def endomorphism_ring(self):
k = NumberField(self._domain.frobenius().minpoly(), 'c')
self._field = k
self.endomorphism_index()
basis = k.maximal_order().basis()
basis = [basis[0] * self._index, basis[1] * self._index]
self._order = k.order(basis)
def __init__(self, n):
r"""
Hecke triangle group (2, n, infinity).
Namely the von Dyck group corresponding to the triangle group
with angles (pi/2, pi/n, 0).
INPUT:
- ``n`` - ``infinity`` or an integer greater or equal to ``3``.
OUTPUT:
The Hecke triangle group for the given parameter ``n``.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.hecke_triangle_groups import HeckeTriangleGroup
sage: G = HeckeTriangleGroup(12)
sage: G
Hecke triangle group for n = 12
sage: G.category()
Category of groups
"""
self._n = n
self.element_repr_method("default")
if n in [3, infinity]:
self._base_ring = ZZ
self._lam = ZZ(1) if n == 3 else ZZ(2)
else:
lam_symbolic = 2 * cos(pi / n)
K = NumberField(self.lam_minpoly(),
'lam',
embedding=coerce_AA(lam_symbolic))
#self._base_ring = K.order(K.gens())
self._base_ring = K.maximal_order()
self._lam = self._base_ring.gen(1)
T = matrix(self._base_ring, [[1, self._lam], [0, 1]])
S = matrix(self._base_ring, [[0, -1], [1, 0]])
FinitelyGeneratedMatrixGroup_generic.__init__(self, ZZ(2),
self._base_ring, [S, T])
def __init__(self, n):
r"""
Hecke triangle group (2, n, infinity).
Namely the von Dyck group corresponding to the triangle group
with angles (pi/2, pi/n, 0).
INPUT:
- ``n`` - ``infinity`` or an integer greater or equal to ``3``.
OUTPUT:
The Hecke triangle group for the given parameter ``n``.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.hecke_triangle_groups import HeckeTriangleGroup
sage: G = HeckeTriangleGroup(12)
sage: G
Hecke triangle group for n = 12
sage: G.category()
Category of groups
"""
self._n = n
self.element_repr_method("default")
if n in [3, infinity]:
self._base_ring = ZZ
self._lam = ZZ(1) if n==3 else ZZ(2)
else:
lam_symbolic = 2*cos(pi/n)
K = NumberField(self.lam_minpoly(), 'lam', embedding = coerce_AA(lam_symbolic))
#self._base_ring = K.order(K.gens())
self._base_ring = K.maximal_order()
self._lam = self._base_ring.gen(1)
T = matrix(self._base_ring, [[1,self._lam],[0,1]])
S = matrix(self._base_ring, [[0,-1],[1,0]])
FinitelyGeneratedMatrixGroup_generic.__init__(self, ZZ(2), self._base_ring, [S, T])
