From 13b4c9da2c3aef6aea58174653905712f93cc78b Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 20 Oct 2023 10:12:16 +0200
Subject: Pass Semigroups and Groups representations

TestFiniteSemigroupRepresentation TestFiniteSemigroupConstruct TestFiniteMonoidRepresentation TestFiniteGroupRepresentation
---
 src/act4e_solutions/semigroups_representation.py | 114 +++++++++++++++++++++--
 1 file changed, 108 insertions(+), 6 deletions(-)

(limited to 'src')

diff --git a/src/act4e_solutions/semigroups_representation.py b/src/act4e_solutions/semigroups_representation.py
index 4d75708..f5c2780 100644
--- a/src/act4e_solutions/semigroups_representation.py
+++ b/src/act4e_solutions/semigroups_representation.py
@@ -1,29 +1,131 @@
 from typing import Any, TypeVar
 
 import act4e_interfaces as I
+from .sets_representation import MyFiniteSet, SolFiniteSetRepresentation
+from .sets_product import MyFiniteSetProduct
+from .maps_representation import MyFiniteMap, SolFiniteMapRepresentation
 
 X = TypeVar("X")
 
+class MyFiniteSemigroup(I.FiniteSemigroup[X]):
+    _carrier: I.FiniteSet[X]
+    _composition: I.FiniteMap[X, X]
+
+    def __init__(self, s: I.FiniteSet[X], f: I.FiniteMap[X, X]):
+        self._carrier = s
+        self._composition = f
+
+    def carrier(self) -> I.FiniteSet[X]:
+        return self._carrier
+
+    def composition(self) -> I.FiniteMap[X, X]:
+        return self._composition
+
+    def compose(self, a: X, b: X) -> X:
+        p = self._composition.source().pack([a, b])
+        return self._composition(p)
+
+
+class MyFiniteMonoid(MyFiniteSemigroup, I.FiniteMonoid[X]):
+    _identity: X
+    def __init__(self, s: I.FiniteSet[X], f: I.FiniteMap[X, X], e: X):
+        super().__init__(s, f)
+        self._identity = e
+
+    # def compose(self, a: X, b: X) -> X:
+    #     if self.carrier().equal(a, self._identity):
+    #         return b
+    #     elif self.carrier().equal(b, self._identity):
+    #         return a
+    #     else:
+    #         return super().compose(a, b)
+
+    def identity(self) -> X:
+        return self._identity
+
+
+class MyFiniteGroup(MyFiniteMonoid, I.FiniteGroup[X]):
+    _inverse: I.FiniteMap[X, X]
+    def __init__(self, s: I.FiniteSet[X], f: I.FiniteMap[X, X], e: X, i: I.FiniteMap[X, X]):
+        super().__init__(s, f, e)
+        self._inverse = i
+
+    def inverse(self, a: X):
+        return self._inverse(a)
+
 
 class SolFiniteSemigroupRepresentation(I.FiniteSemigroupRepresentation):
     def load(self, h: I.IOHelper, s: I.FiniteSemigroup_desc) -> I.FiniteSemigroup[Any]:
-        raise NotImplementedError()
+        if not all(k in s.keys() for k in ["carrier", "composition"]):
+            raise I.InvalidFormat()
+
+        fsr = SolFiniteSetRepresentation()
+        A = fsr.load(h, s["carrier"])
+
+        # FIXME: maybe use this?
+        # fmr = SolFiniteMapRepresentation()
+        for inp, out in s["composition"]:
+            if not all(A.contains(i) for i in inp):
+                raise I.InvalidFormat()
+
+            if not A.contains(out):
+                raise I.InvalidFormat()
+
+        p = MyFiniteSetProduct([A, A])
+        f = MyFiniteMap(p, A, s["composition"])
+        return MyFiniteSemigroup(A, f)
 
     def save(self, h: I.IOHelper, m: I.FiniteSemigroup[Any]) -> I.FiniteSemigroup_desc:
-        raise NotImplementedError()
+        fsr = SolFiniteSetRepresentation()
+        fmr = SolFiniteMapRepresentation()
+
+        d = {"carrier": fsr.save(h, m.carrier()),
+             "composition": []}
+
+        for a in m.carrier().elements():
+            for b in m.carrier().elements():
+                e = m.composition().source().pack([a, b])
+                d["composition"].append([e, m.compose(a, b)])
+
+        return d
 
 
 class SolFiniteMonoidRepresentation(I.FiniteMonoidRepresentation):
     def load(self, h: I.IOHelper, s: I.FiniteMonoid_desc) -> I.FiniteMonoid[X]:
-        raise NotImplementedError()
+        fsgr = SolFiniteSemigroupRepresentation()
+        semi = fsgr.load(h, s)
+
+        if not ("neutral" in s.keys()):
+            raise I.InvalidFormat()
+
+        e = s["neutral"]
+        if not semi.carrier().contains(e):
+            raise I.InvalidFormat()
+
+        return MyFiniteMonoid(semi.carrier(), semi.composition(), e)
 
     def save(self, h: I.IOHelper, m: I.FiniteMonoid[Any]) -> I.FiniteMonoid_desc:
-        raise NotImplementedError()
+        fsgr = SolFiniteSemigroupRepresentation()
+        d = fsgr.save(h, m)
+        d["neutral"] = m.identity()
+        return d
 
 
 class SolFiniteGroupRepresentation(I.FiniteGroupRepresentation):
     def load(self, h: I.IOHelper, s: I.FiniteGroup_desc) -> I.FiniteGroup[X]:
-        raise NotImplementedError()
+        fmor = SolFiniteMonoidRepresentation()
+        m = fmor.load(h, s)
+
+        if not "inverse" in s.keys():
+            raise I.InvalidFormat()
+
+        i = MyFiniteMap(m.carrier(), m.carrier(), s["inverse"])
+        return MyFiniteGroup(m.carrier(), m.composition(), m.identity(), i)
 
     def save(self, h: I.IOHelper, m: I.FiniteGroup[Any]) -> I.FiniteGroup_desc:
-        raise NotImplementedError()
+        fmor = SolFiniteMonoidRepresentation()
+        d = fmor.save(h, m)
+        d["inverse"] = []
+        for c in m.carrier().elements():
+            d["inverse"].append([c, m.inverse(c)])
+        return d
-- 
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