# 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