Módulo Math

Este módulo proporciona acceso a las funciones matemáticas que permiten realizar tanto operaciones matemáticas básicas como sumar, restar, multiplicar y dividir, así como para trabajar con operaciones avanzadas con números complejos, raíces cuadradas, logaritmos, etc. En este artículo aprenderemos a cómo usar el módulo math de Python.

Importar el módulo math

Antes de usar el módulo math, debemos importarlo al comienzo de su programa. Esto se hace usando la instrucción import de la siguiente manera:

import math

Una vez importado podemos hacer uso de todas las funciones que provee este módulo. Para hacernos una idea de la gran cantidad de funciones que tiene este módulo, podemos abrir el interprete y escribir lo siguiente:

import math

help(math)

Help on built-in module math:

NAME
    math

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

FUNCTIONS
    acos(x, /)
        Return the arc cosine (measured in radians) of x.

        The result is between 0 and pi.

    acosh(x, /)
        Return the inverse hyperbolic cosine of x.

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

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

    asinh(x, /)
        Return the inverse hyperbolic sine of x.

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

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

    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(x, /)
        Return the inverse hyperbolic tangent of x.

    cbrt(x, /)
        Return the cube root of x.

    ceil(x, /)
        Return the ceiling of x as an Integral.

        This is the smallest integer >= x.

    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(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(x, /)
        Return the cosine of x (measured in radians).

    cosh(x, /)
        Return the hyperbolic cosine of x.

    degrees(x, /)
        Convert angle x from radians to degrees.

    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(x, /)
        Error function at x.

    erfc(x, /)
        Complementary error function at x.

    exp(x, /)
        Return e raised to the power of x.

    exp2(x, /)
        Return 2 raised to the power of x.

    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(x, /)
        Return the absolute value of the float x.

    factorial(n, /)
        Find n!.

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

    floor(x, /)
        Return the floor of x as an Integral.

        This is the largest integer <= x.

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

        x % y may differ.

    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(seq, /)
        Return an accurate floating point sum of values in the iterable seq.

        Assumes IEEE-754 floating point arithmetic.

    gamma(x, /)
        Gamma function at x.

    gcd(*integers)
        Greatest Common Divisor.

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

    isinf(x, /)
        Return True if x is a positive or negative infinity, and False otherwise.

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

    isqrt(n, /)
        Return the integer part of the square root of the input.

    lcm(*integers)
        Least Common Multiple.

    ldexp(x, i, /)
        Return x * (2**i).

        This is essentially the inverse of frexp().

    lgamma(x, /)
        Natural logarithm of absolute value of Gamma function at x.

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

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

    log10(x, /)
        Return the base 10 logarithm of x.

    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(x, /)
        Return the base 2 logarithm of x.

    modf(x, /)
        Return the fractional and integer parts of x.

        Both results carry the sign of x and are floats.

    nextafter(x, y, /, *, steps=None)
        Return the floating-point value the given number of steps after x towards y.

        If steps is not specified or is None, it defaults to 1.

        Raises a TypeError, if x or y is not a double, or if steps is not an integer.
        Raises ValueError if steps is negative.

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

    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(x, /)
        Convert angle x from degrees to radians.

    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(x, /)
        Return the sine of x (measured in radians).

    sinh(x, /)
        Return the hyperbolic sine of x.

    sqrt(x, /)
        Return the square root of x.

    sumprod(p, q, /)
        Return the sum of products of values from two iterables p and q.

        Roughly equivalent to:

            sum(itertools.starmap(operator.mul, zip(p, q, strict=True)))

        For float and mixed int/float inputs, the intermediate products
        and sums are computed with extended precision.

    tan(x, /)
        Return the tangent of x (measured in radians).

    tanh(x, /)
        Return the hyperbolic tangent of x.

    trunc(x, /)
        Truncates the Real x to the nearest Integral toward 0.

        Uses the __trunc__ magic method.

    ulp(x, /)
        Return the value of the least significant bit of the float x.

DATA
    e = 2.718281828459045
    inf = inf
    nan = nan
    pi = 3.141592653589793
    tau = 6.283185307179586

FILE
    (built-in)

Obtener raíces cuadradas

Encontrar la raíz cuadrada de un número es sencillo a través de la función sqrt. Veamos algunos ejemplos:

# importar módulo
import math

# Retornamos la raíz cuadrada de diferentes números:

print(math.sqrt(8))
print(math.sqrt(27))
print(math.sqrt(64))

2.8284271247461903
5.196152422706632
8.0

Como podemos ver el resultado que nos retorna la función math.sqrt() es un vamor de tipo float. Si quieres redondar el resultado debes usar la función integrada round(). Repitamos el ejercicio anterior aplicando valores redondeado a 1 decimal:

# importar módulo
import math

# Retornamos la raíz cuadrada de diferentes números:

print(round(math.sqrt(8), 1))
print(round(math.sqrt(27), 1))
print(round(math.sqrt(64), 1))

2.8
5.1
8.0

Calcular potencias

En python tenemos diferentes alternativas para calcular potencias, sin embargo la función math.pow() es la que nos interesa conocer, si queremos calcular una potencia de un número debemos pasar dicho número como primer argumento a la función y como segundo argumento la potencia a elevar lo que se traduce a lo siguiente:

math.pow(x, y) # retorna x elevado a la potencia y

A diferencia de utilizar el operador incorporado **, la función math.pow() convierte ambos argumentos al tipo float.

Utiliza ** o la función incorporada pow() para calcular potencias enteras exactas.

Veamos aquellas diferencia en el siguiente ejemplo:

import math

print(pow(2, 4))
print(2 ** 4)
print(math.pow(2, 4))

16
16
16.0

Calcular la distancia entre dos puntos

Poder calcular la distancia entre dos puntos tenemos la función math.dist() claro que estamos hablando de la distancia euclidiana también conocida como distancia “ordinaria” que es una variación del teorema de Pitágoras.

La función math.dist() recibe dos parámetros (p y q) que deben tener las mismas dimensiones. Veamos un caso de uso:

import math 

p = [3, 3] 
q = [6, 12] 

# Calcular la distancia euclidiana
print (math.dist(p, q))

9.486832980505138