updated example files

Author: mohamed-barakat

examples/doc/IntegersAsMonoid.g

@@ -7,7 +7,13 @@ LoadPackage( "Algebroids" );
 #! @Example
 q := RightQuiver( "q(o)[m:o->o,i:o->o]" );
 #! q(o)[m:o->o,i:o->o]
-L := [ [ q.m * q.i, q.o ], [ q.i * q.m, q.o ] ];
+o := q.o;
+#! (o)
+m := q.m;
+#! (m)
+i := q.i;
+#! (i)
+L := [ [ m * i, o ], [ i * m, o ] ];
 #! [ [ (m*i), (o) ], [ (i*m), (o) ] ]
 #! @EndExample
 
@@ -20,6 +26,8 @@ IsCommutative( ZZ );
 #! true
 ZZ.o;
 #! <(o)>
+IsWellDefined( ZZ.o );
+#! true
 m := ZZ.m;
 #! (o)-[(m)]->(o)
 i := ZZ.i;
@@ -30,24 +38,26 @@ SetOfGeneratingMorphisms( ZZ );
 #! [ (o)-[(m)]->(o), (o)-[(i)]->(o) ]
 SetOfGeneratingMorphisms( ZZ, ZZ.o, ZZ.o );
 #! [ (o)-[(m)]->(o), (o)-[(i)]->(o) ]
-ObjectInFpCategory( ZZ, q.o ) = ZZ.o;
+ObjectInFpCategory( ZZ, o ) = ZZ.o;
 #! true
-ZZ.o = q.o / ZZ;
+ZZ.o = o / ZZ;
 #! true
+IdentityMorphism( ZZ.o );
+#! (o)-[(o)]->(o)
 MorphismInFpCategory( ZZ, q.m ) = ZZ.m;
 #! true
 ZZ.m = q.m / ZZ;
 #! true
-IdentityMorphism( ZZ.o );
-#! (o)-[(o)]->(o)
 #! @EndExample
 
 #! We can compute in the algebroids.
 #! For instance we can form compositions.
 
 #! @Example
-PreCompose( [ m, i, m, m, i, m, i, m ] );
+m2 := PreCompose( [ m, i, m, m, i, m, i, m ] );
 #! (o)-[(m*m)]->(o)
+IsWellDefined( m2 );
+#! true
 unit := Unit( ZZ );
 #! Functor from Monoid generated by the right quiver *(1)[]
 #! -> Monoid generated by the right quiver q(o)[m:o->o,i:o->o]

examples/doc/NaturalNumbersAsMonoid.g

@@ -7,6 +7,10 @@ LoadPackage( "Algebroids" );
 #! @Example
 q := RightQuiver( "q(o)[m:o->o]" );
 #! q(o)[m:o->o]
+o := q.o;
+#! (o)
+m := q.m;
+#! (m)
 #! @EndExample
 
 #! Create a monoid from $q$.
@@ -26,16 +30,16 @@ SetOfGeneratingMorphisms( N );
 #! [ (o)-[(m)]->(o) ]
 SetOfGeneratingMorphisms( N, N.o, N.o );
 #! [ (o)-[(m)]->(o) ]
-ObjectInFpCategory( N, q.o ) = N.o;
+ObjectInFpCategory( N, o ) = N.o;
 #! true
-N.o = q.o / N;
-#! true
-MorphismInFpCategory( N, q.m ) = N.m;
-#! true
-N.m = q.m / N;
+N.o = o / N;
 #! true
 IdentityMorphism( N.o );
 #! (o)-[(o)]->(o)
+MorphismInFpCategory( N, m ) = N.m;
+#! true
+N.m = m / N;
+#! true
 #! @EndExample
 
 #! We can compute in the algebroids.