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| * Uses Denis Simon's pari code for solving and parametrizing conics over QQ | * Uses Denis Simon's pari code for solving and parametrizing conics over QQ. |
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| * Uses pari's rnfisnorm for finding points on conics over number fields | * Uses pari's rnfisnorm for finding points on conics over number fields. |
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| == To do == | * Parametrize any conic given a rational point. |
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| * I forgot to include "sage/schemes/plane_conics/__init__.py" (which is empty), so the patch actually doesn't work * Use a good Hilbert symbol, such as the one of Trac ticket 9334 or the one of Pari. http://trac.sagemath.org/sage_trac/ticket/9334 * Make a hierarchy of Conic classes (modelled after the hierarchy of Elliptic curve classes?), each with special functionality * Fix broken doctests: * sage -t "sage/schemes/plane_conics/conic_solve.py" * sage -t "sage/schemes/plane_conics/hilbert.py" * sage -t "sage/schemes/plane_conics/projective_conic.py * Add missing doctests (e.g. pickling) |
* A hierarchy of Conic classes (modelled after the hierarchy of Elliptic curve classes and building upon the hierarchy of plane curve classes) |
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== Extensions == * Hilbert symbols (for local solubility of conics): * http://trac.sagemath.org/sage_trac/ticket/9334 * Pari has Hilbert symbols * Conics over polynomial rings: http://trac.sagemath.org/sage_trac/ticket/6881 * An is_norm() function to replace the file "rnfisnorm.py" of ticket 727: http://trac.sagemath.org/sage_trac/ticket/2329 |
Coding Sprint Project: Solving Conics
- People: Marco Streng, Mak Trifkovic, Peter Bruin, John Cremona
This is Trac ticket 727: http://trac.sagemath.org/sage_trac/ticket/727
Conic class currently available at the ticket
- Uses Denis Simon's pari code for solving and parametrizing conics over QQ.
- Uses pari's rnfisnorm for finding points on conics over number fields.
- Solves conics over finite fields and RR and CC.
- Parametrize any conic given a rational point.
- A hierarchy of Conic classes (modelled after the hierarchy of Elliptic curve classes and building upon the hierarchy of plane curve classes)
- Change the constructor of Curve to return a Conic if the curve is a Conic
Extensions
- Hilbert symbols (for local solubility of conics):
- Pari has Hilbert symbols
Conics over polynomial rings: http://trac.sagemath.org/sage_trac/ticket/6881
An is_norm() function to replace the file "rnfisnorm.py" of ticket 727: http://trac.sagemath.org/sage_trac/ticket/2329