Numeric and Mathematical Modules

The modules described in this chapter provide numeric and math-related functions and data types. The numbers module defines an abstract hierarchy of numeric types. The math and cmath modules contain various mathematical functions for floating-point and complex numbers. The decimal module supports exact representations of decimal numbers, using arbitrary precision arithmetic.

The following modules are documented in this chapter:

• numbers — Numeric abstract base classes
  • Number
  • The numeric tower
    • Complex
      • real
      • imag
      • conjugate()
    • Real
    • Rational
      • numerator
      • denominator
    • Integral
  • Notes for type implementers
    • Adding More Numeric ABCs
    • Implementing the arithmetic operations
• math — Mathematical functions
  • Number-theoretic and representation functions
    • ceil()
    • comb()
    • copysign()
    • fabs()
    • factorial()
    • floor()
    • fma()
    • fmod()
    • frexp()
    • fsum()
    • gcd()
    • isclose()
    • isfinite()
    • isinf()
    • isnan()
    • isqrt()
    • lcm()
    • ldexp()
    • modf()
    • nextafter()
    • perm()
    • prod()
    • remainder()
    • sumprod()
    • trunc()
    • ulp()
  • Power and logarithmic functions
    • cbrt()
    • exp()
    • exp2()
    • expm1()
    • log()
    • log1p()
    • log2()
    • log10()
    • pow()
    • sqrt()
  • Trigonometric functions
    • acos()
    • asin()
    • atan()
    • atan2()
    • cos()
    • dist()
    • hypot()
    • sin()
    • tan()
  • Angular conversion
    • degrees()
    • radians()
  • Hyperbolic functions
    • acosh()
    • asinh()
    • atanh()
    • cosh()
    • sinh()
    • tanh()
  • Special functions
    • erf()
    • erfc()
    • gamma()
    • lgamma()
  • Constants
    • pi
    • e
    • tau
    • inf
    • nan
• cmath — Mathematical functions for complex numbers
  • Conversions to and from polar coordinates
    • phase()
    • polar()
    • rect()
  • Power and logarithmic functions
    • exp()
    • log()
    • log10()
    • sqrt()
  • Trigonometric functions
    • acos()
    • asin()
    • atan()
    • cos()
    • sin()
    • tan()
  • Hyperbolic functions
    • acosh()
    • asinh()
    • atanh()
    • cosh()
    • sinh()
    • tanh()
  • Classification functions
    • isfinite()
    • isinf()
    • isnan()
    • isclose()
  • Constants
    • pi
    • e
    • tau
    • inf
    • infj
    • nan
    • nanj
• decimal — Decimal fixed-point and floating-point arithmetic
  • Quick-start Tutorial
  • Decimal objects
    • Decimal
      • adjusted()
      • as_integer_ratio()
      • as_tuple()
      • canonical()
      • compare()
      • compare_signal()
      • compare_total()
      • compare_total_mag()
      • conjugate()
      • copy_abs()
      • copy_negate()
      • copy_sign()
      • exp()
      • from_float()
      • fma()
      • is_canonical()
      • is_finite()
      • is_infinite()
      • is_nan()
      • is_normal()
      • is_qnan()
      • is_signed()
      • is_snan()
      • is_subnormal()
      • is_zero()
      • ln()
      • log10()
      • logb()
      • logical_and()
      • logical_invert()
      • logical_or()
      • logical_xor()
      • max()
      • max_mag()
      • min()
      • min_mag()
      • next_minus()
      • next_plus()
      • next_toward()
      • normalize()
      • number_class()
      • quantize()
      • radix()
      • remainder_near()
      • rotate()
      • same_quantum()
      • scaleb()
      • shift()
      • sqrt()
      • to_eng_string()
      • to_integral()
      • to_integral_exact()
      • to_integral_value()
    • Logical operands
  • Context objects
    • getcontext()
    • setcontext()
    • localcontext()
    • BasicContext
    • ExtendedContext
    • DefaultContext
    • Context
      • clear_flags()
      • clear_traps()
      • copy()
      • copy_decimal()
      • create_decimal()
      • create_decimal_from_float()
      • Etiny()
      • Etop()
      • abs()
      • add()
      • canonical()
      • compare()
      • compare_signal()
      • compare_total()
      • compare_total_mag()
      • copy_abs()
      • copy_negate()
      • copy_sign()
      • divide()
      • divide_int()
      • divmod()
      • exp()
      • fma()
      • is_canonical()
      • is_finite()
      • is_infinite()
      • is_nan()
      • is_normal()
      • is_qnan()
      • is_signed()
      • is_snan()
      • is_subnormal()
      • is_zero()
      • ln()
      • log10()
      • logb()
      • logical_and()
      • logical_invert()
      • logical_or()
      • logical_xor()
      • max()
      • max_mag()
      • min()
      • min_mag()
      • minus()
      • multiply()
      • next_minus()
      • next_plus()
      • next_toward()
      • normalize()
      • number_class()
      • plus()
      • power()
      • quantize()
      • radix()
      • remainder()
      • remainder_near()
      • rotate()
      • same_quantum()
      • scaleb()
      • shift()
      • sqrt()
      • subtract()
      • to_eng_string()
      • to_integral_exact()
      • to_sci_string()
  • Constants
    • MAX_PREC
    • MAX_EMAX
    • MIN_EMIN
    • MIN_ETINY
    • HAVE_THREADS
    • HAVE_CONTEXTVAR
  • Rounding modes
    • ROUND_CEILING
    • ROUND_DOWN
    • ROUND_FLOOR
    • ROUND_HALF_DOWN
    • ROUND_HALF_EVEN
    • ROUND_HALF_UP
    • ROUND_UP
    • ROUND_05UP
  • Signals
    • Clamped
    • DecimalException
    • DivisionByZero
    • Inexact
    • InvalidOperation
    • Overflow
    • Rounded
    • Subnormal
    • Underflow
    • FloatOperation
  • Floating-Point Notes
    • Mitigating round-off error with increased precision
    • Special values
  • Working with threads
  • Recipes
  • Decimal FAQ
• fractions — Rational numbers
  • Fraction
    • numerator
    • denominator
    • as_integer_ratio()
    • is_integer()
    • from_float()
    • from_decimal()
    • limit_denominator()
    • __floor__()
    • __ceil__()
    • __round__()
    • __format__()
• random — Generate pseudo-random numbers
  • Bookkeeping functions
    • seed()
    • getstate()
    • setstate()
  • Functions for bytes
    • randbytes()
  • Functions for integers
    • randrange()
    • randint()
    • getrandbits()
  • Functions for sequences
    • choice()
    • choices()
    • shuffle()
    • sample()
  • Discrete distributions
    • binomialvariate()
  • Real-valued distributions
    • random()
    • uniform()
    • triangular()
    • betavariate()
    • expovariate()
    • gammavariate()
    • gauss()
    • lognormvariate()
    • normalvariate()
    • vonmisesvariate()
    • paretovariate()
    • weibullvariate()
  • Alternative Generator
    • Random
      • seed()
      • getstate()
      • setstate()
      • random()
      • getrandbits()
    • SystemRandom
  • Notes on Reproducibility
  • Examples
  • Recipes
  • Command-line usage
  • Command-line example
• statistics — Mathematical statistics functions
  • Averages and measures of central location
  • Measures of spread
  • Statistics for relations between two inputs
  • Function details
    • mean()
    • fmean()
    • geometric_mean()
    • harmonic_mean()
    • kde()
    • kde_random()
    • median()
    • median_low()
    • median_high()
    • median_grouped()
    • mode()
    • multimode()
    • pstdev()
    • pvariance()
    • stdev()
    • variance()
    • quantiles()
    • covariance()
    • correlation()
    • linear_regression()
  • Exceptions
    • StatisticsError
  • NormalDist objects
    • NormalDist
      • mean
      • median
      • mode
      • stdev
      • variance
      • from_samples()
      • samples()
      • pdf()
      • cdf()
      • inv_cdf()
      • overlap()
      • quantiles()
      • zscore()
  • Examples and Recipes
    • Classic probability problems
    • Monte Carlo inputs for simulations
    • Approximating binomial distributions
    • Naive bayesian classifier