From 3147c2b18fb78d7e1719918c1bb078aaea83b1be Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Fri, 8 Nov 2024 01:14:29 +0100
Subject: [PATCH] Fix SMTX.InvariantSesquilinearForm for reducible case

... by deleting unnecessary 'normalization' (???) code.
---
 lib/meataxe.gi              | 17 ++---------------
 tst/testinstall/meataxe.tst | 10 ++++++++++
 2 files changed, 12 insertions(+), 15 deletions(-)

diff --git a/lib/meataxe.gi b/lib/meataxe.gi
index 90c375cfd8..baa80b0260 100644
--- a/lib/meataxe.gi
+++ b/lib/meataxe.gi
@@ -3369,7 +3369,7 @@ end;
 ## Look for an invariant sesquililinear form of the GModule module.
 ## Return fail, or the matrix of the form.
 SMTX.InvariantSesquilinearForm:=function( module  )
-   local DM, q, r, iso, isot, l;
+   local DM, iso;
 
    if not SMTX.IsMTXModule(module) then
       Error("Argument of InvariantSesquilinearForm is not a module");
@@ -3383,20 +3383,7 @@ SMTX.InvariantSesquilinearForm:=function( module  )
        SMTX.SetInvariantSesquilinearForm(module, fail);
        return fail;
    fi;
-   # Replace iso by a scalar multiple to get iso twisted symmetric
-   q:=Size(module.field);
-   r:=RootInt(q,2);
-   isot:=List( TransposedMat(iso), x -> List(x, y->y^r) );
-   isot:=iso * isot^-1;
-   if not IsDiagonalMat(isot) then
-     Error("Form does not seem to be of the right kind (non-diagonal)!");
-   fi;
-   l:=LogFFE(isot[1,1],Z(q));
-   if l mod (r-1) <> 0 then
-     Error("Form does not seem to be of the right kind (not (q-1)st root)!");
-   fi;
-   iso:=Z(q)^(l/(r-1)) * iso;
-   iso:=ImmutableMatrix(GF(q), iso);
+   iso:=ImmutableMatrix(module.field, iso);
    SMTX.SetInvariantSesquilinearForm(module, iso);
    return iso;
 end;
diff --git a/tst/testinstall/meataxe.tst b/tst/testinstall/meataxe.tst
index 0dddfd4bfe..699b772915 100644
--- a/tst/testinstall/meataxe.tst
+++ b/tst/testinstall/meataxe.tst
@@ -105,6 +105,16 @@ gap> MTX.OrthogonalSign(M2);
 gap> SMTX.RandomIrreducibleSubGModule(M2); # returns false for irreducible module
 false
 
+# test invariant form detection on reducible module with two isomorphic
+# components (hence many automorphisms exist)
+gap> g1:= GeneratorsOfGroup(SU(4, 5));;
+gap> g2:= GeneratorsOfGroup(SU(4, 5));;
+gap> m:= GModuleByMats(SMTX.MatrixSum(g1,g2), GF(25));;
+gap> form:= MTX.InvariantSesquilinearForm( m );;
+gap> frob5 := g -> List(g,row->List(row,x->x^5));; # field involution
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(frob5(x)) = form);
+true
+
 #
 gap> Display(MTX.IsomorphismModules(M,M));
  1 . . . .