def transitive(self, other=None):
r"""
TBD
"""
if other is None:
raise ValueError, "Enter a reduction map as a parameter"
elif self.get_B() != other.get_A():
raise ValueError, "These are not good candidate sets for reduction mapping"
else:
dic_h = dict()
dic_h0 = dict()
A = self.get_A()
B = self.get_B()
C = other.get_B()
f = self.get_SRWP()
f0 = self.get_SPWP()
g = other.get_SRWP()
g0 = other.get_SPWP()
for elm in A:
if elm in fixed_points(f):
if f0(elm) in fixed_points(g):
dic_h0[elm] = g0(f0(elm))
dic_h[elm] = elm
else:
dic_h[elm] = inverse(f0)(g(f0(elm)))
else:
dic_h[elm] = f(elm)
h = FiniteSetMaps(A, A).from_dict(dic_h)
h0 = FiniteSetMaps(CombinatorialScalarWrapper(dic_h0.keys()),
C).from_dict(dic_h0)
return ReductionMaps(A, C, h, h0)
def transitive(self,other=None):
r"""
TBD
"""
if other is None:
raise ValueError, "Enter a reduction map as a parameter"
elif self.get_B() != other.get_A():
raise ValueError, "These are not good candidate sets for reduction mapping"
else:
dic_h = dict()
dic_h0 = dict()
A = self.get_A()
B = self.get_B()
C = other.get_B()
f = self.get_SRWP()
f0 = self.get_SPWP()
g = other.get_SRWP()
g0 = other.get_SPWP()
for elm in A:
if elm in fixed_points(f):
if f0(elm) in fixed_points(g):
dic_h0[elm] = g0(f0(elm))
dic_h[elm] = elm
else:
dic_h[elm] = inverse(f0)(g(f0(elm)))
else:
dic_h[elm] = f(elm)
h = FiniteSetMaps(A,A).from_dict(dic_h)
h0 = FiniteSetMaps(CombinatorialScalarWrapper(dic_h0.keys()),C).from_dict(dic_h0)
return ReductionMaps(A,C,h,h0)
def reverse(self):
if self.get_A().get_size() != self.get_B().get_size():
raise ValueError, "Reduction direction cannot be reversed unless scalars are equivalent"
else:
A = self.get_B()
B = self.get_A()
f0 = inverse(self.get_SPWP())
dic_f = dict()
for elm in A:
dic_f[elm] = elm
f = FiniteSetMaps(A, A).from_dict(dic_f)
return ReductionMaps(A, B, f, f0)
def reverse(self):
if self.get_A().get_size() != self.get_B().get_size():
raise ValueError, "Reduction direction cannot be reversed unless scalars are equivalent"
else:
A = self.get_B()
B = self.get_A()
f0 = inverse(self.get_SPWP())
dic_f = dict()
for elm in A:
dic_f[elm] = elm
f = FiniteSetMaps(A,A).from_dict(dic_f)
return ReductionMaps(A,B,f,f0)
def confluence(self, other=None):
r"""
Returns the reduction of C to B, where the usage is:
r1.confluence(r2), and r1 maps A to B, B fully cancelled,
and r2 maps A to C.
"""
if other is None:
raise ValueError, "Enter a redution map as a parameter"
elif self.get_A() != other.get_A():
raise ValueError, """ "A" """ " sets have to match"
elif not (self.get_B().is_fully_cancelled()):
raise ValueError, """ "B" """ " on the left is not fully cancelled"
else:
dic_h = dict()
dic_h0 = dict()
A = self.get_A()
B = self.get_B()
C = other.get_B()
f = self.get_SRWP()
f0 = self.get_SPWP()
g = other.get_SRWP()
g0 = other.get_SPWP()
fxd_f = fixed_points(self.get_SRWP())
fxd_g = fixed_points(other.get_SRWP())
for c in C:
x = inverse(g0)(c)
while True:
if x in fxd_f: #a fixed point of h
dic_h[c] = c
dic_h0[c] = f0(x)
break
else:
x = f(x)
if x in fxd_g: #not a fixed point of h
dic_h[c] = g0(x)
break
else:
x = g(x)
h = FiniteSetMaps(C, C).from_dict(dic_h)
h0 = FiniteSetMaps(CombinatorialScalarWrapper(dic_h0.keys()),
B).from_dict(dic_h0)
return ReductionMaps(C, B, h, h0)
def confluence(self,other=None):
r"""
Returns the reduction of C to B, where the usage is:
r1.confluence(r2), and r1 maps A to B, B fully cancelled,
and r2 maps A to C.
"""
if other is None:
raise ValueError, "Enter a redution map as a parameter"
elif self.get_A() != other.get_A():
raise ValueError, """ "A" """ " sets have to match"
elif not(self.get_B().is_fully_cancelled()):
raise ValueError, """ "B" """ " on the left is not fully cancelled"
else:
dic_h = dict()
dic_h0 = dict()
A = self.get_A()
B = self.get_B()
C = other.get_B()
f = self.get_SRWP()
f0 = self.get_SPWP()
g = other.get_SRWP()
g0 = other.get_SPWP()
fxd_f = fixed_points(self.get_SRWP())
fxd_g = fixed_points(other.get_SRWP())
for c in C:
x = inverse(g0)(c)
while True:
if x in fxd_f: #a fixed point of h
dic_h[c] = c
dic_h0[c] = f0(x)
break
else:
x = f(x)
if x in fxd_g: #not a fixed point of h
dic_h[c]=g0(x)
break
else:
x = g(x)
h = FiniteSetMaps(C,C).from_dict(dic_h)
h0 = FiniteSetMaps(CombinatorialScalarWrapper(dic_h0.keys()),B).from_dict(dic_h0)
return ReductionMaps(C,B,h,h0)