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:  sage6.10 
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: 
Description (last modified by )
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 (CremonaRoberts), 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
 Component changed from algebra to algebraic geometry
comment:2 Changed 11 years ago by
 Report Upstream set to N/A
comment:3 Changed 11 years ago by
 Cc mstreng added
comment:4 Changed 11 years ago by
 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.
 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.
 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
 Owner changed from tbd to lackermans
comment:6 Changed 6 years ago by
 Branch set to public/conics_rational_function_field
comment:7 Changed 6 years ago by
 Commit set to 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 6 years ago by
 Commit changed from 10cfe65b0ea45af8603d3a48aede6c2b6aa55cda to 73b7b05dfd2584ccb29964310d3241aee1d1f82b
Branch pushed to git repo; I updated commit sha1. New commits:
73b7b05  Fixed has_rational_point and added some documentation

comment:9 Changed 6 years ago by
 Commit changed from 73b7b05dfd2584ccb29964310d3241aee1d1f82b to 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 6 years ago by
comment:11 Changed 6 years ago by
 Status changed from new to needs_review
comment:12 Changed 6 years ago by
 Commit changed from 8f4d0f46e9a4b021e0d113bf80c636f2be038d2a to 8a9d34fd202d381912a41e7b189fad21b0126408
Branch pushed to git repo; I updated commit sha1. New commits:
8a9d34f  Fixed documentation bug

comment:13 Changed 6 years ago by
 Description modified (diff)
 Keywords function field added
 Reviewers set to Marco Streng
See #727 A patch defining a conic class and using Simon's algorithms for finding points over Q is in progress.