Opened 12 years ago

Last modified 6 years ago

#6881 closed enhancement

Solving conics over polynomial rings. — at Version 13

Reported by: victor Owned by: lackermans
Priority: major Milestone: sage-6.10
Component: algebraic geometry Keywords: conic, curve, function field
Cc: mstreng Merged in:
Authors: Lennart Ackermans Reviewers: Marco Streng
Report Upstream: N/A Work issues:
Branch: public/conics_rational_function_field (Commits, GitHub, GitLab) Commit: 8a9d34fd202d381912a41e7b189fad21b0126408
Dependencies: Stopgaps:

Status badges

Description (last modified by mstreng)

Implement the algorithm of John Cremona and Mark van Hoeij for finding conics over fraction fields of polynomial rings.

The article http://www.warwick.ac.uk/~masgaj/papers/conicFT.pdf contains references to implementations in Maple (van Hoeij) and Magma (Cremona-Roberts), but these implementations heavily rely on things specific to these systems.

#727 provides classes for conic curves that this code should build upon

Change History (13)

comment:1 Changed 12 years ago by AlexGhitza

  • Component changed from algebra to algebraic geometry

comment:2 Changed 11 years ago by mstreng

  • Report Upstream set to N/A

See #727 A patch defining a conic class and using Simon's algorithms for finding points over Q is in progress.

comment:3 Changed 11 years ago by mstreng

  • Cc mstreng added

comment:4 Changed 11 years ago by mstreng

  • Description modified (diff)
  • Summary changed from Conics to Solving conics over polynomial rings.

I changed the description to better fit what is already in #727. Besides things that are already in #727, all that I removed from the original description were the following two requests.

  1. Use John Cremona's algorithms for finding points on conics over QQ.

It seems that Simon's algorithms (in #727) are better, but that doesn't have to stop us from giving Cremona's code as an option. It is inside mwrank, which is part of Sage. If someone wants to do it, then it can be made into a separate ticket.

  1. Getting primes of bad reduction of conics.

This is as good as in #727: make a Conic C. Then do C.determinant().factor()

comment:5 Changed 6 years ago by lackermans

  • Owner changed from tbd to lackermans

comment:6 Changed 6 years ago by lackermans

  • Branch set to public/conics_rational_function_field

comment:7 Changed 6 years ago by git

  • Commit set to 10cfe65b0ea45af8603d3a48aede6c2b6aa55cda

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

10cfe65Continuing has_rational_point() on conics over rational function fields. Currently returns incorrect solution.

comment:8 Changed 6 years ago by git

  • Commit changed from 10cfe65b0ea45af8603d3a48aede6c2b6aa55cda to 73b7b05dfd2584ccb29964310d3241aee1d1f82b

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

73b7b05Fixed has_rational_point and added some documentation

comment:9 Changed 6 years ago by git

  • Commit changed from 73b7b05dfd2584ccb29964310d3241aee1d1f82b to 8f4d0f46e9a4b021e0d113bf80c636f2be038d2a

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

8f4d0f4Added documentation and bugfixes to con_rational_function_field

comment:10 Changed 6 years ago by lackermans

  • Authors changed from Victor Miller to Lennart Ackermans

comment:11 Changed 6 years ago by lackermans

  • Status changed from new to needs_review

comment:12 Changed 6 years ago by git

  • Commit changed from 8f4d0f46e9a4b021e0d113bf80c636f2be038d2a to 8a9d34fd202d381912a41e7b189fad21b0126408

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

8a9d34fFixed documentation bug

comment:13 Changed 6 years ago by mstreng

  • Description modified (diff)
  • Keywords function field added
  • Reviewers set to Marco Streng
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