Suggestions on syntax to express mathematical formula concisely

Question

I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible.

I posted a proto

Answer 1

You may want to look at APLish languages for inspiration. By working with the matrix/array as a whole, you can get the brevity down quite a bit. I'm going to use Q below, and unless I misread your post, your second statement can be written as:

sum raze (T-flip T) div e

To understand T minus flip T, you need to look at an example. Imagine we have T set to the following matrix:

0 1 2
3 4 5
6 7 8

flip T swaps the top two dimensions, which results in:

0 3 6
1 4 7
2 5 8

So T-flip T is basically T(i,j)-T(j,i) but a lot less typing, and thus a lot less error-prone.

The raze reduces an array to a single dimension, so razing this:

0 3 6
1 4 7
2 5 8

turns it into this:

0 3 6 1 4 7 2 5 8

Finally, the sum is sum-over; it basically adds up all of the members of its list, so

sum 0 3 6 1 4 7 2 5 8

means:

0+3+6+1+4+7+2+5+8

Implementing this kind of thing in C++ isn't that difficult; you could:

sum(raze((T-flip(T))/e))

with the right level of operator overloading.

By the way, K is even more brief:

+/,/(T-+:T)%e