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nums1
http://www.openmath.org/cd
http://www.openmath.org/cd/nums1.ocd
2014-04-01
2009-04-01
4
0
Author: OpenMath Consortium SourceURL: https://github.com/OpenMath/CDs
official
This CD is intended to be `compatible' with the MathML view of constructors for numbers (integers to an arbitrary base, rationals) and symbols for some common numerical constants. This CD holds a set of symbols for creating numbers, including some defined constants (i.e. nullary constructors).
based_integer
application
This symbol represents the constructor function for integers, specifying the base. It takes two arguments, the first is a positive integer to denote the base to which the number is represented, the second argument is a string which contains an optional sign and the digits of the integer, using 0-9a-z (as a consequence of this no radix greater than 36 is supported). Base 16 and base 10 are already covered in the encodings of integers.
A representation of 8 (radix 10) base 8
8
8
10
based_float
application
This symbol represents the constructor function for floating point numbers, specifying the base. It takes two arguments, the first is a positive integer to denote the base to which the number is represented, the second argument is a string which contains an optional sign and the digits of the number, using 0-9a-z and optionally a "." (as a consequence of this no radix greater than 36 is supported).
A representation of 8.5 (radix 10) base 8
8
10.4
rational
application
This symbol represents the constructor function for rational numbers. It takes two arguments, the first is an integer p to denote the numerator and the second a nonzero integer q to denote the denominator of the rational p/q.
A representation of the rational number 1/2
1
2
infinity
constant
A symbol to represent the notion of infinity.
if x is a real number then x < infinity
e
constant
This symbol represents the base of the natural logarithm, approximately 2.718. See Abramowitz and Stegun, Handbook of Mathematical Functions, section 4.1.
e = the sum as j ranges from 0 to infinity of 1/(j!)
2.718 = The decimal approximation to 3 significant places of e
i
constant
This symbol represents the square root of -1.
i^2 = -1
2
pi
constant
A symbol to convey the notion of pi, approximately 3.142. The ratio of the circumference of a circle to its diameter.
pi = 4 * the sum as j ranges from 0 to infinity of ((1/(4j+1))-(1/(4j+3)))
4
4
4
3
3.142 = The decimal approximation to 3 significant places of pi
gamma
constant
A symbol to convey the notion of the gamma constant as defined in Abramowitz and Stegun, Handbook of Mathematical Functions, section 6.1.3. It is the limit of 1 + 1/2 + 1/3 + ... + 1/m - ln m as m tends to infinity, this is approximately 0.5772 15664.
gamma = limit_(m -> infinity)(sum_(j ranges from 1 to m)(1/j) - ln m)
1
0.577 = The decimal approximation to 3 significant places of gamma
NaN
constant
A symbol to convey the notion of not-a-number. The result of an ill-posed floating computation. See IEEE standard for floating point representations.
NaN is not equal to NaN