Fix error in RECOG.SmallHomomorphicImageProjectiveGroup (#336)

This unexpected error was triggered by a matrix group with compressed matrices
over GF(q^k), k > 1, as generator, where the matrix entries actually all were
over the subfield GF(q). So the matrix generators were compressed over a field
that is larger than necessary. This can easily happen when considering
subgroups of a larger matrix group.

Unfortunately multiplying a compressed matrix over GF(q) by a matrix over
GF(q^k) produces an uncompressed matrix, and this then trips up the hash
functions used by orb, resulting in an unexpected error.

This issue was revealed by tests in the ClassicalMaximals package.

CHANGES

@@ -1,10 +1,19 @@
 This file describes changes in the recog package.
 
+1.4.4 (2025-01-DD)
+  - Fix an unexpected error during recognition when trying to split
+    group as direct products (in `RECOG.DirectFactorsFinder`)
+  - Fix an unexpected error in `RECOG.SmallHomomorphicImageProjectiveGroup`
+  - Fix an unexpected error in the C6 recognition code (a call to
+    `ConvertToMatrixRep` was missing)
+  - Remove left-over debug message which sometimes printed "With 2" or
+    similar messages during recognition
+
 1.4.3 (2024-10-16)
-   - Stop overriding the system library function `MTX.InvariantBilinearForm`
-     with an old version (this was meant to fix a bug in GAP but has been
-     unnecessary for a couple years, and now impedes improvements for this
-     function in GAP)
+  - Stop overriding the system library function `MTX.InvariantBilinearForm`
+    with an old version (this was meant to fix a bug in GAP but has been
+    unnecessary for a couple years, and now impedes improvements for this
+    function in GAP)
   - Various internal and janitorial changes
 
 1.4.2 (2022-09-27)

gap/matrix/matimpr.gi

@@ -70,7 +70,7 @@ RECOG.IndexMaxSub := function( hm, grp, d )
     sub := MTX.ProperSubmoduleBasis(hm);
     sub := MutableCopyMat( sub );  # make mutable copy
     # FIXME: this will be unnecessary:
-    ConvertToMatrixRep(sub);
+    ConvertToMatrixRep(sub,hm.field);
     lastsub := fail;
     lastorb := fail;
     repeat
@@ -98,7 +98,7 @@ RECOG.IndexMaxSub := function( hm, grp, d )
         fi;
         # we try intersecting the subspaces in the orbit:
         Info(InfoRecog,2,"Calculating intersections...");
-        f := FieldOfMatrixGroup(grp);
+        f := hm.field;
         sp := VectorSpace(f,orb[1]);
         dim := Dimension(sp);
         for i in [2..Length(orb)] do
@@ -120,15 +120,15 @@ RECOG.IndexMaxSub := function( hm, grp, d )
         lastorb := orb;
         sub := MutableCopyMat(AsList(Basis(sp)));
         # FIXME: This will vanish:
-        ConvertToMatrixRep(sub);
+        ConvertToMatrixRep(sub,hm.field);
     until false;
 end;
 
 RECOG.SmallHomomorphicImageProjectiveGroup := function ( grp )
 
     local hm, findred, ans, fld, d, i, gens;
 
-    fld := FieldOfMatrixGroup(grp);
+    fld := DefaultFieldOfMatrixGroup(grp);
     d := DimensionOfMatrixGroup(grp);
 
     findred := function( gens )

tst/working/quick/bugfix.tst

@@ -61,6 +61,23 @@ gap> RecogniseGroup(SL(2,5));
 gap> RECOG.IsThisSL2Natural([ [ [ 0*Z(5), Z(5^2)^9 ], [ Z(5^2)^3, 0*Z(5) ] ], [ [ Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^3 ] ] ], GF(5^2));
 false
 
+# Bug in RECOG.SmallHomomorphicImageProjectiveGroup triggered by given matrix
+# group generated by compressed matrices over GF(q^k), k > 1, where the matrix
+# entries actually all were over the subfield GF(q).
+#
+# Unfortunately multiplying a compressed matrix over GF(q) by a matrix over
+# GF(q^k) produces an uncompressed matrix, and this then trips up the hash
+# functions used by orb, resulting in an unexpected error.
+gap> gens:=Z(3)^0*[   # all generators over GF(3)
+> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]],
+> [[0,0,0,0,2],[0,1,0,0,0],[0,0,2,0,0],[0,0,0,1,0],[2,0,0,0,0]],
+> [[1,1,0,0,0],[2,0,0,0,0],[1,1,1,0,0],[2,2,0,1,2],[0,1,2,1,0]],
+> [[1,1,1,1,0],[1,1,1,0,1],[1,1,0,1,1],[1,0,1,1,1],[0,1,1,1,1]],
+> ];;
+gap> G:=Group(List(gens, g -> ImmutableMatrix(GF(9), g)));; # ... but compress generators over GF(9)
+gap> RECOG.SmallHomomorphicImageProjectiveGroup(G);  # this call used to raise an error
+fail
+
 #
 gap> SetInfoLevel(InfoRecog, oldInfoLevel);
 gap> STOP_TEST("bugfix.tst");