Fix IsDigraphHomomorphism

Author: james-d-mitchell

doc/grahom.xml

@@ -648,14 +648,27 @@ gap> EmbeddingsDigraphs(D1, D2);
     A permutation or transformation <A>x</A> is a <E>homomorphism</E> from a
     digraph <A>src</A> to a digraph <A>ran</A> if the following hold:
     <List>
-      <Item>
-        <C>[u ^ <A>x</A>, v ^ <A>x</A>]</C> is an edge of
-        <A>ran</A> whenever <C>[u, v]</C> is an
-        edge of <A>src</A>; and </Item>
-      <Item>
-        <A>x</A> fixes every <C>i</C> which is not a vertex of <A>src</A>.
-      </Item>
+    <Item>
+    <C>[u ^ <A>x</A>, v ^
+    <A>x</A>]</C> is an edge of <A>ran</A> whenever <C>[u, v]</C> is an edge of
+    <A>src</A>; and
+    </Item>
+    <Item>
+    <A>x</A> maps the vertices of <A>src</A> to a subset of the vertices of
+    <A>ran</A>, i.e. <C>IsSubset(DigraphVertices(<A>ran</A>),
+    OnSets(DigraphVertices(<A>src</A>), <A>x</A>))</C> is <K>true</K>.
+    </Item>
     </List>
+
+    Note that if <C>i</C> is any integer greater than
+    <C>DigraphNrVertice(<A>src</A>)</C>, then the action of <A>x</A> on
+    <C>i</C> is ignored by this function. One consequence of this is that
+    distinct transformations or permutations might represent the same
+    homomorphism. For example, if <A>src</A> and <A>ran</A> are
+    <C>CycleDigraph(2)</C>, then both the permutations <C>(1, 2)</C> and <C>(1,
+    2)(3, 4)</C> represent the same automorphism of <A>src</A>.
+    <P/>
+
     See also <Ref Func="GeneratorsOfEndomorphismMonoid"/>.<P/>
 
 

doc/isomorph.xml

@@ -814,7 +814,7 @@ true
 gap> IsDigraphAutomorphism(src, (2, 3), [2, 2, 1]);
 false
 gap> IsDigraphAutomorphism(src, (2, 3)(4, 5));
-false
+true
 gap> IsDigraphAutomorphism(src, (1, 4));
 false
 gap> IsDigraphAutomorphism(src, ());

gap/grahom.gi

@@ -576,7 +576,7 @@ function(src, ran, x)
   if IsMultiDigraph(src) or IsMultiDigraph(ran) then
     ErrorNoReturn("the 1st and 2nd arguments <src> and <ran> must be digraphs",
                   " with no multiple edges,");
-  elif LargestMovedPoint(x) > DigraphNrVertices(src) then
+  elif not IsSubset(DigraphVertices(ran), OnSets(DigraphVertices(src), x)) then
     return false;
   fi;
   for i in DigraphVertices(src) do

src/homos.c

@@ -1748,6 +1748,7 @@ static bool init_data_from_args(Obj digraph1_obj,
   set_bit_array_from_gap_list(IMAGE_RESTRICT, image_obj);
   if (INT_INTOBJ(injective_obj) > 0
       && size_bit_array(IMAGE_RESTRICT, nr1) < nr1) {
+    // TODO shouldn't the first nr1 be nr2?
     // homomorphisms should be injective (by injective_obj) but are not since
     // the image is too restricted.
     return false;

src/perms.c

@@ -25,34 +25,29 @@ Perm new_perm(uint16_t const degree) {
 }
 
 Perm new_perm_from_gap(Obj gap_perm_obj, uint16_t const degree) {
-  UInt lmp = LargestMovedPointPerm(gap_perm_obj);
-  DIGRAPHS_ASSERT(lmp <= MAXVERTS);
-  if (lmp > MAXVERTS) {
-    ErrorQuit("expected permutations of degree at most %d, but got a "
-              "permutation of degree %d",
-              MAXVERTS,
-              lmp);
-  }
-
-  DIGRAPHS_ASSERT(lmp <= degree);
-
   Perm p = new_perm(degree > 0 ? degree : 1);
 
+  size_t copy_up_to = degree;
+  size_t lmp        = LargestMovedPointPerm(gap_perm_obj);
+  if (degree > lmp) {
+    copy_up_to = lmp;
+  }
+
   if (IS_PERM2(gap_perm_obj)) {
     UInt2* gap_perm_ptr = ADDR_PERM2(gap_perm_obj);
-    for (UInt i = 0; i < lmp; ++i) {
+    for (UInt i = 0; i < copy_up_to; ++i) {
       p[i] = gap_perm_ptr[i];
     }
-    for (UInt i = lmp; i < degree; ++i) {
+    for (UInt i = copy_up_to; i < degree; ++i) {
       p[i] = i;
     }
   } else {
     DIGRAPHS_ASSERT(IS_PERM4(gap_perm_obj));
     UInt4* gap_perm_ptr = ADDR_PERM4(gap_perm_obj);
-    for (UInt i = 0; i < lmp; ++i) {
+    for (UInt i = 0; i < copy_up_to; ++i) {
       p[i] = gap_perm_ptr[i];
     }
-    for (UInt i = lmp; i < degree; ++i) {
+    for (UInt i = copy_up_to; i < degree; ++i) {
       p[i] = i;
     }
   }