Is there a proper way to distinguish base from index variable?
For this instance, let's say we have a paper that deals with cryptographic keys both in different bases and with different indices.
For different bases we might say that our binary function outputs a binary key and our ternary function outputs a ternary key: $$f_2(x) = K_2$$ $$f_3(x) = K_3$$
For indices we might later describe a process in which we have sub-functions that generate sub-keys (think hash family): $$f_1(x) = K_1$$ $$f_2(x) = K_2$$ $$f_3(x) = K_3$$
Some things I've considered:
- Specifying in english that the subscript is either base or index ($i$).
- Prefixing base with 'b': $K_{b3}$.
- Prefixing the index with 'i': $K_{i3}$
- Using lowercase for keys with indices and uppercase for keys with base. I don't like this because it leads a reader to mistakenly infer that a based key can be described in some form of sub-keys.
My favorite of the options I listed is 1.
Mathematicians use subscripts and superscripts for many, many different things. Usually the meaning is clear from the context. For example, in algebra if you saw "$x^i$", you would expect this to be some number $x$ raised to the $i$-th power. But in differential geometry, you would expect it to be the $i$-th coordinate in some coordinate system.
When the context of your subscript or superscript is not sufficient to distinguish between possible meanings, one should always explain which is meant (your option 1), or if needed, use a different notation than subscripts or superscripts.