def __invert__(self):
"""
Return the inverse of self.
EXAMPLES::
sage: Gamma0(11)([1,-1,0,1]).__invert__()
[1 1]
[0 1]
"""
I = mi2x2(M2Z, [self.__x[1,1], -self.__x[0,1], -self.__x[1,0], self.__x[0,0]], copy=True, coerce=True)
return self.parent()(I, check=False)
def __init__(self, parent, x, check=True):
"""
Create an element of an arithmetic subgroup.
INPUT:
- parent - an arithmetic subgroup
- x - data defining a 2x2 matrix over ZZ
which lives in parent
- check - if True, check that parent
is an arithmetic subgroup, and that
x defines a matrix of determinant 1
We tend not to create elements of arithmetic subgroups that aren't
SL2Z, in order to avoid coercion issues (that is, the other arithmetic
subgroups are "facade parents").
EXAMPLES::
sage: G = Gamma0(27)
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [4,1,27,7])
[ 4 1]
[27 7]
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(Integers(3), [4,1,27,7])
Traceback (most recent call last):
...
TypeError: parent (= Ring of integers modulo 3) must be an arithmetic subgroup
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [2,0,0,2])
Traceback (most recent call last):
...
TypeError: matrix must have determinant 1
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [2,0,0,2], check=False)
[2, 0, 0, 2]
sage: x = Gamma0(11)([2,1,11,6])
sage: x == loads(dumps(x))
True
sage: x = Gamma0(5).0
sage: SL2Z(x)
[1 1]
[0 1]
sage: x in SL2Z
True
"""
if check:
if not is_ArithmeticSubgroup(parent):
raise TypeError, "parent (= %s) must be an arithmetic subgroup" % parent
x = mi2x2(M2Z, x, copy=True, coerce=True)
if x.determinant() != 1:
raise TypeError, "matrix must have determinant 1"
try:
x.set_immutable()
except AttributeError:
pass
MultiplicativeGroupElement.__init__(self, parent)
self.__x = x
def __init__(self, parent, x, check=True):
"""
Create an element of an arithmetic subgroup.
INPUT:
- parent - an arithmetic subgroup
- x - data defining a 2x2 matrix over ZZ
which lives in parent
- check - if True, check that parent
is an arithmetic subgroup, and that
x defines a matrix of determinant 1
We tend not to create elements of arithmetic subgroups that aren't
SL2Z, in order to avoid coercion issues (that is, the other arithmetic
subgroups are "facade parents").
EXAMPLES::
sage: G = Gamma0(27)
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [4,1,27,7])
[ 4 1]
[27 7]
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(Integers(3), [4,1,27,7])
Traceback (most recent call last):
...
TypeError: parent (= Ring of integers modulo 3) must be an arithmetic subgroup
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [2,0,0,2])
Traceback (most recent call last):
...
TypeError: matrix must have determinant 1
sage: sage.modular.arithgroup.arithgroup_element.ArithmeticSubgroupElement(G, [2,0,0,2], check=False)
[2, 0, 0, 2]
sage: x = Gamma0(11)([2,1,11,6])
sage: x == loads(dumps(x))
True
sage: x = Gamma0(5).0
sage: SL2Z(x)
[1 1]
[0 1]
sage: x in SL2Z
True
"""
if check:
if not is_ArithmeticSubgroup(parent):
raise TypeError, "parent (= %s) must be an arithmetic subgroup"%parent
x = mi2x2(M2Z, x, copy=True, coerce=True)
if x.determinant() != 1:
raise TypeError, "matrix must have determinant 1"
try:
x.set_immutable()
except AttributeError:
pass
MultiplicativeGroupElement.__init__(self, parent)
self.__x = x
