fixed ConsiderStructureConstants (#5487)

* fixed `ConsiderStructureConstants`

It may happen that `ConsiderStructureConstants` excludes all candidates.
Up to now, it was possible that one runs into an error in such a case
because the function wants to proceed and tries to access entries in an
empty list.

Benjamin Sambale found an example in which the `quick` parameter is set
to `true` and hence some candidates do not get excluded in an earlier step,
but the error could in principle happen also with the default setting
`quick:= false`.

* improve the documentation of `PossibleClassFunctions`

* make those tests happy that do not provide ctbllib

* fixed duplicate "for which"

lib/ctblmaps.gd

@@ -956,7 +956,12 @@ DeclareAttributeSuppCT( "NamesOfFusionSources",
 ##    for the argument <A>quick</A>;
 ##    especially, as soon as only one possibility remains
 ##    then this possibility is returned immediately;
-##    the default value is <K>false</K>,
+##    the default value is <K>false</K>
+##    (note that in situations where the group of <A>tbl</A> has no subgroups
+##    with character table <A>subtbl</A>, it may happen that setting
+##    <C>quick</C> to <K>true</K> causes <Ref Oper="PossibleClassFusions"/>
+##    to return solutions,
+##    whereas the value <K>false</K> yields an empty list),
 ##  </Item>
 ##  <Mark><C>verify</C></Mark>
 ##  <Item>
@@ -2492,7 +2497,7 @@ DeclareGlobalFunction( "FusionsAllowedByRestrictions" );
 ##  constants.
 ##  <P/>
 ##  The argument <A>quick</A> must be a Boolean; if it is <K>true</K> then
-##  only those triples are checked for which for which at least two entries
+##  only those triples are checked for which at least two entries
 ##  in <A>fusions</A> have different images.
 ##  </Description>
 ##  </ManSection>

lib/ctblmaps.gi

@@ -4492,11 +4492,17 @@ InstallGlobalFunction( ConsiderStructureConstants,
               sc:= ClassMultiplicationCoefficient( tbl, trpl[1], trpl[2],
                        trpl[3] );
               if sc < subsc then
+                fusions:= Filtered( fusions,
+                                    x -> x{ [ i, j, kk ] } <> trpl );
+                if Length( fusions ) = 0 then
+                  Info( InfoCharacterTable, 2,
+                        "ConsiderStructureConstants: contradiction for ",
+                        [ i, j, kk ] );
+                  return fusions;
+                fi;
                 Info( InfoCharacterTable, 2,
                       "ConsiderStructureConstants: improvement for ",
                       [ i, j, kk ] );
-                fusions:= Filtered( fusions,
-                                    x -> x{ [ i, j, kk ] } <> trpl );
                 parm:= Parametrized( fusions );
               fi;
             od;

tst/testinstall/ctblmaps.tst

@@ -0,0 +1,18 @@
+#@local s, t, maps
+gap> START_TEST( "ctblmaps.tst" );
+
+# `ConsiderStructureConstants` can unexpectedly exclude all candidates.
+# (Benjamin Sambale found examples for that.)
+gap> if TestPackageAvailability("ctbllib") <> fail and
+>       LoadPackage("ctbllib", false) <> fail then
+>      s:= CharacterTable( "2.A6" );;
+>      t:= CharacterTable( "Co3" );;
+>      maps:= [ [ 1, 2, 8, 4, 11, 4, 13, 18, 18, 9, 22, 9, 22 ],
+>               [ 1, 2, 8, 4, 11, 4, 13, 17, 17, 9, 22, 9, 22 ] ];;
+>      if Length( ConsiderStructureConstants( s, t, maps, true ) ) <> 0 then
+>        Error( "test of ConsiderStructureConstants failed" );
+>      fi;
+>    fi;
+
+#
+gap> STOP_TEST( "ctblmaps.tst" );