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14 Mathematics
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Know About Floating-Point Arithmetic by David Goldberg, in Computing Surveys, Association for Computing Machinery, March 1991 is also a worthy read (this article is easy to find on the Internet if you simply search for the title) The IBM General Decimal Arithmetic Specification contains more information and can be easily located online through search engines
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The fractions module defines a class Fraction that represents a rational number Instances can be created in three different ways using the class constructor:
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Fraction([numerator [,denominator]])
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Creates a new rational number numerator and denominator have integral values and default to 0 and 1, respectively
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Fraction(fraction)
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If fraction is an instance of numbersRational, creates a new rational number with the same value as fraction
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Fraction(s)
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If s is a string containing a fraction such as "3/7" or "-4/7", a fraction with the same value is created If s is a decimal number such as "125", a fraction with that value is created (eg, Fraction(5,4)) The following class methods can create Fraction instances from other types of objects:
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Fractionfrom_float(f)
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Creates a fraction representing the exact value of the floating-point number f
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Fractionfrom_decimal(d)
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Creates a fraction representing the exact value of the Decimal number d Here are some examples of using these functions:
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>>> f = fractionsFraction(3,4) >>> g = fractionsFraction("175") >>> g Fraction(7, 4) >>> h = fractionsFractionfrom_float(31415926) Fraction(3537118815677477, 1125899906842624) >>>
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An instance f of Fraction supports all of the usual mathematical operationsThe numerator and denominator are stored in the fnumerator and fdenominator attributes, respectively In addition, the following method is defined:
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flimit_denominator([max_denominator])
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Returns the fraction that has the closest value to f max_denominator specifies the largest denominator to use and defaults to 1000000
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math
Here are some examples of using Fraction instances (using the values created in the earlier example):
>>> f + g Fraction(5, 2) >>> f * g Fraction(21, 16) >>> hlimit_denominator(10) Fraction(22, 7) >>>
The fractions module also defines a single function:
gcd(a, b)
Computes the greatest common divisor of integers a and bThe result has the same sign as b if b is nonzero; otherwise, it s the same sign as a
math
The math module defines the following standard mathematical functionsThese functions operate on integers and floats but don t work with complex numbers (a separate module cmath can be used to perform similar operations on complex numbers)The return value of all functions is a float All trigonometric functions assume the use of radians
Function
acos(x) acosh(x) asin(x) asinh(x) atan(x) atan2(y, x) atanh(x) ceil(x) copysign(x,y) cos(x) cosh(x) degrees(x) radians(x) exp(x) fabs(x) factorial(x) floor(x) fmod(x, y) frexp(x) fsum(s) hypot(x, y)
Description
Returns the arc cosine of x Returns the hyperbolic arc cosine of x Returns the arc sine of x Returns the hyperbolic arc sine of x Returns the arc tangent of x Returns atan(y / x) Returns the hyperbolic arc tangent of x Returns the ceiling of x Returns x with the same sign as y Returns the cosine of x Returns the hyperbolic cosine of x Converts x from radians to degrees Converts x from degrees to radians Returns e ** x Returns the absolute value of x Returns x factorial Returns the floor of x Returns x % y as computed by the C fmod() function Returns the positive mantissa and exponent of x as a tuple Returns the full precision sum of floating-point values in the iterable sequence s See the following note for a description Returns the Euclidean distance, sqrt(x * x + y * y) continues
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Function
isinf(x) isnan(x) ldexp(x, i) log(x [, base]) log10(x) log1p(x) modf(x) pow(x, y) sin(x) sinh(x) sqrt(x) tan(x) tanh(x) trunc(x)
Description
Return True if x is infinity Returns True if x is NaN Returns x * (2 ** i) Returns the logarithm of x to the given base If base is omitted, this function computes the natural logarithm Returns the base 10 logarithm of x Returns the natural logarithm of 1+x Returns the fractional and integer parts of x as a tuple Both have the same sign as x Returns x ** y Returns the sine of x Returns the hyperbolic sine of x Returns the square root of x Returns the tangent of x Returns the hyperbolic tangent of x Truncates x to the nearest integer towards 0
The following constants are defined: