diff --git a/gap/field.gi b/gap/field.gi
index d1801d7..52ea9c8 100644
--- a/gap/field.gi
+++ b/gap/field.gi
@@ -75,21 +75,20 @@ end );
 ##  
 InstallMethod(MaximalOrderBasis, "for number field", true,[IsNumberField], 0, 
 function( F ) 
-    local e, T, b, B;
+    local e, Tb, B;
   
     if DegreeOverPrimeField(F)=1 then
         return EquationOrderBasis(F);
     fi;
     e := EquationOrderBasis(F);
-    T := AL_FUNCS.MaximalOrderDescription(F);
-    b := List( T, x -> LinearCombination( e, x ) );
+    Tb := AL_FUNCS.MaximalOrderDescription(F);
     B := Objectify(NewType(FamilyObj(F), IsFiniteBasisDefault and
                                          IsRelativeBasisDefaultRep),
                            rec());
     SetUnderlyingLeftModule( B, F );
-    SetBasisVectors( B, b );
+    SetBasisVectors( B, Tb[2] );
     B!.basis := e;
-    B!.basechangeMatrix := Immutable( T^-1 );
+    B!.basechangeMatrix := Immutable( Tb[1]^-1 );
     return B;
 end );
 
@@ -140,17 +139,12 @@ BindGlobal( "AddUnitGroupOfNumberField", function( F, units )
 end );
 
 BindGlobal( "UnitGroupOfNumberField", function( F )
-    local eqn, uni, gen, G, r, H, nat;
+    local uni, G;
 
     # determine generators
-    eqn := EquationOrderBasis(F);
     uni := AL_FUNCS.UnitGroupDescription(F);
-    if uni=[-1] then
-        G:=GroupByGenerators([-1*eqn[1]]);
-    else
-        gen := List( uni, x -> LinearCombination( eqn, x ) );
-        G := GroupByGenerators(gen);
-    fi;
+    G := GroupByGenerators(uni);
+
     # add info
     SetIsUnitGroup( G, true );
     SetFieldOfUnitGroup( G, F );
@@ -161,8 +155,7 @@ BindGlobal( "UnitGroupOfNumberField", function( F )
 end );
 
 InstallMethod( UnitGroup, "for number field", true,
-[IsNumberField], 0, function( F ) return
-UnitGroupOfNumberField( F ); end);
+[IsNumberField], UnitGroupOfNumberField);
 
 #############################################################################
 ##
diff --git a/gap/oscar.gi b/gap/oscar.gi
index 1a13a9f..ce58e21 100644
--- a/gap/oscar.gi
+++ b/gap/oscar.gi
@@ -24,17 +24,24 @@ BindGlobal("_OscarField", function(F)
 end);
 
 BindGlobal("MaximalOrderDescriptionOscar", function(F)
-  local K, O, basis;
+  local K, O, basis, T, eqn, b;
 
   K := _OscarField(F);
   O := Oscar.maximal_order(K);
   basis := Julia.map(Oscar.coordinates,Oscar.basis(O,K));
 
-  return JuliaToGAP(IsList, basis, true);
+  T := JuliaToGAP(IsList, basis, true);
+
+  # convert to GAP
+  eqn := EquationOrderBasis(F);
+  b := List( T, x -> LinearCombination( eqn, x ) );
+
+  # return result
+  return [T, b];
 end);
 
 BindGlobal("UnitGroupDescriptionOscar", function(F)
-  local K, O, U_m, U, m, basis;
+  local K, O, U_m, U, m, basis, result, eqn;
 
   K := _OscarField(F);
   O := Oscar.maximal_order(K);
@@ -44,7 +51,18 @@ BindGlobal("UnitGroupDescriptionOscar", function(F)
 
   basis := Julia.map(Oscar.coordinates, Julia.map(K, Julia.map(m, Oscar.gens(U))));
 
-  return JuliaToGAP(IsList, basis, true);
+  result := JuliaToGAP(IsList, basis, true);
+
+  # convert to GAP
+  eqn := EquationOrderBasis(F);
+  if result = [-1] then
+      result := [-1*eqn[1]];
+  else
+      result := List( result, x -> LinearCombination( eqn, x ) );
+  fi;
+
+  # return result
+  return result;
 end);
 
 BindGlobal("ExponentsOfUnitsDescriptionWithRankOscar", function(F, elms)
diff --git a/gap/pari.gi b/gap/pari.gi
index dbdff6d..a0ec0f2 100644
--- a/gap/pari.gi
+++ b/gap/pari.gi
@@ -89,7 +89,7 @@ end);
 #F MaximalOrderDescriptionPari( F )
 ##
 BindGlobal("MaximalOrderDescriptionPari", function( F )
-    local input, result;
+    local input, T, eqn, b;
  
     if IsPrimeField(F) then return [1]; fi;
 
@@ -97,10 +97,14 @@ BindGlobal("MaximalOrderDescriptionPari", function( F )
     input := PolynomialWithNameToStringList(IntegerDefiningPolynomial(F));
 
     # execute PARI/GP
-    result := ProcessPariGP(Concatenation(input), "maxord.gp");
+    T := ProcessPariGP(Concatenation(input), "maxord.gp");
+
+    # convert to GAP
+    eqn := EquationOrderBasis(F);
+    b := List( T, x -> LinearCombination( eqn, x ) );
 
     # return result
-    return result;
+    return [T, b];
 end);
 
 #############################################################################
@@ -108,7 +112,7 @@ end);
 #F UnitGroupDescriptionPari( F )
 ##
 BindGlobal("UnitGroupDescriptionPari", function( F )
-    local input, result;
+    local input, result, eqn;
 
     if IsPrimeField( F ) then return [-1]; fi;
     
@@ -118,6 +122,14 @@ BindGlobal("UnitGroupDescriptionPari", function( F )
     # execute PARI/GP
     result := ProcessPariGP(Concatenation(input), "units.gp");
 
+    # convert to GAP
+    eqn := EquationOrderBasis(F);
+    if result = [-1] then
+        result := [-1*eqn[1]];
+    else
+        result := List( result, x -> LinearCombination( eqn, x ) );
+    fi;
+
     # return result
     return result;
 end);