Clean mathematical notation of a for-loop

Question

I am sorry if this doesn't really belong here but I'm looking for a way to describe the mathematical background of my code. Using numpy I sum two more dimensional arrays:

a.shape = (10, 5, 2)
b.shape = (5, 2)
c = a + b
c.shape = (10, 5, 2)

Is there a pure mathematical notation for this (so WITHOUT indroducing for-loops or numpy conventions in my text)? What I'm trying to avoid is to have to write something like this:

c_{1, y, z} = a_{1, y, z} + b_{y, z}

c_{2, y, z} = a_{2, y, z} + b_{y, z}

...

c_{10, y, z} = a_{10, y, z} + b_{y, z}

Any thoughts?

Edit: I'm using LaTeX for the documentation, so indexing is no problem. I'm currently using more or less the suggestion from Tobias. I was just hoping that there may be some other solution I haven't thought of.

Answer 1

Just write

for .

You find this form often in books on numerics like Numerical Recipes (e.g., page 57).

If you have larger sections of code an alternative is to use pseudo-code.