def canonical_parameters(group, weight, sign, base_ring):
"""
Return the canonically normalized parameters associated to a choice
of group, weight, sign, and base_ring. That is, normalize each of
these to be of the correct type, perform all appropriate type
checking, etc.
EXAMPLES::
sage: p1 = sage.modular.modsym.modsym.canonical_parameters(5,int(2),1,QQ) ; p1
(Congruence Subgroup Gamma0(5), 2, 1, Rational Field)
sage: p2 = sage.modular.modsym.modsym.canonical_parameters(Gamma0(5),2,1,QQ) ; p2
(Congruence Subgroup Gamma0(5), 2, 1, Rational Field)
sage: p1 == p2
True
sage: type(p1[1])
<type 'sage.rings.integer.Integer'>
"""
sign = rings.Integer(sign)
if not (sign in [-1, 0, 1]):
raise ValueError("sign must be -1, 0, or 1")
weight = rings.Integer(weight)
if weight <= 1:
raise ValueError("the weight must be at least 2")
if isinstance(group, (int, rings.Integer)):
group = arithgroup.Gamma0(group)
elif isinstance(group, dirichlet.DirichletCharacter):
try:
eps = group.minimize_base_ring()
except NotImplementedError:
# TODO -- implement minimize_base_ring over finite fields
eps = group
G = eps.parent()
if eps.is_trivial():
group = arithgroup.Gamma0(eps.modulus())
else:
group = (eps, G)
if base_ring is None: base_ring = eps.base_ring()
if base_ring is None: base_ring = rational_field.RationalField()
if not is_CommutativeRing(base_ring):
raise TypeError("base_ring (=%s) must be a commutative ring" %
base_ring)
if not base_ring.is_field():
raise TypeError("(currently) base_ring (=%s) must be a field" %
base_ring)
return group, weight, sign, base_ring
# Copyright (C) 2007 William Stein <*****@*****.**>
#
# Distributed under the terms of the GNU General Public License (GPL)
# as published by the Free Software Foundation; either version 2 of
# the License, or (at your option) any later version.
# http://www.gnu.org/licenses/
#*****************************************************************************
from number_field_ideal import NumberFieldFractionalIdeal
from sage.structure.factorization import Factorization
from sage.structure.proof.proof import get_flag
import sage.rings.rational_field as rational_field
import sage.rings.integer_ring as integer_ring
QQ = rational_field.RationalField()
ZZ = integer_ring.IntegerRing()
class NumberFieldFractionalIdeal_rel(NumberFieldFractionalIdeal):
"""
An ideal of a relative number field.
EXAMPLES::
sage: K.<a> = NumberField([x^2 + 1, x^2 + 2]); K
Number Field in a0 with defining polynomial x^2 + 1 over its base field
sage: i = K.ideal(38); i
Fractional ideal (38)
sage: K.<a0, a1> = NumberField([x^2 + 1, x^2 + 2]); K
Number Field in a0 with defining polynomial x^2 + 1 over its base field
