From eed628a7a2fb1b7880b0a048a8e4b70d68bd8780 Mon Sep 17 00:00:00 2001
From: ThomasBreuer <sam@math.rwth-aachen.de>
Date: Tue, 23 Oct 2018 13:00:19 +0200
Subject: [PATCH] fixed `ImaginaryPart` for quaternion algebras

---
 lib/algsc.gi              |  5 +++--
 tst/testinstall/algsc.tst | 16 ++++++++++++++++
 2 files changed, 19 insertions(+), 2 deletions(-)

diff --git a/lib/algsc.gi b/lib/algsc.gi
index d6b86bee22..94496b44d4 100644
--- a/lib/algsc.gi
+++ b/lib/algsc.gi
@@ -884,11 +884,12 @@ InstallMethod( ImaginaryPart,
     "for a quaternion",
     [ IsQuaternion and IsSCAlgebraObj ],
     function( quat )
-    local v, z;
+    local v, z, a;
 
     v:= ExtRepOfObj( quat );
     z:= Zero( v[1] );
-    return ObjByExtRep( FamilyObj( quat ), [ v[2], z, v[4], -v[3] ] );
+    a:= FamilyObj( quat )!.sctable[2][2][2][1];  # the first parameter
+    return ObjByExtRep( FamilyObj( quat ), [ v[2], z, -v[4], -v[3]/a ] );
     end );
 
 
diff --git a/tst/testinstall/algsc.tst b/tst/testinstall/algsc.tst
index a55ee7d8f8..f2b841e00f 100644
--- a/tst/testinstall/algsc.tst
+++ b/tst/testinstall/algsc.tst
@@ -107,6 +107,22 @@ gap> v:= Subspace( a, [ v, 0*v, v^0, w ] );
 gap> Dimension( v );
 3
 
+#
+gap> a:= QuaternionAlgebra( Rationals, -2, -3 );;
+gap> gens:= GeneratorsOfAlgebra( a );
+[ e, i, j, k ]
+gap> List( gens, RealPart );
+[ e, 0*e, 0*e, 0*e ]
+gap> List( gens, ImaginaryPart ) * gens[2];
+[ 0*e, i, j, k ]
+gap> vecs := Concatenation( gens, [ Sum( gens ) ] );
+[ e, i, j, k, e+i+j+k ]
+gap> ForAll( vecs, v -> (v + ComplexConjugate( v )) / 2 = RealPart( v ) );
+true
+gap> ForAll( vecs, v -> (v - ComplexConjugate( v )) / (2*gens[2])
+>                       = ImaginaryPart( v ) );
+true
+
 #############################################################################
 ##
 ##  Expl. 1: $2.A6$, gen. by 20 quaternionic reflections over $H(\sqrt{3})$