Improve DefineTensor

It actually works as it should now. It takes two arguments, the symbol
which will be used in tensor expressions and the symbol which represents
its numerical discretisation.

Tools/CodeGen/xTensorKranc.m

@@ -22,7 +22,7 @@
 ];
 
 DefineTensor::usage = "DefineTensor[T[a, b, ...]] defines the tensor T with indices a, b, c, ....";
-DefineDerivative::usage = "DefineDerivative[pd] registers a symbol to be used as a derivative operator.";
+DefineDerivative::usage = "DefineDerivative[pd, nd] registers a symbol pd to be used as a derivative operator, with numerical discretisation nd.";
 SetComponents::usage = "SetComponents[T[a, b, ...], v] defines the components of the tensor T to be the values given in the list v."
 
 CreateGroupFromTensor::usage = "CreateGroupFromTensor[T[a, b, ...]] Creates a variable group from the tensor T";
@@ -70,10 +70,15 @@
 DefineTensor[t_[inds___], opts___] :=
  Block[{$DefInfoQ = False}, DefTensor[t[inds], KrancManifold, opts]];
 
-DefineDerivative[pd_] :=
+DefineDerivative[pd_, numderiv_] :=
  Block[{$DefInfoQ = False},
   InfoMessage[InfoFull, "Defining derivative:", pd];
-  DefCovD[pd[-$KrancIndices[[1]]], Curvature -> False, Torsion -> False]
+  Module[{nd},
+    DefInertHead[nd];
+    NumericalDiscretisation[nd] ^= numderiv;
+    pd[i_][t_] := nd[PDKrancBasis[i][t]];
+    pd[t_, i_] := nd[PDKrancBasis[i][t]];
+  ]
 ];
 
 toBasis[x_] :=
@@ -106,8 +111,8 @@
       SymbolJoin[t, Sequence @@ ToString /@ {i}[[All, 1]]], 
     t_Symbol?xTensorQ[] :> t,
     (* FIXME: Better handling of derivatives *)
-    (* pd_?CovDQ[i : (_?CIndexQ ..)][t_?xTensorQ] :> SymbolJoin[pd, krancForm[t], i[[1]]] *)
-    PDKrancBasis[i_][t_] :> Global`PDstandard2nd[krancForm[t], i[[1]]]};
+    nd_[pd_?CovDQ[i : (_?CIndexQ ..)][t_?xTensorQ[inds__]]] :> NumericalDiscretisation[nd][krancForm[t[inds]], i[[1]]]
+  };
 
 SetAttributes[ExpandComponents, Listable];
 ExpandComponents[lhs_ -> rhs_] :=