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-rw-r--r--Homeworks.md16
-rw-r--r--src/act4e_solutions/semigroups_morphisms.py49
-rw-r--r--src/act4e_solutions/semigroups_morphisms_representation.py99
3 files changed, 150 insertions, 14 deletions
diff --git a/Homeworks.md b/Homeworks.md
index c0eaacc..fc0c091 100644
--- a/Homeworks.md
+++ b/Homeworks.md
@@ -28,14 +28,14 @@ $ make docker-check
- [?] TestFiniteEndorelationProperties
- [?] TestFiniteEndorelationOperations
-- [ ] TestFiniteSemigroupRepresentation
-- [ ] TestFiniteSemigroupConstruct
-- [ ] TestFiniteMonoidRepresentation
-- [ ] TestFiniteGroupRepresentation
-
-- [ ] TestFiniteSemigroupMorphismRepresentation
-- [ ] TestFiniteMonoidMorphismRepresentation
-- [ ] TestFiniteGroupMorphismRepresentation
+- [X] TestFiniteSemigroupRepresentation
+- [?] TestFiniteSemigroupConstruct
+- [X] TestFiniteMonoidRepresentation
+- [X] TestFiniteGroupRepresentation
+
+- [X] TestFiniteSemigroupMorphismRepresentation
+- [X] TestFiniteMonoidMorphismRepresentation
+- [X] TestFiniteGroupMorphismRepresentation
- [ ] TestFiniteSemigroupMorphismsChecks
- [ ] TestFinitePosetRepresentation
diff --git a/src/act4e_solutions/semigroups_morphisms.py b/src/act4e_solutions/semigroups_morphisms.py
new file mode 100644
index 0000000..5d832ee
--- /dev/null
+++ b/src/act4e_solutions/semigroups_morphisms.py
@@ -0,0 +1,49 @@
+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
diff --git a/src/act4e_solutions/semigroups_morphisms_representation.py b/src/act4e_solutions/semigroups_morphisms_representation.py
index 43df89f..abc2216 100644
--- a/src/act4e_solutions/semigroups_morphisms_representation.py
+++ b/src/act4e_solutions/semigroups_morphisms_representation.py
@@ -2,26 +2,113 @@ from typing import Any, TypeVar
import act4e_interfaces as I
+from .maps_representation import SolFiniteMapRepresentation
+from .semigroups_representation import (MyFiniteSemigroup, MyFiniteMonoid, MyFiniteGroup,
+ SolFiniteSemigroupRepresentation,
+ SolFiniteMonoidRepresentation,
+ SolFiniteGroupRepresentation)
+
+A = TypeVar("A")
+B = TypeVar("B")
+
+class MyFiniteSemigroupMorphism(I.FiniteSemigroupMorphism[A, B]):
+ _source: I.FiniteSemigroup[A]
+ _target: I.FiniteSemigroup[B]
+ _mapping: I.FiniteMap[A, B]
+
+ def __init__(self, s: I.FiniteSemigroup[A], t: I.FiniteSemigroup[B], f: I.FiniteMap[A, B]):
+ self._source = s
+ self._target = t
+ self._mapping = f
+
+ def source(self) -> I.FiniteSemigroup[A]:
+ return self._source
+
+ def target(self) -> I.FiniteSemigroup[B]:
+ return self._target
+
+ def mapping(self) -> I.FiniteMap[A, B]:
+ return self._mapping
+
+
+class MyFiniteMonoidMorphism(MyFiniteSemigroupMorphism, I.FiniteMonoidMorphism[A, B]):
+ _source: I.FiniteMonoid[A]
+ _target: I.FiniteMonoid[B]
+
+
+class MyFiniteGroupMorphism(MyFiniteMonoidMorphism, I.FiniteGroupMorphism[A, B]):
+ _source: I.FiniteGroup[A]
+ _target: I.FiniteGroup[B]
+
+
class SolFiniteSemigroupMorphismRepresentation(I.FiniteSemigroupMorphismRepresentation):
def load(self, h: I.IOHelper, s: I.FiniteSemigroupMorphism_desc) -> I.FiniteSemigroupMorphism[Any, Any]:
- raise NotImplementedError()
+ if not all(k in s.keys() for k in ["source", "target", "mapping"]):
+ raise I.InvalidFormat()
+
+ fsgr = SolFiniteSemigroupRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ A = fsgr.load(h, s["source"])
+ B = fsgr.load(h, s["target"])
+ f = fmr.load(h, s["mapping"])
+
+ return MyFiniteSemigroupMorphism(A, B, f)
def save(self, h: I.IOHelper, m: I.FiniteSemigroupMorphism[Any, Any]) -> I.FiniteSemigroupMorphism_desc:
- raise NotImplementedError()
+ fsgr = SolFiniteSemigroupRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ d = {"source": fsgr.save(h, m.source()),
+ "target": fsgr.save(h, m.target()),
+ "mapping": fmr.save(h, m.mapping())}
+ return d
class SolFiniteMonoidMorphismRepresentation(I.FiniteMonoidMorphismRepresentation):
def load(self, h: I.IOHelper, s: I.FiniteMonoidMorphism_desc) -> I.FiniteMonoidMorphism[Any, Any]:
- raise NotImplementedError()
+ if not all(k in s.keys() for k in ["source", "target", "mapping"]):
+ raise I.InvalidFormat()
+
+ fmor = SolFiniteMonoidRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ A = fmor.load(h, s["source"])
+ B = fmor.load(h, s["target"])
+ f = fmr.load(h, s["mapping"])
+
+ return MyFiniteMonoidMorphism(A, B, f)
def save(self, h: I.IOHelper, m: I.FiniteMonoidMorphism[Any, Any]) -> I.FiniteMonoidMorphism_desc:
- raise NotImplementedError()
+ fmor = SolFiniteMonoidRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ d = {"source": fmor.save(h, m.source()),
+ "target": fmor.save(h, m.target()),
+ "mapping": fmr.save(h, m.mapping())}
+ return d
class SolFiniteGroupMorphismRepresentation(I.FiniteGroupMorphismRepresentation):
def load(self, h: I.IOHelper, s: I.FiniteGroupMorphism_desc) -> I.FiniteGroupMorphism[Any, Any]:
- raise NotImplementedError()
+ if not all(k in s.keys() for k in ["source", "target", "mapping"]):
+ raise I.InvalidFormat()
+
+ fgr = SolFiniteGroupRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ A = fgr.load(h, s["source"])
+ B = fgr.load(h, s["target"])
+ f = fmr.load(h, s["mapping"])
+
+ return MyFiniteGroupMorphism(A, B, f)
def save(self, h: I.IOHelper, m: I.FiniteGroupMorphism[Any, Any]) -> I.FiniteGroupMorphism_desc:
- raise NotImplementedError()
+ fgr = SolFiniteGroupRepresentation()
+ fmr = SolFiniteMapRepresentation()
+
+ d = {"source": fgr.save(h, m.source()),
+ "target": fgr.save(h, m.target()),
+ "mapping": fmr.save(h, m.mapping())}
+ return d
generated by cgit v1.2.1 (git 2.18.0) at 2024-11-25 11:04:44 +0100