Mod
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21-10-2020
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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
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 |
![[x]](https://mathworld.wolfram.com/images/equations/Mod/Inline12.gif) |
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 ![<span style=]() {x}" src="https://mathworld.wolfram.com/images/equations/Mod/Inline18.gif" style="height:15px; width:17px" /> |
SawtoothWave[x] |
 |
fractional part |
 |
no name |
FractionalPart[x] |
 |
integer part |
 |
no name |
IntegerPart[x] |
 |
nearest integer function |
-- |
-- |
Round[x] |
 |
quotient |
-- |
-- |
Quotient[m, n] |
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