def compose(self,F):
Operation.check_compose(self,F)
(f,g) = tuple(F)
if self.idem and f==g:
return f
h = dict()
for x in product(range(self.dom),repeat=f.arity):
h[x] = self[(f[x],g[x])]
if f.arity == 2:
commutes = True
for (a,b) in combinations(range(self.dom),2):
if h[(a,b)] != h[(b,a)]:
commutes = False
if commutes:
for (a,b) in combinations(range(self.dom),2):
del h[(b,a)]
idempotent = True
for a in range(self.dom):
if h[(a,a)] != a:
idempotent = False
if idempotent:
for a in range(self.dom):
del h[(a,a)]
return BinaryOperation(self.dom,h,commutes,idempotent)
else:
return ExplicitOperation(f,arity,self.dom,h)
def __getitem__(self,x):
Operation.check_input(self,x)
(a,b) = x
if self.idem and a==b:
return a
if self.comm and b < a:
tmp = a
a = b
b = tmp
return self.f[(a,b)]