Add cov_diff

1 files changed, 34 insertions, 0 deletions

diff --git a/tensors.mac b/tensors.mac
index 2249b0d..b396991 100644
--- a/tensors.mac
+++ b/tensors.mac
@@ -24,3 +24,37 @@ box_op(func) := (
 mappend(f, list) := apply(append, map(f, list));
 
 ensure_list(x) := if listp(x) then x else [x];
+
+/*
+WARNING: Preppended "-" means covariant index *not* contravariant like in
+         itensor package
+
+TODO: Handle sums
+NOTE: Does not work on complex expressions, just indexed arrays
+*/
+cov_diff(sim,i) ::= (
+  if atom(sim) then (
+    buildq([sim, i], cdiff(sim, i)))
+  elseif op(sim) = "+" then (
+    buildq([terms : args(sim), i],
+      apply("+", map(lambda([x], cov_diff(x, i)), terms))))
+  else block(
+    [ten : op(sim), inds : args(sim), covp, terms],
+    if not listp(inds) then (
+      error(printf(false, "Expected indexed object, got ~a", inds))),
+    covp : map(lambda([x], not atom(x) and op(x)="-"), inds),
+    inds : map(lambda([x], if atom(x) then x else first(args(x))), inds),
+    terms : map(lambda([sgn,index],
+        block([k : gensym()],
+          /* Covariant */
+          if sgn then buildq(
+            [ten, inds : subst(index=k, inds), i, index, k],
+            - sum(mcs[i, index, k] * ten[splice(inds)],k,1,4))
+          /* Contravariant */
+          else buildq(
+            [ten, inds : subst(index=k, inds), i, index, k],
+            sum(mcs[i, k, index] * ten[splice(inds)],k,1,4)))),
+      covp, inds),
+    buildq(
+      [i, ten, inds, terms : apply("+", terms)],
+      cdiff(ten[splice(inds)], i) + terms)));