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con_prime_finite_field.py
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con_prime_finite_field.py
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r"""
Projective plane conics over prime finite fields
AUTHORS:
- Marco Streng (2010-07-20)
"""
#*****************************************************************************
# Copyright (C) 2010 Marco Streng <marco.streng@gmail.com>
#
# Distributed under the terms of the GNU General Public License (GPL)
#
# This code is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# The full text of the GPL is available at:
#
# http://www.gnu.org/licenses/
#*****************************************************************************
from sage.schemes.curves.projective_curve import ProjectivePlaneCurve_prime_finite_field
from con_finite_field import ProjectiveConic_finite_field
class ProjectiveConic_prime_finite_field(ProjectiveConic_finite_field, ProjectivePlaneCurve_prime_finite_field):
r"""
Create a projective plane conic curve over a prime finite field.
See ``Conic`` for full documentation.
EXAMPLES::
sage: P.<X, Y, Z> = FiniteField(5)[]
sage: Conic(X^2 + Y^2 - 2*Z^2)
Projective Conic Curve over Finite Field of size 5 defined by X^2 + Y^2 - 2*Z^2
TESTS::
sage: Conic([FiniteField(7)(1), 1, -1])._test_pickling()
"""
def __init__(self, A, f):
r"""
See ``Conic`` for full documentation.
EXAMPLES ::
sage: Conic([GF(3)(1), 1, 1])
Projective Conic Curve over Finite Field of size 3 defined by x^2 + y^2 + z^2
"""
ProjectiveConic_finite_field.__init__(self, A, f)
ProjectivePlaneCurve_prime_finite_field.__init__(self, A, f)