math
This module contains functions and constants to make trigonometric and
non-trignonometric mathematics a breeze. The module also defines a couple
of commonly used scientific and mathematical constants such as PI.
Properties
-
PI:
represents the ratio of the circumference of a circle to its diameter
-
E:
represents Euler's number, the base of natural logarithms
-
LOG_10:
represents the natural logarithm of 10
-
LOG_10_E:
represents the base 10 logarithm of e
-
LOG_2:
represents the natural logarithm of 2
-
LOG_2_E:
represents the base 2 logarithm of e
-
ROOT_2:
represents the square root of 2
-
ROOT_3:
represents the square root of 3
-
ROOT_HALF:
represents the square root of 1/2
-
Infinity:
Mathematical infinity
-
NaN:
Mathematical NaN
Functions
factorial(n)
factorial(n: number) calculates the product of all positive numbers less than or equal to a given positive number n
Example:
%> import math
%> math.factorial(60)
8.320987112741392e+81Returns
- number
sin(n)
Returns a numeric value between -1 and 1, which represents the sine of the angle given in radians.
Example:
%> math.sin(46)
0.9017883476488092Parameters
- number n
Returns
- number
cos(n)
Returns a numeric value between -1 and 1, which represents the cosine of the angle.
Example:
%> math.cos(93)
0.3174287015197017Parameters
- number n
Returns
- number
tan(n)
Returns a numeric value that represents the tangent of the angle given.
Example:
%> math.tan(11.43)
-2.155225644164932Parameters
- number n
Returns
- number
sinh(n)
Returns the hyperbolic sine (in radians) of number n.
Example:
%> math.sinh(1.4)
1.904301501451534Parameters
- number n
Returns
- number
cosh(n)
Returns the hyperbolic cosine (in radians) of number n.
Example:
%> math.cosh(1.91)
3.450584592563374Parameters
- number n
Returns
- number
tanh(n)
Returns the hyperbolic tangent (in radians) of number n.
Example:
%> math.tanh(2.19)
0.975
Parameters
- number n
Returns
- number2591705196751
asin(n)
Returns a numeric value between -(π/2) and π/2 radians for x between -1 and 1. If the value of x is outside this range, it returns NaN.
Example:
%> math.asin(0.123)
0.123312275191872Parameters
- number n
Returns
- number
acos(n)
Returns a numeric value between 0 and π radians for x between -1 and 1. If the value of x is outside this range, it returns NaN.
Example:
%> math.acos(0.471)
1.080372275769021Parameters
- number n
Returns
- number
atan(n)
Returns a numeric value between -(π/2) and π/2 radians.
Example:
%> math.atan(math.Infinity)
1.570796326794897Parameters
- number n
Returns
- number
atan2(x, y)
Returns a numeric value between -π and π representing the angle theta of an (x, y) point. This is the counterclockwise angle, measured in radians, between the positive X axis, and the point (x, y).
Example:
%> math.atan2(math.Infinity, -math.Infinity)
2.356194490192345
%> math.atan2(1, 2)
0.4636476090008061
%> math.atan2(-1.5, 2.4)
-0.5585993153435624Parameters
- number n
Returns
- number
Notes
- the arguments to this function pass the y-coordinate first and the x-coordinate second.
asinh(n)
Returns the hyperbolic arcsine (in radians) of number n.
Example:
%> math.asinh(3.42)
1.943507380182802Parameters
- number n
Returns
- number
acosh(n)
Returns the hyperbolic arccosine (in radians) of number n.
Example:
%> math.acosh(1.21)
0.637237379754108Parameters
- number n
Returns
- number
atanh(n)
Returns the hyperbolic arctangent (in radians) of number n.
Example:
%> math.atanh(0.11)
0.1104469157900971Parameters
- number n
Returns
- number
exp(n)
Returns e ** x, where x is the argument, and e is Euler's number (also known as Napier's constant), the base of the natural logarithms.
Example:
%> math.exp(4)
54.59815003314424Parameters
- number n
Returns
- number
expm1(n)
Returns (e ** x) - 1, where x is the argument, and e the base of the natural logarithms.
Example:
%> math.expm1(1)
1.718281828459045Parameters
- number n
Returns
- number
ceil(n)
Returns number n rounded up to the next largest integer.
Example:
%> math.ceil(1.65)
2
%> math.ceil(1.01)
2Parameters
- number n
Returns
- number
round(n)
Returns the value of a number rounded to the nearest integer.
Example:
%> math.round(103.51)
104
%> math.round(103.49)
103Parameters
- number n
Returns
- number
log(n)
Returns the natural logarithm (base e) of a number (mathematical ln(x)).
Example:
%> math.log(45)
3.80666248977032Parameters
- number n
Returns
- number
Notes
- If the value of x is 0, the return value is always -inf.
- If the value of x is negative, the return value is always NaN.
log2(n)
Returns the base 2 logarithm of the given number. If the number is negative, NaN is returned
Example:
%> math.log2(45)
5.491853096329675Parameters
- number n
Returns
- number
log10(n)
Returns the base 10 logarithm of the given number. If the number is negative, NaN is returned.
Example:
%> math.log10(45)
1.653212513775344Parameters
- number n
Returns
- number
log1p(n)
For very small values of x, adding 1 can reduce or eliminate precision.
The double floats used in JS give you about 15 digits of precision.
1 + 1e-15 = 1.000000000000001, but 1 + 1e-16 = 1.000000000000000 and therefore
exactly 1.0 in that arithmetic, because digits past 15 are rounded off.
When you calculate log(1 + x), you should get an answer very close to x,
if x is small (that's why these are called 'natural' logarithms).
If you calculate log(1 + 1.1111111111e-15) you should get an answer
close to 1.1111111111e-15.
Instead, you will end up taking the logarithm of 1.00000000000000111022
(the roundoff is in binary so sometimes it gets ugly), so you get the answer
1.11022...e-15, with only 3 correct digits.
If, instead, you calculate log1p(1.1111111111e-15) you will get a much
more accurate answer 1.1111111110999995e-15 with 15 correct digits of precision
(actually 16 in this case).
returns the natural logarithm (base e) of 1 + a number If the value of x is less than -1, the return value is always NaN.
Example:
%> math.log1p(45)
3.828641396489095Parameters
- number n
Returns
- number
cbrt(n)
Returns the cube root of a number n.
Example:
%> math.cbrt(64)
4Parameters
- number n
Returns
- number
sign(n)
Returns either a positive or negative +/- 1, indicating the sign of a number passed into the argument. If the number passed into sign() is 0, it will return a 0.
Example:
%> math.sign(10)
1
%> math.sign(-20)
-1
%> math.sign(-0)
-0
%> math.sign(0)
0Parameters
- number n
Returns
- number
floor(n)
A number representing the largest integer less than or equal to the specified number
Example:
%> math.floor(1.92)
1Parameters
- number n
Returns
- number
is_nan(n)
is_nan(n: number)
returns true if the given number is equal to NaN or false otherwise.
Parameters
- number n
Returns
- bool
is_inf(n)
Returns true if the given number is equal to Infinity or -Infinity
or false otherwise.
Example:
%> math.is_inf(math.Infinity)
true
%> math.is_inf(-math.Infinity)
true
%> math.is_inf(0)
falseParameters
- number n
Returns
- bool
is_finite(n)
Return true if x is neither an Infinity nor a NaN, and false otherwise.
Example:
%> math.is_finite(0)
true
%> math.is_finite(math.NaN)
true
%> math.is_finite(-math.Infinity)
falseParameters
- number n
Returns
- bool
trunc(n)
Returns the integer part of a number by removing any fractional.
Example:
%> math.trunc(1.92)
1
%> math.trunc(1.0)
1
%> math.trunc(1.01)
1
%> math.trunc(-1.01)
-1Parameters
- number n
Returns
- number
sqrt(n)
Returns the square root of a nunmber.
Example:
%> math.sqrt(100)
10Parameters
- number n
Returns
- number
sum(arg)
Calculates the sum of all the elements in the input iterable the default start value for the product is 1. when the iterable is empty, it returns 1
Example:
%> math.sum([1, 2, [3, 4, [5, 6]]])
21Parameters
- iterable arg
Returns
- number
product(arg)
Calculates the product of all the elements in the input iterable the default start value for the product is 1. when the iterable is empty, it returns 1
Example:
%> math.product([1, 2, [3, 4, [5, 6]]])
720Parameters
- iterable arg
Returns
- number
fraction(n)
Returns the fractional part of a number as a whole number by removing any integer
Example:
%> math.fraction(1.92)
92Parameters
- number n
Returns
- number