Quotient
المؤلف:
Graham, R. L.; Knuth, D. E.; and Patashnik, O
المصدر:
Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley
الجزء والصفحة:
...
18-11-2019
1689
Quotient
The term "quotient" is most commonly used to refer to the ratio 
of two quantities 
and 
, where 
.
Less commonly, the term quotient is also used to mean the integer part of such a ratio. In the Wolfram Language, the command Quotient[r, s] is defined in this latter sense, returning
where 
is the floor function. This is sometimes called 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]](http://mathworld.wolfram.com/images/equations/Quotient/Inline6.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="http://mathworld.wolfram.com/images/equations/Quotient/Inline12.gif" style="height:14px; 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] |
REFERENCES:
Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.
Spanier, J. and Oldham, K. B. An Atlas of Functions. Washington, DC: Hemisphere, p. 74, 1987.
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