Elementary Mathematical Array operations especially matrix multiplication

[oxinabox]

• *
• +
• -

This needs to be done such that:

• If both operations are NamedDimsArrays then they must have the same named dimensions.

• If 1 operand is a NamedDimsArray, and one is not, then the answer uses the named dimensions of the one that is provided.

  • This lets you use a + parent(b) to add a and b that have different named dimensions.

• * is special,

  • for a * b then we only require the the the name of the last dimension of a needs to match that of the first of b.
  • if one of the operands is not a NamedDimsArray then the result of the operation will have to insert made up names for one of the dimensions.
    • Possibly for ease of implementation we should define names(::AbstractArray) to return those names.
    • I originally thought dim1 and dim2, however on further reflection I think that just calling all artificial dimensions :_ is best.
    • using dim1 and dim2 doesn't help much with avoiding named clashes: Consider where b has names and a does not then the name of ``(abb'a')is(:dim1, :dim2)`. And the mathematically equivalent: `(ab)(ab)'` would get the name `(:dim1, :dim1)`.
      - repairing names of something that has a name `(:, :)` by premultiplcation by something with names `(:time, :)` and post-multiplcation by `(:, :value)` seems easier if you don't have to workout where (prepositionally) the original dimension that was added was from.
      • We might even want to make :_ a special case that is an exception to the rule of dimension names must match for NamedDimArray-NamedDimArray operation.