feat: IsLeftRightAlternative method

limakzi · Sep 5, 2024 · 910b2ef · 910b2ef
1 parent f21bc56
commit 910b2ef
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Showing 3 changed files with 38 additions and 1 deletion.
diff --git a/lib/properties.gd b/lib/properties.gd
@@ -319,4 +319,22 @@ DeclareProperty( "IsLeftFPFInducted", IsMagma );
 #! @EndExampleSession
 #!
 #!
-DeclareProperty( "IsRightFPFInducted", IsMagma );
+DeclareProperty( "IsRightFPFInducted", IsMagma );
+
+#! @Arguments M
+#! @Description
+#! is a left-alternatve magma <A>M</A>.
+#!
+#! @BeginExampleSession
+#! @EndExampleSession
+#!
+DeclareProperty( "IsLeftAlternative", IsMagma );
+
+#! @Arguments M
+#! @Description
+#! is a right-alternatve magma <A>M</A>.
+#!
+#! @BeginExampleSession
+#! @EndExampleSession
+#!
+DeclareProperty( "IsRightAlternative", IsMagma );
diff --git a/lib/properties.gi b/lib/properties.gi
@@ -242,4 +242,14 @@ end);
 InstallMethod(IsRightFPFInducted, "for a magma", [IsMagma],
     function(M)
         return ForAll(M, m -> Size( Unique( Elements(M) * m ) ) = 1 and First( Unique( Elements(M) * m ) ) <> m);
+end);
+
+InstallMethod(IsLeftAlternative, "for a magma", [IsMagma],
+    function(M)
+        return ForAll(EnumeratorOfTuples(M, 2), c -> c[1] * ( c[1] * c[2] ) = ( c[1] * c[1] ) * c[2] );
+end);
+
+InstallMethod(IsRightAlternative, "for a magma", [IsMagma],
+    function(M)
+        return ForAll(EnumeratorOfTuples(M, 2), c -> c[1] * ( c[2] * c[2] ) = ( c[1] * c[2] ) * c[2] );
 end);
diff --git a/tst/test_properties_magma_isleftrightalternative.tst b/tst/test_properties_magma_isleftrightalternative.tst
@@ -0,0 +1,9 @@
+gap> START_TEST( "test_properties_magma_isleftrightalternative.tst" );
+
+gap> ForAny(AllSmallAntimagmas([2 .. 3]), M -> IsLeftAlternative(M) );
+false
+
+gap> ForAny(AllSmallAntimagmas([2 .. 3]), M -> IsRightAlternative(M) );
+false
+
+gap> STOP_TEST( "test_properties_magma_isleftrightalternative.tst" );