mod

From the SETL Wiki

mod
Category	arithmetic
Syntax	infix
Compatibility
CIMS SETL	yes
SETL-S	yes
SETL2	yes
GNU SETL	yes

Contents 1 Purpose 2 Synopsis 3 Description 4 Examples 5 Notes

Purpose

Integer modulus or symmetric set difference

Synopsis

 x mod y

Description

Either

1. x and y must both be integers, and the result is the positive remainder when x is divided by y, or
2. x and y must both be sets, and the result is a set containing every element in either x or y (but not in both).

The first case can also be defined as the smallest non-negative integer z such that (x - z) is an exact multiple of y.
In the second case it is equivalent to (x + y) - (x * y).

Examples

1. {1, 2, 3, 4, 5} mod {4, 5, 6}
   

   Result: {1, 2, 3, 6}

2. 14 mod 10
   

   Result: 4

3. -14 mod 10
   

   Result: 6

Notes

There is a difference between implementations when y is negative:

• In SETL-S and GNU SETL it is equivalent to x mod abs y.
• In SETL2 it is equivalent to -x mod -y.

In all cases the result is non-negative.