def restrict_map_fixed(func):
r"""
Returns the same map whose domain is restricted to its fixed points.
"""
fxd = fixed_points(func)
M = FiniteSetMaps(fxd)
d = dict()
for i in fxd:
d[i] = func(i)
return M.from_dict(d)
def __init__(self, n):
ambient_monoid = FiniteSetMaps(range(-n, 0) + range(1, n + 1),
action="right")
pi = Family(
range(1, n), lambda j: ambient_monoid.from_dict(
dict([(i, i) for i in range(1, n + 1) if i != j + 1] + [(
j + 1, j)] + [(i, i) for i in range(-n, 0)
if i != -j] + [(-j, -j - 1)])))
category = Monoids().JTrivial().Finite() & Monoids().Transformation(
).Subobjects()
AutomaticMonoid.__init__(self,
pi,
ambient_monoid,
one=ambient_monoid.one(),
mul=operator.mul,
category=category)
def _involution_dict(mat):
r"""
Returns a dictionary of arbitrary involutions on the entries of a Combinatorial Matrix.
Note all weights must be 1 for this. It may be extended upon in the future.
"""
mat_gen_func = matrix_generating_function(mat)
if mat_gen_func != mat_gen_func.parent().identity_matrix():
raise ValueError, "Input needs to be equal to the identity."
else:
func = dict()
for x in range(mat.nrows()):
for y in range(mat.ncols()):
if x <> y:
func[(x,y)] = mat[x,y].create_involution()
else:
t = mat[x,y]
for i in t:
_M = FiniteSetMaps(t,t)
func[(x,y)] = _M.from_dict({i:i})
return func
