tensor_arith.md
In ricci: Ricci Calculus

tensor multiplication yields correct errors

Code
  a %_% .(i) * b %_% .(+i)
Condition
  Error in `` `*`() ``:
  ! Tensor index dimensions do not agree.
  x Tensor index `i` has dimension 4 in `e1`.
  x Tensor index `i` has dimension 3 in `e2`.
  i Operation can only be carried out with two tensors having identical index dimensions.

tensor addition works

Code
  arr %_% .(i, j) + arr %_% .(k, l)
Condition
  Error in `` `+`() ``:
  ! Tensor indices do not agree.
  x Tensor index `i` and `j` appear in `e1` but not in `e2`.
  x Tensor index `k` and `l` appear in `e2` but not in `e1`.
  i Operation can only be carried out with two tensors having identical indices.

Code
  arr %_% .(i, j) + arr2 %_% .(i)
Condition
  Error in `` `+`() ``:
  ! Tensor ranks do not agree.
  x Tensor rank of `e1` is 2.
  x Tensor rank of `e2` is 1.
  i Operation can only be carried out with two tensors of same rank.

Code
  arr %_% .(i, j) + arr %_% .(+i, j)
Condition
  Error in `` `+`() ``:
  ! Tensor index positions do not agree.
  x Tensor index `i` appears with different positions in `e1` and `e2`.
  i Operation can only be carried out with two tensors having identical index positions.