def ideal(self, *gens):
"""
Returns the fractional ideal generated by ``gens``.
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: O = K.maximal_order()
sage: O.ideal(x)
Ideal (x) of Maximal order in Rational function field in x over Rational Field
sage: O.ideal([x,1/x]) == O.ideal(x,1/x) # multiple generators may be given as a list
True
sage: O.ideal(x^3+1,x^3+6)
Ideal (1) of Maximal order in Rational function field in x over Rational Field
sage: I = O.ideal((x^2+1)*(x^3+1),(x^3+6)*(x^2+1)); I
Ideal (x^2 + 1) of Maximal order in Rational function field in x over Rational Field
sage: O.ideal(I)
Ideal (x^2 + 1) of Maximal order in Rational function field in x over Rational Field
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
if is_Ideal(gens):
gens = gens.gens()
else:
gens = (gens, )
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
def ideal(self, *gens):
"""
Returns the fractional ideal generated by ``gens``.
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: O = K.maximal_order()
sage: O.ideal(x)
Ideal (x) of Maximal order in Rational function field in x over Rational Field
sage: O.ideal([x,1/x]) == O.ideal(x,1/x) # multiple generators may be given as a list
True
sage: O.ideal(x^3+1,x^3+6)
Ideal (1) of Maximal order in Rational function field in x over Rational Field
sage: I = O.ideal((x^2+1)*(x^3+1),(x^3+6)*(x^2+1)); I
Ideal (x^2 + 1) of Maximal order in Rational function field in x over Rational Field
sage: O.ideal(I)
Ideal (x^2 + 1) of Maximal order in Rational function field in x over Rational Field
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
if is_Ideal(gens):
gens = gens.gens()
else:
gens = (gens,)
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
def ideal(self, *gens):
"""
Return the fractional ideal generated by the element gens or
the elements in gens if gens is a list.
EXAMPLES::
sage: R.<y> = FunctionField(QQ)
sage: S = R.maximal_order()
sage: S.ideal(y)
Ideal (y) of Maximal order in Rational function field in y over Rational Field
A fractional ideal of a nontrivial extension::
sage: R.<x> = FunctionField(GF(7)); S.<y> = R[]
sage: L.<y> = R.extension(y^2 - x^3 - 1)
sage: M = L.equation_order()
sage: M.ideal(1/y)
Ideal (1, (6/(x^3 + 1))*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
gens = [gens]
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
def ideal(self, *gens):
"""
Return the fractional ideal generated by the element gens or
the elements in gens if gens is a list.
EXAMPLES::
sage: R.<y> = FunctionField(QQ)
sage: S = R.maximal_order()
sage: S.ideal(y)
Ideal (y) of Maximal order in Rational function field in y over Rational Field
A fractional ideal of a nontrivial extension::
sage: R.<x> = FunctionField(GF(7)); S.<y> = R[]
sage: L.<y> = R.extension(y^2 - x^3 - 1)
sage: M = L.equation_order()
sage: M.ideal(1/y)
Ideal (1, (6/(x^3 + 1))*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
gens = [gens]
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
def ideal(self, *gens):
"""
Returns the fractional ideal generated by the elements in ``gens``.
INPUT:
- ``gens`` -- a list of generators or an ideal in a ring which
coerces to this order.
EXAMPLES::
sage: K.<y> = FunctionField(QQ)
sage: O = K.maximal_order()
sage: O.ideal(y)
Ideal (y) of Maximal order in Rational function field in y over Rational Field
sage: O.ideal([y,1/y]) == O.ideal(y,1/y) # multiple generators may be given as a list
True
A fractional ideal of a nontrivial extension::
sage: K.<x> = FunctionField(GF(7)); R.<y> = K[]
sage: O = K.maximal_order()
sage: I = O.ideal(x^2-4)
sage: L.<y> = K.extension(y^2 - x^3 - 1)
sage: S = L.equation_order()
sage: S.ideal(1/y)
Ideal (1, (6/(x^3 + 1))*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
sage: I2 = S.ideal(x^2-4); I2
Ideal (x^2 + 3, (x^2 + 3)*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
sage: I2 == S.ideal(I)
True
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
if is_Ideal(gens):
gens = gens.gens()
else:
gens = [gens]
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
def ideal(self, *gens):
"""
Returns the fractional ideal generated by the elements in ``gens``.
INPUT:
- ``gens`` -- a list of generators or an ideal in a ring which
coerces to this order.
EXAMPLES::
sage: K.<y> = FunctionField(QQ)
sage: O = K.maximal_order()
sage: O.ideal(y)
Ideal (y) of Maximal order in Rational function field in y over Rational Field
sage: O.ideal([y,1/y]) == O.ideal(y,1/y) # multiple generators may be given as a list
True
A fractional ideal of a nontrivial extension::
sage: K.<x> = FunctionField(GF(7)); R.<y> = K[]
sage: O = K.maximal_order()
sage: I = O.ideal(x^2-4)
sage: L.<y> = K.extension(y^2 - x^3 - 1)
sage: S = L.equation_order()
sage: S.ideal(1/y)
Ideal (1, (6/(x^3 + 1))*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
sage: I2 = S.ideal(x^2-4); I2
Ideal (x^2 + 3, (x^2 + 3)*y) of Order in Function field in y defined by y^2 + 6*x^3 + 6
sage: I2 == S.ideal(I)
True
"""
if len(gens) == 1:
gens = gens[0]
if not isinstance(gens, (list, tuple)):
if is_Ideal(gens):
gens = gens.gens()
else:
gens = [gens]
from function_field_ideal import ideal_with_gens
return ideal_with_gens(self, gens)
