Opened 13 years ago

# Solving conics over polynomial rings. — at Version 14

Reported by: Owned by: Victor S. Miller Lennart Ackermans major sage-6.10 algebraic geometry conic, curve, function field Marco Streng Lennart Ackermans Marco Streng N/A public/conics_rational_function_field 8a9d34fd202d381912a41e7b189fad21b0126408

Implement the algorithm of John Cremona and Mark van Hoeij for solving 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

### comment:1 Changed 13 years ago by Alex Ghitza

Component: algebra → algebraic geometry

### comment:2 Changed 12 years ago by Marco Streng

Report Upstream: → N/A

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

### comment:4 Changed 12 years ago by Marco Streng

Description: modified (diff) Conics → 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 7 years ago by Lennart Ackermans

Owner: changed from tbd to Lennart Ackermans

### comment:6 Changed 7 years ago by Lennart Ackermans

Branch: → public/conics_rational_function_field

### comment:7 Changed 7 years ago by git

Commit: → 10cfe65b0ea45af8603d3a48aede6c2b6aa55cda

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

 ​10cfe65 `Continuing has_rational_point() on conics over rational function fields. Currently returns incorrect solution.`

### comment:8 Changed 7 years ago by git

Commit: 10cfe65b0ea45af8603d3a48aede6c2b6aa55cda → 73b7b05dfd2584ccb29964310d3241aee1d1f82b

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

 ​73b7b05 `Fixed has_rational_point and added some documentation`

### comment:9 Changed 7 years ago by git

Commit: 73b7b05dfd2584ccb29964310d3241aee1d1f82b → 8f4d0f46e9a4b021e0d113bf80c636f2be038d2a

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

 ​8f4d0f4 `Added documentation and bugfixes to con_rational_function_field`

### comment:10 Changed 7 years ago by Lennart Ackermans

Authors: Victor Miller → Lennart Ackermans

### comment:11 Changed 7 years ago by Lennart Ackermans

Status: new → needs_review

### comment:12 Changed 7 years ago by git

 ​8a9d34f `Fixed documentation bug`