math

This module provides access to the mathematical functions
defined by the C standard.

Functions

acos

acos(x, /)

  Return the arc cosine (measured in radians) of x.

  The result is between 0 and pi.

acosh

acosh(x, /)

  Return the inverse hyperbolic cosine of x.

asin

asin(x, /)

  Return the arc sine (measured in radians) of x.

  The result is between -pi/2 and pi/2.

asinh

asinh(x, /)

  Return the inverse hyperbolic sine of x.

atan

atan(x, /)

  Return the arc tangent (measured in radians) of x.

  The result is between -pi/2 and pi/2.

atan2

atan2(y, x, /)

  Return the arc tangent (measured in radians) of y/x.

  Unlike atan(y/x), the signs of both x and y are considered.

atanh

atanh(x, /)

  Return the inverse hyperbolic tangent of x.

ceil

ceil(x, /)

  Return the ceiling of x as an Integral.

  This is the smallest integer >= x.

comb

comb(n, k, /)

  Number of ways to choose k items from n items without repetition and without order.

  Evaluates to n! / (k! * (n - k)!) when k <= n and evaluates
  to zero when k > n.

  Also called the binomial coefficient because it is equivalent
  to the coefficient of k-th term in polynomial expansion of the
  expression (1 + x)**n.

  Raises TypeError if either of the arguments are not integers.
  Raises ValueError if either of the arguments are negative.

copysign

copysign(x, y, /)

  Return a float with the magnitude (absolute value) of x but the sign of y.

  On platforms that support signed zeros, copysign(1.0, -0.0)
  returns -1.0.

cos

cos(x, /)

  Return the cosine of x (measured in radians).

cosh

cosh(x, /)

  Return the hyperbolic cosine of x.

degrees

degrees(x, /)

  Convert angle x from radians to degrees.

dist

dist(p, q, /)

  Return the Euclidean distance between two points p and q.

  The points should be specified as sequences (or iterables) of
  coordinates.  Both inputs must have the same dimension.

  Roughly equivalent to:
      sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))

erf

erf(x, /)

  Error function at x.

erfc

erfc(x, /)

  Complementary error function at x.

exp

exp(x, /)

  Return e raised to the power of x.

expm1

expm1(x, /)

  Return exp(x)-1.

  This function avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small x.

fabs

fabs(x, /)

  Return the absolute value of the float x.

factorial

factorial(x, /)

  Find x!.

  Raise a ValueError if x is negative or non-integral.

floor

floor(x, /)

  Return the floor of x as an Integral.

  This is the largest integer <= x.

fmod

fmod(x, y, /)

  Return fmod(x, y), according to platform C.

  x % y may differ.

frexp

frexp(x, /)

  Return the mantissa and exponent of x, as pair (m, e).

  m is a float and e is an int, such that x = m * 2.**e.
  If x is 0, m and e are both 0.  Else 0.5 <= abs(m) < 1.0.

fsum

fsum(seq, /)

  Return an accurate floating point sum of values in the iterable seq.

  Assumes IEEE-754 floating point arithmetic.

gamma

gamma(x, /)

  Gamma function at x.

gcd

gcd(*integers)

  Greatest Common Divisor.

hypot

hypot(...)

  hypot(*coordinates) -> value

  Multidimensional Euclidean distance from the origin to a point.

  Roughly equivalent to:
      sqrt(sum(x**2 for x in coordinates))

  For a two dimensional point (x, y), gives the hypotenuse
  using the Pythagorean theorem:  sqrt(x*x + y*y).

  For example, the hypotenuse of a 3/4/5 right triangle is:

      >>> hypot(3.0, 4.0)
      5.0

isclose

isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)

  Determine whether two floating point numbers are close in value.

    rel_tol
      maximum difference for being considered "close", relative to the
      magnitude of the input values
    abs_tol
      maximum difference for being considered "close", regardless of the
      magnitude of the input values

  Return True if a is close in value to b, and False otherwise.

  For the values to be considered close, the difference between them
  must be smaller than at least one of the tolerances.

  -inf, inf and NaN behave similarly to the IEEE 754 Standard.  That
  is, NaN is not close to anything, even itself.  inf and -inf are
  only close to themselves.

isfinite

isfinite(x, /)

  Return True if x is neither an infinity nor a NaN, and False otherwise.

isinf

isinf(x, /)

  Return True if x is a positive or negative infinity, and False otherwise.

isnan

isnan(x, /)

  Return True if x is a NaN (not a number), and False otherwise.

isqrt

isqrt(n, /)

  Return the integer part of the square root of the input.

lcm

lcm(*integers)

  Least Common Multiple.

ldexp

ldexp(x, i, /)

  Return x * (2**i).

  This is essentially the inverse of frexp().

lgamma

lgamma(x, /)

  Natural logarithm of absolute value of Gamma function at x.

log

log(...)

  log(x, [base=math.e])
  Return the logarithm of x to the given base.

  If the base not specified, returns the natural logarithm (base e) of x.

log10

log10(x, /)

  Return the base 10 logarithm of x.

log1p

log1p(x, /)

  Return the natural logarithm of 1+x (base e).

  The result is computed in a way which is accurate for x near zero.

log2

log2(x, /)

  Return the base 2 logarithm of x.

modf

modf(x, /)

  Return the fractional and integer parts of x.

  Both results carry the sign of x and are floats.

nextafter

nextafter(x, y, /)

  Return the next floating-point value after x towards y.

perm

perm(n, k=None, /)

  Number of ways to choose k items from n items without repetition and with order.

  Evaluates to n! / (n - k)! when k <= n and evaluates
  to zero when k > n.

  If k is not specified or is None, then k defaults to n
  and the function returns n!.

  Raises TypeError if either of the arguments are not integers.
  Raises ValueError if either of the arguments are negative.

pow

pow(x, y, /)

  Return x**y (x to the power of y).

prod

prod(iterable, /, *, start=1)

  Calculate the product of all the elements in the input iterable.

  The default start value for the product is 1.

  When the iterable is empty, return the start value.  This function is
  intended specifically for use with numeric values and may reject
  non-numeric types.

radians

radians(x, /)

  Convert angle x from degrees to radians.

remainder

remainder(x, y, /)

  Difference between x and the closest integer multiple of y.

  Return x - n*y where n*y is the closest integer multiple of y.
  In the case where x is exactly halfway between two multiples of
  y, the nearest even value of n is used. The result is always exact.

sin

sin(x, /)

  Return the sine of x (measured in radians).

sinh

sinh(x, /)

  Return the hyperbolic sine of x.

sqrt

sqrt(x, /)

  Return the square root of x.

tan

tan(x, /)

  Return the tangent of x (measured in radians).

tanh

tanh(x, /)

  Return the hyperbolic tangent of x.

trunc

trunc(x, /)

  Truncates the Real x to the nearest Integral toward 0.

  Uses the __trunc__ magic method.

ulp

ulp(x, /)

  Return the value of the least significant bit of the float x.

Other members

e = 2.718281828459045

inf = inf

nan = nan

pi = 3.141592653589793

tau = 6.283185307179586