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/* Contract indices in expression */
/* NOTE: buildq works like splicing a list with quasiquote in lisp; escaped
items are defined at start of quote */
contr(expr, var) ::= (
if listp(var) and length(var) > 1 then buildq(
[expr, head : first(var), tail : rest(var)],
sum(contr(expr, tail), head, 1, 4))
elseif listp(var) and length(var) = 1 then buildq(
[expr, head : first(var)], sum(expr, head, 1, 4))
elseif listp(var) then (
expr)
else buildq([expr, var],
sum(expr, var, 1, 4)));
/* Differentiate with respect to nth coordinate */
cdiff(func, coord) := diff(func, ct_coords[coord])$
/* Wave operator */
box_op(func) := (
expand(contr(ug[μ,ν] * cdiff(cdiff(func, ν), μ), [μ,ν])
- contr(ug[μ,ν] * mcs[μ,ν,ρ] * cdiff(func, ρ), [μ,ν,ρ])))$
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)));
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