def character(self, values):
r"""
Return a group character from ``values``, where ``values`` is
a list of the values of the character evaluated on the conjugacy
classes.
INPUT:
- ``values`` -- a list of values of the character
OUTPUT: a group character
EXAMPLES::
sage: G = MatrixGroup(AlternatingGroup(4))
sage: G.character([1]*len(G.conjugacy_classes_representatives()))
Character of Matrix group over Integer Ring with 12 generators
::
sage: G = GL(2,ZZ)
sage: G.character([1,1,1,1])
Traceback (most recent call last):
...
NotImplementedError: only implemented for finite groups
"""
if not self.is_finite():
raise NotImplementedError("only implemented for finite groups")
return ClassFunction_libgap(self, values)
def irreducible_characters(self):
"""
Return the irreducible characters of the group.
OUTPUT:
A tuple containing all irreducible characters.
EXAMPLES::
sage: G = GL(2,2)
sage: G.irreducible_characters()
(Character of General Linear Group of degree 2 over Finite Field of size 2,
Character of General Linear Group of degree 2 over Finite Field of size 2,
Character of General Linear Group of degree 2 over Finite Field of size 2)
::
sage: GL(2,ZZ).irreducible_characters()
Traceback (most recent call last):
...
NotImplementedError: only implemented for finite groups
"""
if not self.is_finite():
raise NotImplementedError("only implemented for finite groups")
Irr = self.gap().Irr()
L = []
for irr in Irr:
L.append(ClassFunction_libgap(self, irr))
return tuple(L)
def class_function(self, values):
"""
Return the class function with given values.
INPUT:
- ``values`` -- list/tuple/iterable of numbers. The values of the
class function on the conjugacy classes, in that order.
EXAMPLES::
sage: G = GL(2,GF(3))
sage: chi = G.class_function(range(8))
sage: list(chi)
[0, 1, 2, 3, 4, 5, 6, 7]
"""
from sage.groups.class_function import ClassFunction_libgap
return ClassFunction_libgap(self, values)
def irreducible_characters(self):
"""
Returns the irreducible characters of the group.
OUTPUT:
A tuple containing all irreducible characters.
EXAMPLES::
sage: G = GL(2,2)
sage: G.irreducible_characters()
(Character of General Linear Group of degree 2 over Finite Field of size 2,
Character of General Linear Group of degree 2 over Finite Field of size 2,
Character of General Linear Group of degree 2 over Finite Field of size 2)
"""
Irr = self.gap().Irr()
L = []
from sage.groups.class_function import ClassFunction_libgap
for irr in Irr:
L.append(ClassFunction_libgap(self, irr))
return tuple(L)