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from typing import Any, TypeVar
from .semigroups_representation import MyFiniteSemigroup, MyFiniteMonoid, MyFiniteGroup
import act4e_interfaces as I
A = TypeVar("A")
B = TypeVar("B")
class SolFiniteSemigroupMorphismsChecks(I.FiniteSemigroupMorphismsChecks):
def is_semigroup_morphism(self, a: I.FiniteSemigroup[A], b: I.FiniteSemigroup[B], f: I.FiniteMap[A, B]) -> bool:
# Semigroup preserves the structure
# f(xy) = f(x) f(y) for all x, y in a
# converse:
# there is an x or a y in a such that
# f(xy) neq f(x) f(y)
for x in a.carrier().elements():
for y in a.carrier().elements():
inside = f(a.compose(x, y))
outside = b.compose(f(x), f(y))
if not b.carrier().equal(inside, outside):
return False
return True
def is_monoid_morphism(self, a: I.FiniteMonoid[A], b: I.FiniteMonoid[B], f: I.FiniteMap[A, B]) -> bool:
# Monoid morphism is a semigroup morphism that maps identity to identity
if not self.is_semigroup_morphism(a, b, f):
return False
if not b.carrier().equal(b.identity(), f(a.identity())):
return False
return True
def is_group_morphism(self, a: I.FiniteGroup[A], b: I.FiniteGroup[B], f: I.FiniteMap[A, B]) -> bool:
# Group morphism preserve
# f(xy) = f(x)f(y) for all x, y in a
# converse is
# exists x, y in a such that
# f(xy) neq f(x)f(y)
for x in a.carrier().elements():
for y in a.carrier().elements():
inside = f(a.compose(x, y))
outside = b.compose(f(x), f(y))
if not b.carrier().equal(inside, outside):
return False
return True
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