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integer1
http://www.openmath.org/cd
http://www.openmath.org/cd/integer1.ocd
2006-03-30
2004-03-30
3
1
Author: OpenMath Consortium SourceURL: https://github.com/OpenMath/CDs
official
This CD holds a collection of basic integer functions. This CD is intended to be `compatible' with the corresponding elements in Content MathML.
factorof
application
This is the binary OpenMath operator that is used to indicate the mathematical relationship a "is a factor of" b, where a is the first argument and b is the second. This relationship is true if and only if b mod a = 0.
b is a factor of a iff remainder of a divided by b = 0
factorial
application
The symbol to represent a unary factorial function on non-negative integers.
factorial n = product [1..n]
1
quotient
application
The symbol to represent the integer (binary) division operator. That is, for integers a and b, quotient(a,b) denotes q such that a=b*q+r, with |r| less than |b| and a*r positive.
for all a,b with a,b Integers | a = b * quotient(a,b) + remainder(a,b) and abs(remainder(a,b)) is less than abs(b) and a*remainder(a,b) >= 0
remainder
application
The symbol to represent the integer remainder after (binary) division. For integers a and b, remainder(a,b) denotes r such that a=b*q+r, with |r| less than |b| and a*r positive.
for all a,b with a,b Integers | a = b * quotient(a,b) + remainder(a,b) and abs(remainder(a,b)) is less than abs(b) and a*remainder(a,b) >= 0