mod {numbers}

Modulo Operator

Description

Modulo operator.

Usage

mod(n, m)

modq(a, b, k)

Arguments

n

numeric vector (preferably of integers)

m

integer vector (positive, zero, or negative)

a, b

whole numbers (scalars)

k

integer greater than 1

Details

mod(n, m) is the modulo operator and returns n mod m. mod(n, 0) is n, and the result always has the same sign as m.

modq(a, b, k) is the modulo operator for rational numbers and returns a/b mod k. b and k must be coprime, otherwise NA is returned.

Value

a numeric (integer) value or vector/matrix, resp. an integer number

Note

The following relation is fulfilled (for m != 0):

mod(n, m) = n - m * floor(n/m)

See Also

rem, div

Examples

mod(c(-5:5), 5)
mod(c(-5:5), -5)
mod(0, 1)         #=> 0
mod(1, 0)         #=> 1

modq(5, 66, 5)    # 0  (Bernoulli 10)
modq(5, 66, 7)    # 4
modq(5, 66, 13)   # 5
modq(5, 66, 25)   # 5
modq(5, 66, 35)   # 25
modq(-1,  30, 7)  # 3  (Bernoulli 8)
modq( 1, -30, 7)  # 3

# Warning messages:
# modq(5, 66, 77)       : Arguments 'b' and 'm' must be coprime.
# Error messages
# modq(5, 66, 1)        : Argument 'm' mustbe a natural number > 1.
# modq(5, 66, 1.5)      : All arguments of 'modq' must be integers.
# modq(5, 66, c(5, 7))  : Function 'modq' is *not* vectorized.