Does the function $f(x,y) = ((x-1) \mod y)+1$ have an existing name?


`f(1,5) = 1`   

`f(2,5) = 2`   

`f(3,5) = 3`   

`f(4,5) = 4`   

`f(5,5) = 5`   

`f(6,5) = 1`   

`f(7,5) = 2`   




What is the name of the function f(x,y) = ((x-1) mod y)+1  ?
In math, as opposed to in computer science, when you apply "mod y" you land in the integers modulo y, denoted Z/yZ, not back in the integers. This means that mod 7, the symbols 1 and 8 *denote the same thing*, i.e. the equivalence class {...,-13,-6,1,8,15,...}. 


A more computer-y way to say this is that for mathematicians, "integer mod 7" is a different kind of data class than "integer."


All this is just a long way of saying that this is probably the wrong place to ask your question.


If I were defining this function in a math paper I'd say something like "Let f(x,y) denote the unique number in {1,2,...,y} which is congruent to x modulo y" or "By the division algorithm there exists a unique number in {1,2,...,y} which is congruent to x modulo y, we denote this number f(x,y)."


