Mod

In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of (mod ) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language).

The function is related to the floor function by

			(1)
			(2)

where denotes the quotient, i.e., integer division.

Since usage concerning fractional part/value and integer part/value can be confusing, the following table gives a summary of names and notations used. Here, S&O indicates Spanier and Oldham (1987).

notation	name	S&O	Graham et al.	Wolfram Language
	ceiling function	--	ceiling, least integer	Ceiling[x]
	congruence	--	--	Mod[m, n]
	floor function		floor, greatest integer, integer part	Floor[x]
	fractional value		fractional part or	SawtoothWave[x]
	fractional part		no name	FractionalPart[x]
	integer part		no name	IntegerPart[x]
	nearest integer function	--	--	Round[x]
	quotient	--	--	Quotient[m, n]