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Date: 14-7-2020
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Date: 14-3-2020
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Date: 17-12-2019
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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
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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 |
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ceiling function | -- | ceiling, least integer | Ceiling[x] |
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congruence | -- | -- | Mod[m, n] |
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floor function | ![]() |
floor, greatest integer, integer part | Floor[x] |
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fractional value | ![]() |
fractional part or ![]() |
SawtoothWave[x] |
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fractional part | ![]() |
no name | FractionalPart[x] |
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integer part | ![]() |
no name | IntegerPart[x] |
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nearest integer function | -- | -- | Round[x] |
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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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