def module_test(self):
return frozenset([CON.Eq(TA.f(TA.C(1)),\
TA.Z(self._n+1,TA.f(TA.C(1))))])
bound to mul(..) and '.' is bound to Zlmul(..)"""
raise Exception('Ring does not give terms in generators for elements!')
def test(self):
"""Returns a set of EquivalenceTermConstraints that is sufficient to
tell whether a morphism defined by the images of gen() that
respects 0 and 1 is also a RingHom"""
raise Exception('Ring does not have a testing set for homomorphisms')
def module_test(self):
"""Returns a set of EquivalenceTermConstraints that is sufficient to
tell whether a morphism defined by the images of the unit as generating
set for the ring viewed as module that respects the 0."""
raise Exception('Ring does not have a testing set for module homomorphisms')
testRingHom = CON.Eq(TA.C(0),TA.f(TA.C(0))) & CON.Eq(TA.C(1),TA.f(TA.C(1)))
class RingHom(object):
"""Base class for ring homomorphisms"""
def __init__(self):
raise Exception\
('RingHom is an abstract class that cannot be instantiated')
def __contains__(self,item):
"""Returns true, if item is a pair (x,y) with y = f(x)"""
if type(item) == tuple:
if len(item) == 2:
if item[0] in self.dom() and \
item[1] in self.cod():
return item[1] == self(item[0])
return False
