mod

Modulus

x mod y    mod[x;y]

Where x and y are numeric, returns the remainder of x%y.

q)-3 -2 -1 0 1 2 3 4 mod 3
0 1 2 0 1 2 0 1

q)7 mod 2 3 4
1 1 3

q)-7 7 mod/:\:-2.5 -2 2 2.5
-2   -1 1 0.5
-0.5 -1 1 2

Implicit iteration

mod is an atomic function.

q)(10;20 30)mod(7 13;-12)
3  10
-4 -6

It applies to dictionaries and keyed tables.

q)d mod 5
a| 0 4 3
b| 4 0 4

q)5 mod d
a| 5 -16 2
b| 1 0   -1

q)k mod 5
k  | a b
---| ---
abc| 0 4
def| 4 0
ghi| 3 4

Domain and range

    b g x h i j e f c s p m d z n u v t
----------------------------------------
b | i . i i i j e f . . p m d z n u v t
g | . . . . . . . . . . . . . . . . . .
x | i . i i i j e f . . p m d z n u v t
h | i . i i i j e f . . p m d z n u v t
i | i . i i i j e f . . p m d z n u v t
j | j . j j j j e f . . p m d z n u v t
e | f . f f f f f f f . f f z z f f f f
f | f . f f f f f f f . f f z z f f f f
c | . . . . . . . f . . p m d z n u v t
s | . . . . . . . . . . . . . . . . . .
p | n . n n n n n f n . . . . . . . . .
m | i . i i i i i f i . . . . . . . . .
d | i . i i i i i . i . . . . . . . . .
z | f . f f f f f f f . . . . . . . . .
n | n . n n n n n f n . . . . . . . . .
u | u . u u u u u f u . . . . . . . . .
v | v . v v v v v f v . . . . . . . . .
t | t . t t t t t f t . . . . . . . . .

Range: defijmnptuvz

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% Divide, div, reciprocal
Mathematics
Q for Mortals: §4.8.1 Integer Division div and Modulus mod