feat: Add tons of stuff (#32)

* feat: Add generate all possible diagonals method

* feat(tst): Add more tests

* feat: Add IdSmallAntimagma

* feat: Add MagmaIsomorphismInvariants

* chore: Order methods

* chore: Change error-log

* feat: Add linting for tests, simplified tests

* feat: Remove support for 4.11

* chore: Fixed and linted examples

* chore: Reformat test

* chore: Reformat test

.github/workflows/pull-request-gap-tests.yaml

@@ -25,7 +25,6 @@ jobs:
           - master
           - stable-4.13
           - stable-4.12
-          - stable-4.11
 
     steps:
       - uses: actions/checkout@v4

.github/workflows/pull-request-gaplint.yaml

@@ -32,3 +32,5 @@ jobs:
           find . -name '*.gi' | xargs -n1 gaplint
           echo "::group:: gaplint -- *.gd"
           find . -name '*.gd' | xargs -n1 gaplint
+          echo "::group:: gaplint -- *.tst"
+          find . -name '*.tst' | xargs -n1 gaplint

Makefile

@@ -1,4 +1,4 @@
-test: test_linting test_docs test_gap
+test: test_docs test_linting test_gap
 
 test_docs:
 	gap ./makedoc.g
@@ -10,3 +10,4 @@ test_linting:
 	find . -type f -name "*.g" | xargs -n1 gaplint
 	find . -type f -name "*.gi" | xargs -n1 gaplint
 	find . -type f -name "*.gd" | xargs -n1 gaplint
+	find . -type f -name "*.tst" | xargs -n1 gaplint

PackageInfo.g

@@ -230,7 +230,7 @@ PackageDoc := rec(
   # a longer title of the book, this together with the book name should
   # fit on a single text line (appears with the '?books' command in GAP)
   # LongTitle := "Elementary Divisors of Integer Matrices",
-  LongTitle := "smallantimagmas/An antiassociative magmas package",
+  LongTitle := "smallantimagmas/Antimagmas package",
   Autoload  := true
 ),
 
@@ -239,7 +239,7 @@ PackageDoc := rec(
 Dependencies := rec(
   # GAP version, use the version string for specifying a least version,
   # prepend a '=' for specifying an exact version.
-  GAP := "4.10",
+  GAP := "4.12",
 
   # list of pairs [package name, version], package name is case
   # insensitive, exact version denoted with '=' prepended to version string.

lib/helper.gd

@@ -2,21 +2,21 @@ __SmallAntimagmaHelper := rec();
 
 __SmallAntimagmaHelper.checkOrder := function(order)
         if not IsInt(order) then
-            ErrorNoReturn("SmallAntimagmas: ", "<order> must be an integer");
+            ErrorNoReturn("smallantimagmas: ", "<order> must be an integer");
         fi;
 
         if order < 1 then
-            ErrorNoReturn("SmallAntimagmas:", "<order> must greater than or equal to 1");
+            ErrorNoReturn("smallantimagmas:", "<order> must greater than or equal to 1");
         fi;
 end;
 
 __SmallAntimagmaHelper.checkId := function(id)
         if not IsInt(id) then
-            ErrorNoReturn("SmallAntimagmas: ", "<id> must be an integer");
+            ErrorNoReturn("smallantimagmas: ", "<id> must be an integer");
         fi;
 
         if id < 1 then
-            ErrorNoReturn("SmallAntimagmas:", "<id> must greater than or equal to 1");
+            ErrorNoReturn("smallantimagmas:", "<id> must greater than or equal to 1");
         fi;
 end;
 
@@ -30,10 +30,10 @@ __SmallAntimagmaHelper.getSmallAntimagmaMetadataDirectory := function(order)
     __SmallAntimagmaHelper.checkOrder(order);
     result := DirectoriesPackageLibrary("smallantimagmas", Concatenation(["data", "/", "non-isomorphic", "/", String(order)]));
     if Size(result) = 0 then
-        ErrorNoReturn("SmallAntimagmas:", "<order> is not yet implemeneted");
+        ErrorNoReturn("smallantimagmas:", "<order> is not yet implemeneted");
     fi;
     if Size(result) > 1 then
-        ErrorNoReturn("SmallAntimagmas:", "metadata directory must not be ambigous");
+        ErrorNoReturn("smallantimagmas:", "metadata directory must not be ambigous");
     fi;
     return First(result);
 end;
@@ -50,10 +50,10 @@ __SmallAntimagmaHelper.getAllSmallAntimagmaMetadataDirectory := function(order)
     __SmallAntimagmaHelper.checkOrder(order);
     result := DirectoriesPackageLibrary("smallantimagmas", Concatenation(["data", "/", "all", "/", String(order)]));
     if Size(result) = 0 then
-        ErrorNoReturn("SmallAntimagmas:", "<order> is not yet implemeneted");
+        ErrorNoReturn("smallantimagmas:", "<order> is not yet implemeneted");
     fi;
     if Size(result) > 1 then
-        ErrorNoReturn("SmallAntimagmas:", "metadata directory must not be ambigous");
+        ErrorNoReturn("smallantimagmas:", "metadata directory must not be ambigous");
     fi;
     return First(result);
 end;

lib/properties.gd

@@ -11,7 +11,7 @@
 #! <pc group of size 4 with 2 generators>
 #! gap> AssociativityIndex(OneSmallGroup(4));
 #! 64
-#! gap> AssociativityIndex(OneSmallGroup(4)) = 4^3;
+#! gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3;
 #! true
 #! @EndExampleSession
 #!
@@ -45,6 +45,26 @@ DeclareGlobalFunction( "AllSubmagmas" );
 #!
 DeclareProperty( "IsAntiassociative", IsMagma );
 
+#! @Arguments M
+#! @Description
+#! identifies class of antiassociative magma <A>M</A>.
+#!
+#! @BeginExampleSession
+#! gap> IsAntiassociative(OneSmallGroup(16));
+#! false
+#! gap> IsAntiassociative(OneSmallAntimagma(2));
+#! true
+#! gap> IsAntiassociative(OneSmallAntimagma(3));
+#! true
+#! @EndExampleSession
+#!
+DeclareAttribute( "IdSmallAntimagma", IsMagma );
+
+#! @Arguments M
+#! @Description
+#! computes isomorphism invariants of <A>M</A>.
+DeclareGlobalFunction( "MagmaIsomorphismInvariants" );
+
 #! @Arguments M, N
 #! @Description
 #! computes an isomoprhism between magmas <A>M</A>, <A>N</A>.
@@ -103,7 +123,7 @@ DeclareGlobalFunction( "IsMagmaIsomorphic" );
 #! @BeginExampleSession
 #! gap> N := SmallAntimagma(2, 1);
 #! <magma with 2 generators>
-#! gap> M:= SmallAntimagma(2, 1);
+#! gap> M := SmallAntimagma(2, 1);
 #! <magma with 2 generators>
 #! gap> N := SmallAntimagma(2, 2);
 #! <magma with 2 generators>

lib/properties.gi

@@ -32,10 +32,16 @@ InstallGlobalFunction(TransposedMagma,
         return MagmaByMultiplicationTable(TransposedMat(MultiplicationTable(M)));
 end);
 
+InstallGlobalFunction(MagmaIsomorphismInvariants,
+    function(M)
+        return [ Size(M), IsLeftCancellative(M), IsRightCancellative(M) ];
+end);
+
 InstallGlobalFunction(MagmaIsomorphism,
     function(M, N)
         local psi, n, p, m, elms;
-        if Size(M) <> Size(N) then
+
+        if MagmaIsomorphismInvariants(M) <> MagmaIsomorphismInvariants(N) then
             return fail;
         fi;
 
@@ -201,3 +207,9 @@ InstallGlobalFunction(HasPropertyA3,
         od;
         return false;
 end);
+
+InstallMethod(IdSmallAntimagma, "for a magma", [IsMagma],
+    function(N)
+        return [ Size(N),
+                 First( Filtered([1 .. NrSmallAntimagmas(3)], index -> IsMagmaIsomorphic(N, SmallAntimagma(3, index) )) ) ];
+end);

lib/smallantimagmas.gi

@@ -3,27 +3,34 @@ InstallGlobalFunction(NrSmallAntimagmas,
     return Size(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(order)());
 end);
 
-InstallGlobalFunction(ReallyNrSmallAntimagmas,
-    function(order)
-    return Size(__SmallAntimagmaHelper.getAllSmallAntimagmaMetadata(order)());
-end);
-
 InstallGlobalFunction(SmallAntimagma,
     function(order, id)
-    return MagmaByMultiplicationTable(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(order)()[id]);
+        return MagmaByMultiplicationTable(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(order)()[id]);
 end);
 
 InstallGlobalFunction(AllSmallAntimagmas,
     function(order)
-    return List(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(order)(), id -> MagmaByMultiplicationTable(id));
+        if IsList(order) and ForAll(order, o -> IsInt(o)) then
+            return Flat(
+                List(order, o -> List(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(o)(),
+                                    id -> MagmaByMultiplicationTable(id)))
+            );
+        elif IsInt(order) then
+            return List(__SmallAntimagmaHelper.getSmallAntimagmaMetadata(order)(), id -> MagmaByMultiplicationTable(id));
+        fi;
 end);
 
 InstallGlobalFunction(OneSmallAntimagma,
     function(order)
-    return SmallAntimagma(order, Random([1 .. NrSmallAntimagmas(order) ]));
+        return SmallAntimagma(order, Random([1 .. NrSmallAntimagmas(order) ]));
 end);
 
-InstallGlobalFunction(ReallyAllSmallAntimagmas,
+InstallGlobalFunction(ReallyNrSmallAntimagmas,
     function(order)
-    return List(__SmallAntimagmaHelper.getAllSmallAntimagmaMetadata(order)(), id -> MagmaByMultiplicationTable(id) );
+        return Size(__SmallAntimagmaHelper.getAllSmallAntimagmaMetadata(order)());
 end);
+
+InstallGlobalFunction(ReallyAllSmallAntimagmas,
+    function(order)
+        return List(__SmallAntimagmaHelper.getAllSmallAntimagmaMetadata(order)(), id -> MagmaByMultiplicationTable(id) );
+end);

lib/utils.gd

@@ -0,0 +1,4 @@
+#! @Arguments [m, k]
+#! @Description
+#! returns a right order of element <A>m</A>.
+DeclareGlobalFunction( "GeneratePossibleDiagonals" );

lib/utils.gi

@@ -0,0 +1,4 @@
+InstallGlobalFunction(GeneratePossibleDiagonals,
+    function(n)
+        return Filtered(Tuples([1 .. n], n), t -> ForAll([1 .. n], i -> t[i] <> i));
+end);

tst/test_antimagma.tst

@@ -6,13 +6,16 @@ false
 gap> IsAntiassociative(MagmaByMultiplicationTable([[2, 1], [2, 1]]));
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> IsEmpty(Idempotents(M))));
+gap> ForAll(AllSmallAntimagmas([2 .. 3]), M -> IsEmpty(Idempotents(M)));
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> IsEmpty(Center(M))));
+gap> ForAll(AllSmallAntimagmas([2 .. 3]), M -> IsEmpty(Center(M)));
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> IsAntiassociative(M)));
+gap> ForAll(AllSmallAntimagmas([2 .. 3]), M -> IsAntiassociative(M));
 true
 
+gap> Collected( List(ReallyAllSmallAntimagmas(3), M -> IdSmallAntimagma(M)) );
+[ [ [ 3, 1 ], 6 ], [ [ 3, 2 ], 6 ], [ [ 3, 3 ], 6 ], [ [ 3, 4 ], 6 ], [ [ 3, 5 ], 6 ], [ [ 3, 6 ], 6 ], [ [ 3, 7 ], 6 ], [ [ 3, 8 ], 6 ], [ [ 3, 9 ], 2 ], [ [ 3, 10 ], 2 ] ]
+
 gap> STOP_TEST( "test_antimagma.tst" );

tst/test_antimagmas_count.tst

@@ -1,9 +1,9 @@
 gap> START_TEST("test_antimagmas_count.tst");
 
-gap> List([2..4], i -> NrSmallAntimagmas(i));
+gap> List([2 .. 4], i -> NrSmallAntimagmas(i));
 [ 2, 10, 17780 ]
 
-gap> List([2..4], i -> ReallyNrSmallAntimagmas(i));
+gap> List([2 .. 4], i -> ReallyNrSmallAntimagmas(i));
 [ 2, 52, 421560 ]
 
 gap> STOP_TEST( "test_antimagmas_count.tst" );

tst/test_properties_element_left_right_order.tst

@@ -1,15 +1,15 @@
 gap> START_TEST( "test_properties_element_left_right_order.tst" );
 
-gap> ForAll([2..10], n -> ForAll(AllSmallGroups(n), G -> ForAll(Elements(G), g -> Order(g) = LeftOrder(g))));
+gap> ForAll(AllSmallGroups([2 .. 10]), G -> ForAll(Elements(G), g -> Order(g) = LeftOrder(g)));
 true
 
-gap> ForAll([2..10], n -> ForAll(AllSmallGroups(n), G -> ForAll(Elements(G), g -> Order(g) = RightOrder(g))));
+gap> ForAll(AllSmallGroups([2 .. 10]), G -> ForAll(Elements(G), g -> Order(g) = RightOrder(g)));
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> ForAll(Filtered(Elements(M), m -> LeftOrder(m) <> infinity), m -> LeftOrder(m) <> RightOrder(m) ) ) );
+gap> ForAll(AllSmallAntimagmas([2 .. 3]), M -> ForAll(Filtered(Elements(M), m -> LeftOrder(m) <> infinity), m -> LeftOrder(m) <> RightOrder(m)));
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> ForAll(Filtered(Elements(M), m -> RightOrder(m) <> infinity), m -> LeftOrder(m) <> RightOrder(m) ) ) );
+gap> ForAll(AllSmallAntimagmas([2 .. 3]), M -> ForAll(Filtered(Elements(M), m -> RightOrder(m) <> infinity), m -> LeftOrder(m) <> RightOrder(m)));
 true
 
 gap> STOP_TEST( "test_properties_element_left_right_order.tst" );

tst/test_properties_magma_associativity_index.tst

@@ -1,9 +1,9 @@
 gap> START_TEST( "test_properties_magma_associativity_index.txt" );
 
-gap> ForAll([2..12], n -> ForAll(AllSmallGroups(n), M -> AssociativityIndex(M) = n^3));
+gap> ForAll( AllSmallGroups([2 .. 12]), M -> AssociativityIndex(M) = Size(M) ^ 3 );
 true
 
-gap> ForAll([2..3], n -> ForAll(AllSmallAntimagmas(n), M -> AssociativityIndex(M) = 0));
+gap>  ForAll(AllSmallAntimagmas([2 .. 3]), M -> AssociativityIndex(M) = 0);
 true
 
 gap> STOP_TEST( "test_properties_magma_associativity_index.txt" );

tst/test_properties_magma_isomorphism_invariants.tst

@@ -0,0 +1,6 @@
+gap> START_TEST( "test_properties_magma_isomorphism_invariants.tst" );
+
+gap> List([2 .. 3], n -> List(AllSmallAntimagmas(n), M -> MagmaIsomorphismInvariants(M) <> MagmaIsomorphismInvariants(TransposedMagma(M)) ) );
+[ [ true, true ], [ false, false, false, false, false, false, false, false, true, true ] ]
+
+gap> STOP_TEST( "test_properties_magma_isomorphism_invariants.tst" );

tst/test_properties_magma_left_right_cancellative.tst

@@ -1,15 +1,15 @@
 gap> START_TEST(  "test_properties_magma_left_right_cancellative.tst" );
 
-gap> ForAll([2..4], n -> ForAll(AllSmallGroups(n), G -> IsLeftCancellative(G)));
+gap> ForAll(AllSmallGroups([2 .. 4]), G -> IsLeftCancellative(G));
 true
 
-gap> ForAll([2..4], n -> ForAll(AllSmallGroups(n), G -> IsRightCancellative(G))); 
+gap> ForAll(AllSmallGroups([2 .. 4]), G -> IsRightCancellative(G));
 true
 
-gap> ForAll([2..4], n -> ForAll(AllSmallGroups(n), G -> IsCancellative(G)));     
+gap> ForAll(AllSmallGroups([2 .. 4]), G -> IsCancellative(G));
 true
 
-gap> ForAny([2..3], n -> ForAny(AllSmallAntimagmas(n), M -> IsCancellative(M)));
+gap> ForAny(AllSmallAntimagmas([2 .. 3]), M -> IsCancellative(M));
 false
 
 gap> STOP_TEST(  "test_properties_magma_left_right_cancellative.tst" );

tst/test_properties_magma_left_right_cylic.tst

@@ -1,15 +1,15 @@
 gap> START_TEST( "test_properties_magma_left_right_cyclic.tst" );
 
-gap> ForAll([2..12], n -> ForAll(Filtered(AllSmallGroups(n), G -> not IsCyclic(G)), G -> not IsLeftCyclic(G)) );
+gap> ForAll(Filtered(AllSmallGroups([2 .. 12]), G -> not IsCyclic(G)), G -> not IsLeftCyclic(G));
 true
 
-gap> ForAll([2..12], n -> ForAll(Filtered(AllSmallGroups(n), G -> IsCyclic(G)), G -> IsLeftCyclic(G)) );        
+gap> ForAll(Filtered(AllSmallGroups([2 .. 12]), G -> IsCyclic(G)), G -> IsLeftCyclic(G));
 true
 
-gap> ForAll([2..12], n -> ForAll(Filtered(AllSmallGroups(n), G -> not IsCyclic(G)), G -> not IsRightCyclic(G)) );
+gap> ForAll(Filtered(AllSmallGroups([2 .. 12]), G -> not IsCyclic(G)), G -> not IsRightCyclic(G));
 true
 
-gap> ForAll([2..12], n -> ForAll(Filtered(AllSmallGroups(n), G -> IsCyclic(G)), G -> IsRightCyclic(G)) );        
+gap> ForAll(Filtered(AllSmallGroups([2 .. 12]), G -> IsCyclic(G)), G -> IsRightCyclic(G));        
 true
 
 gap> STOP_TEST( "test_properties_magma_left_right_cyclic.tst" );

tst/test_utils.tst

@@ -37,5 +37,47 @@ gap> List(Cartesian(Ms_2, Ms_3), M -> IsMagmaIsomorphic(M[1], M[2]));
 gap> List(Cartesian(Ms_2, Ms_3), M -> MagmaIsomorphism(M[1], M[2]));
 [ fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail ]
 
+gap> GeneratePossibleDiagonals(2);  
+[ [ 2, 1 ] ]
+
+gap> GeneratePossibleDiagonals(3);
+[ 
+    [ 2, 1, 1 ], [ 2, 1, 2 ], 
+    [ 2, 3, 1 ], [ 2, 3, 2 ], 
+    [ 3, 1, 1 ], [ 3, 1, 2 ], 
+    [ 3, 3, 1 ], [ 3, 3, 2 ] 
+]
+
+gap> GeneratePossibleDiagonals(4);
+[ 
+    [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 1, 3 ], 
+    [ 2, 1, 2, 1 ], [ 2, 1, 2, 2 ], [ 2, 1, 2, 3 ], 
+    [ 2, 1, 4, 1 ], [ 2, 1, 4, 2 ], [ 2, 1, 4, 3 ], 
+    [ 2, 3, 1, 1 ], [ 2, 3, 1, 2 ], [ 2, 3, 1, 3 ], 
+    [ 2, 3, 2, 1 ], [ 2, 3, 2, 2 ], [ 2, 3, 2, 3 ], 
+    [ 2, 3, 4, 1 ], [ 2, 3, 4, 2 ], [ 2, 3, 4, 3 ], 
+    [ 2, 4, 1, 1 ], [ 2, 4, 1, 2 ], [ 2, 4, 1, 3 ], 
+    [ 2, 4, 2, 1 ], [ 2, 4, 2, 2 ], [ 2, 4, 2, 3 ], 
+    [ 2, 4, 4, 1 ], [ 2, 4, 4, 2 ], [ 2, 4, 4, 3 ], 
+    [ 3, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 1, 3 ], 
+    [ 3, 1, 2, 1 ], [ 3, 1, 2, 2 ], [ 3, 1, 2, 3 ], 
+    [ 3, 1, 4, 1 ], [ 3, 1, 4, 2 ], [ 3, 1, 4, 3 ], 
+    [ 3, 3, 1, 1 ], [ 3, 3, 1, 2 ], [ 3, 3, 1, 3 ], 
+    [ 3, 3, 2, 1 ], [ 3, 3, 2, 2 ], [ 3, 3, 2, 3 ], 
+    [ 3, 3, 4, 1 ], [ 3, 3, 4, 2 ], [ 3, 3, 4, 3 ], 
+    [ 3, 4, 1, 1 ], [ 3, 4, 1, 2 ], [ 3, 4, 1, 3 ], 
+    [ 3, 4, 2, 1 ], [ 3, 4, 2, 2 ], [ 3, 4, 2, 3 ], 
+    [ 3, 4, 4, 1 ], [ 3, 4, 4, 2 ], [ 3, 4, 4, 3 ], 
+    [ 4, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 1, 3 ], 
+    [ 4, 1, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 1, 2, 3 ], 
+    [ 4, 1, 4, 1 ], [ 4, 1, 4, 2 ], [ 4, 1, 4, 3 ], 
+    [ 4, 3, 1, 1 ], [ 4, 3, 1, 2 ], [ 4, 3, 1, 3 ], 
+    [ 4, 3, 2, 1 ], [ 4, 3, 2, 2 ], [ 4, 3, 2, 3 ], 
+    [ 4, 3, 4, 1 ], [ 4, 3, 4, 2 ], [ 4, 3, 4, 3 ], 
+    [ 4, 4, 1, 1 ], [ 4, 4, 1, 2 ], [ 4, 4, 1, 3 ], 
+    [ 4, 4, 2, 1 ], [ 4, 4, 2, 2 ], [ 4, 4, 2, 3 ], 
+    [ 4, 4, 4, 1 ], [ 4, 4, 4, 2 ], [ 4, 4, 4, 3 ] 
+]
+
 gap> STOP_TEST( "test_utils.tst" );