From 5608416e66323ea37269396b8a614225a9ea5df9 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Fri, 13 Mar 2026 11:05:14 +0100
Subject: [PATCH] Fix Frank's SL2 in nat.rep. code in even char

Also add some Asserts for future debugging
---
 contrib/frank/sl2/NatSL2q.g | 15 +++++++++++----
 1 file changed, 11 insertions(+), 4 deletions(-)

diff --git a/contrib/frank/sl2/NatSL2q.g b/contrib/frank/sl2/NatSL2q.g
index 3e6ca845..7e5c6504 100644
--- a/contrib/frank/sl2/NatSL2q.g
+++ b/contrib/frank/sl2/NatSL2q.g
@@ -40,7 +40,7 @@ RecogNaturalSL2 := function(G, q)
         mat, tm, ym, y, ymat, tr, d, cm, r1, r2, r, log, i, trupm, 
         smm, trlowm, F, a2, bas, e, l, emax, tmp;
   GM := GroupWithMemory(G);
-  one := One(G.1[1,1]);
+  one := OneOfBaseDomain(G.1);
   zero := Zero(one);
   
   # find element x of order q-1
@@ -100,6 +100,8 @@ RecogNaturalSL2 := function(G, q)
   # now y^(tm * mat) = diag(a, a^-1) 
   tr := tm*mat;
 
+  Assert(3, y^(tm * mat) = DiagonalMat([a, a^-1]) );
+
   # a-eigenvector of x in new basis
   d := tr^-1 * [mat[1,1],mat[2,1]];
   # can be scaled to [1,d]
@@ -125,7 +127,7 @@ RecogNaturalSL2 := function(G, q)
       # this will in most cases be a transvection normalized by x
       trupm := Comm(xm, ym^i*cm);
       smm := trupm^mat;
-      if smm[1,2] = zero then
+      if smm[1,2] = zero or smm[2,1] <> zero then
         i := false;
       else
         # rescale first column of mat such that trupm^mat = [[1,1],[0,1]]
@@ -136,6 +138,8 @@ RecogNaturalSL2 := function(G, q)
     fi;
   until IsInt(i);
 
+  Assert(3, trupm^mat = [[1,1],[0,1]] * one);
+
   # same for the other eigenvector of x:
   # 1/a-eigenvector of x in new basis
   d := tr^-1 * [mat[1,2],mat[2,2]];
@@ -164,7 +168,7 @@ RecogNaturalSL2 := function(G, q)
       # that the conjugate matrix is [[1,0],[1,1]]).
       trlowm := Comm(xm, ym^i*cm);
       smm := trlowm^mat;
-      if smm[2,1] = zero then
+      if smm[2,1] = zero or smm[1,2] <> zero then
         i := false;
       fi;
     fi;
@@ -201,15 +205,18 @@ RecogNaturalSL2 := function(G, q)
     od;
   fi;
 
+  Assert(3, trlowm^mat = [[1,0],[1,1]] * one);
+
   # finally power x to change a to 1/Z(q)
   if a <> 1/Z(q) then
     log := DLog(a, 1/Z(q), qm1fac);
     xm := xm^log;
   fi;
 
+  Assert(3, xm^mat = DiagonalMat([Z(q)^-1, Z(q)]));
+
   # return SLPs of elements mapped by mat to 
   # diag(1/Z(q),Z(q))[[1,0],[1,1]], [[1,1],[0,1]],
   # and mat
   return [List([xm, trlowm, trupm], SLPOfElm), mat];
 end;
-