cabdfb6515f9fc011662b6850eab0947a

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

c5363e3added todo block

comment:7 Changed 3 years ago by bhutz

  • Status changed from new to needs_review

comment:8 Changed 3 years ago by git

  • Commit changed from c5363e3cabdfb6515f9fc011662b6850eab0947a to c0894eae89838a5078cddfca5707f1b4449977ec

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

c0894ea17067: fixed doc typos

comment:9 Changed 3 years ago by bhutz

  • Authors set to Ben Hutz

comment:10 Changed 3 years ago by paulfili

  • Status changed from needs_review to positive_review

comment:11 Changed 3 years ago by bhutz

  • Reviewers set to Paul Fili

comment:12 Changed 3 years ago by vbraun

  • Status changed from positive_review to needs_work

Conflicts, probably with #17517

comment:13 Changed 3 years ago by bhutz

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 3 years ago by git

  • Commit changed from c0894eae89838a5078cddfca5707f1b4449977ec to 3cd6d3e8a270d1ba08730c4768d22caab2c8d71d

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

3cd6d3e17067: fix merge issues into 6.5.beta6

comment:15 Changed 3 years ago by git

  • Commit changed from 3cd6d3e8a270d1ba08730c4768d22caab2c8d71d to f71d7072c901c379d8f7ead2f8edd2ba2e0c4cea

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

f71d707Merge branch 'master' into ticket/17067

comment:16 Changed 3 years ago by bhutz

  • 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 3 years ago by paulfili

  • Status changed from needs_review to positive_review

Passes doctests on my 6.5beta6 build, looks good to me.

comment:18 Changed 3 years ago by vbraun

  • Branch changed from u/bhutz/ticket/17067 to f71d7072c901c379d8f7ead2f8edd2ba2e0c4cea
  • Resolution set to fixed
  • Status changed from positive_review to closed
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