In many computer languages (such as FORTRAN or Mathematica), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Mathematica).
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 (D. W. Cantrell, pers. comm.). Here, S&O indicates Spanier and Oldham (1987).
| notation | name | S&O | Graham et al. | Mathematica |
 |
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  |
no name |
 |
fractional part |  |
no name | FractionalPart[ x] |
 |
integer part |  |
no name | IntegerPart[ x] |
 |
nearest integer | -- | -- | Round[ x] |
|
quotient | -- | -- | Quotient[ m, n] |
Ceiling Function, Common Residue, Congruence, Fractional Part, Integer Part, Minimal Residue, Nearest Integer, Quotient, Residue