tensor_ops.md
In ricci: Ricci Calculus

tensor kronecker product works

Code
  kron(arr %_% .(i, +j, k), l <- .(i, +j))
Condition
  Error in `kron()`:
  ! In `...`: indices with different positions cannot be combined.
  x Indices `i` and `j` have different positions.
  i Make sure you combine only indices of the same position.

Code
  kron(arr %_% .(i, j, k), l(m) <- .(i, j))
Condition
  Error in `.()`:
  ! Invalid expression in `...`.
  x Expression `l(m)` cannot be parsed.
  i A valid expressions is of the form {[+|-]<label1>, [+|-]<label2>, ...}.

Code
  kron(arr %_% .(i, j, k), i <- .(i, j), j)
Condition
  Error in `kron()`:
  ! Invalid expression in `...`.
  x Expression `j` cannot be parsed.
  i A valid expressions is of the form {.([+|-]<label1>, [+|-]<label2>, ...) -> [+|-]<label3>}.

raising tensor works

Code
  r(arr %_% .(+i), i)
Condition
  Error in `r()`:
  ! Argument `...` contains index with incorrect position.
  x Position of index `-i` does not match index position in <Labeled Array> [4] .(+i).
  i Make sure you explicitely specify the correct index position.

Code
  r(arr %_% .(i), i, g = g_mink_cart(2))
Condition
  Error in `r()`:
  ! Tensor index dimensions do not agree.
  x Tensor index `i` has dimension 4 in `arr %_% .(i)`.
  x Tensor index `i` has dimension 2 in `g_mink_cart(2)`.
  i Operation can only be carried out with two tensors having identical index dimensions.

substituting labels works

Code
  subst(arr %_% .(i, +j), k <- j)
Condition
  Error in `subst()`:
  ! Argument `...` contains index with incorrect position.
  x Position of index `-j` does not match index position in <Labeled Array> [2x2] .(-i, +j).
  i Make sure you explicitely specify the correct index position.

Code
  subst(arr %_% .(i, j), l <- k)
Condition
  Error in `subst()`:
  ! Argument `...` contains invalid index.
  x Index `k` not present in <Labeled Array> [2x2] .(-i, -j).
  i Make sure you only select indices that match the tensor indices.

Code
  subst(arr %_% .(i, j), error)
Condition
  Error in `subst()`:
  ! Invalid expression in `...`.
  x Expression `error` cannot be parsed.
  i A valid expressions is of the form {[+|-]<label1> -> [+|-]<label2>, ...}.

sym/asym warnings

Code
  sym(arr %_% .(i, j), i)
Condition
  Warning in `sym()`:
  Symmetrization over a single index has no effect.
  i You might want to consider to remove this call.
Output
  <Labeled Array> [2x2] .(-i, -j)
       [,1] [,2]
  [1,]    1    3
  [2,]    2    4

`at` works correctly

Code
  at(tensor("f(x)*y"), c(x = 0))
Condition
  Error in `at()`:
  ! Not all symbols are specified.
  x Symbols `f` and `y` not defined.
  Caused by error in `f()`:
  ! could not find function "f"