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):

  • 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