Как найти корень функции в питоне

9.2.1. Number-theoretic and representation functions¶

math.ceil(x)¶

Return the ceiling of x, the smallest integer greater than or equal to x.
If x is not a float, delegates to x.__ceil__(), which should return an
Integral value.

math.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.

math.fabs(x)¶

Return the absolute value of x.

math.factorial(x)¶

Return x factorial. Raises ValueError if x is not integral or
is negative.

math.floor(x)¶

Return the floor of x, the largest integer less than or equal to x.
If x is not a float, delegates to x.__floor__(), which should return an
Integral value.

math.fmod(x, y)¶

Return fmod(x, y), as defined by the platform C library. Note that the
Python expression x % y may not return the same result. The intent of the C
standard is that fmod(x, y) be exactly (mathematically; to infinite
precision) equal to x - n*y for some integer n such that the result has
the same sign as x and magnitude less than abs(y). Python’s x % y
returns a result with the sign of y instead, and may not be exactly computable
for float arguments. For example, fmod(-1e-100, 1e100) is -1e-100, but
the result of Python’s -1e-100 % 1e100 is 1e100-1e-100, which cannot be
represented exactly as a float, and rounds to the surprising 1e100. For
this reason, function fmod() is generally preferred when working with
floats, while Python’s x % y is preferred when working with integers.

math.frexp(x)¶

Return the mantissa and exponent of x as the pair (m, e). m is a float
and e is an integer such that x == m * 2**e exactly. If x is zero,
returns (0.0, 0), otherwise 0.5 <= abs(m) < 1. This is used to “pick
apart” the internal representation of a float in a portable way.

math.fsum(iterable)¶

Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums:

>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
0.9999999999999999
>>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0

The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even. On some non-Windows
builds, the underlying C library uses extended precision addition and may
occasionally double-round an intermediate sum causing it to be off in its
least significant bit.

For further discussion and two alternative approaches, see the ASPN cookbook
recipes for accurate floating point summation.

math.gcd(a, b)¶

Return the greatest common divisor of the integers a and b. If either
a or b is nonzero, then the value of gcd(a, b) is the largest
positive integer that divides both a and b. gcd(0, 0) returns
0.

New in version 3.5.

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

Return True if the values a and b are close to each other and
False otherwise.

Whether or not two values are considered close is determined according to
given absolute and relative tolerances.

rel_tol is the relative tolerance – it is the maximum allowed difference
between a and b, relative to the larger absolute value of a or b.
For example, to set a tolerance of 5%, pass rel_tol=0.05. The default
tolerance is 1e-09, which assures that the two values are the same
within about 9 decimal digits. rel_tol must be greater than zero.

abs_tol is the minimum absolute tolerance – useful for comparisons near
zero. abs_tol must be at least zero.

If no errors occur, the result will be:
abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol).

The IEEE 754 special values of NaN, inf, and -inf will be
handled according to IEEE rules. Specifically, NaN is not considered
close to any other value, including NaN. inf and -inf are only
considered close to themselves.

New in version 3.5.

See also

PEP 485 – A function for testing approximate equality

math.isfinite(x)¶

Return True if x is neither an infinity nor a NaN, and
False otherwise. (Note that 0.0 is considered finite.)

New in version 3.2.

math.isinf(x)¶

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

math.isnan(x)¶

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

math.ldexp(x, i)¶

Return x * (2**i). This is essentially the inverse of function
frexp().

math.modf(x)¶

Return the fractional and integer parts of x. Both results carry the sign
of x and are floats.

math.remainder(x, y)¶

Return the IEEE 754-style remainder of x with respect to y. For
finite x and finite nonzero y, this is the difference x - n*y,
where n is the closest integer to the exact value of the quotient x /
y. If x / y is exactly halfway between two consecutive integers, the
nearest even integer is used for n. The remainder r = remainder(x,
y) thus always satisfies abs(r) <= 0.5 * abs(y).

Special cases follow IEEE 754: in particular, remainder(x, math.inf) is
x for any finite x, and remainder(x, 0) and
remainder(math.inf, x) raise ValueError for any non-NaN x.
If the result of the remainder operation is zero, that zero will have
the same sign as x.

On platforms using IEEE 754 binary floating-point, the result of this
operation is always exactly representable: no rounding error is introduced.

New in version 3.7.

math.trunc(x)¶

Return the Real value x truncated to an
Integral (usually an integer). Delegates to
x.__trunc__().

Note that frexp() and modf() have a different call/return pattern
than their C equivalents: they take a single argument and return a pair of
values, rather than returning their second return value through an ‘output
parameter’ (there is no such thing in Python).

For the ceil(), floor(), and modf() functions, note that all
floating-point numbers of sufficiently large magnitude are exact integers.
Python floats typically carry no more than 53 bits of precision (the same as the
platform C double type), in which case any float x with abs(x) >= 2**52
necessarily has no fractional bits.

9.2.2. Power and logarithmic functions¶

math.exp(x)¶

Return e raised to the power x, where e = 2.718281… is the base
of natural logarithms. This is usually more accurate than math.e ** x
or pow(math.e, x).

math.expm1(x)¶

Return e raised to the power x, minus 1. Here e is the base of natural
logarithms. For small floats x, the subtraction in exp(x) - 1
can result in a significant loss of precision; the expm1()
function provides a way to compute this quantity to full precision:

>>> from math import exp, expm1
>>> exp(1e-5) - 1  # gives result accurate to 11 places
1.0000050000069649e-05
>>> expm1(1e-5)    # result accurate to full precision
1.0000050000166668e-05

New in version 3.2.

math.log(x[, base])¶

With one argument, return the natural logarithm of x (to base e).

With two arguments, return the logarithm of x to the given base,
calculated as log(x)/log(base).

math.log1p(x)¶

Return the natural logarithm of 1+x (base e). The
result is calculated in a way which is accurate for x near zero.

math.log2(x)¶

Return the base-2 logarithm of x. This is usually more accurate than
log(x, 2).

New in version 3.3.

See also

int.bit_length() returns the number of bits necessary to represent
an integer in binary, excluding the sign and leading zeros.

math.log10(x)¶

Return the base-10 logarithm of x. This is usually more accurate
than log(x, 10).

math.pow(x, y)¶

Return x raised to the power y. Exceptional cases follow
Annex ‘F’ of the C99 standard as far as possible. In particular,
pow(1.0, x) and pow(x, 0.0) always return 1.0, even
when x is a zero or a NaN. If both x and y are finite,
x is negative, and y is not an integer then pow(x, y)
is undefined, and raises ValueError.

Unlike the built-in ** operator, math.pow() converts both
its arguments to type float. Use ** or the built-in
pow() function for computing exact integer powers.

math.sqrt(x)¶

Return the square root of x.

9.2.3. Trigonometric functions¶

math.acos(x)¶

Return the arc cosine of x, in radians.

math.asin(x)¶

Return the arc sine of x, in radians.

math.atan(x)¶

Return the arc tangent of x, in radians.

math.atan2(y, x)¶

Return atan(y / x), in radians. The result is between -pi and pi.
The vector in the plane from the origin to point (x, y) makes this angle
with the positive X axis. The point of atan2() is that the signs of both
inputs are known to it, so it can compute the correct quadrant for the angle.
For example, atan(1) and atan2(1, 1) are both pi/4, but atan2(-1,
-1) is -3*pi/4.

math.cos(x)¶

Return the cosine of x radians.

math.hypot(x, y)¶

Return the Euclidean norm, sqrt(x*x + y*y). This is the length of the vector
from the origin to point (x, y).

math.sin(x)¶

Return the sine of x radians.

math.tan(x)¶

Return the tangent of x radians.

9.2.4. Angular conversion¶

math.degrees(x)¶

Convert angle x from radians to degrees.

math.radians(x)¶

Convert angle x from degrees to radians.

9.2.5. Hyperbolic functions¶

Hyperbolic functions
are analogs of trigonometric functions that are based on hyperbolas
instead of circles.

math.acosh(x)¶

Return the inverse hyperbolic cosine of x.

math.asinh(x)¶

Return the inverse hyperbolic sine of x.

math.atanh(x)¶

Return the inverse hyperbolic tangent of x.

math.cosh(x)¶

Return the hyperbolic cosine of x.

math.sinh(x)¶

Return the hyperbolic sine of x.

math.tanh(x)¶

Return the hyperbolic tangent of x.

9.2.6. Special functions¶

math.erf(x)¶

Return the error function at
x.

The erf() function can be used to compute traditional statistical
functions such as the cumulative standard normal distribution:

def phi(x):
    'Cumulative distribution function for the standard normal distribution'
    return (1.0 + erf(x / sqrt(2.0))) / 2.0

New in version 3.2.

math.erfc(x)¶

Return the complementary error function at x. The complementary error
function is defined as
1.0 - erf(x). It is used for large values of x where a subtraction
from one would cause a loss of significance.

New in version 3.2.

math.gamma(x)¶

Return the Gamma function at
x.

New in version 3.2.

math.lgamma(x)¶

Return the natural logarithm of the absolute value of the Gamma
function at x.

New in version 3.2.

9.2.7. Constants¶

math.pi¶

The mathematical constant π = 3.141592…, to available precision.

math.e¶

The mathematical constant e = 2.718281…, to available precision.

math.tau¶

The mathematical constant τ = 6.283185…, to available precision.
Tau is a circle constant equal to 2π, the ratio of a circle’s circumference to
its radius. To learn more about Tau, check out Vi Hart’s video Pi is (still)
Wrong, and start celebrating
Tau day by eating twice as much pie!

New in version 3.6.

math.inf¶

A floating-point positive infinity. (For negative infinity, use
-math.inf.) Equivalent to the output of float('inf').

New in version 3.5.

math.nan¶

A floating-point “not a number” (NaN) value. Equivalent to the output of
float('nan').

New in version 3.5.

Содержание

1. Введение
2. Арифметические функции
3. Округление чисел. Функции ceil() и floor()
4. Возведение в степень. Функция pow()
5. Квадратный корень числа. Функция sqrt()
6. Модуль числа. Функция fabs()
7. Получение НОД. Функция gcd()
8. Вычисление суммы последовательности. Функция fsum()
9. Экспонента. Функция exp()
10. Тригонометрические функции
11. Константы
12. Логарифмы. Функции log() и log10()
13. Заключение

import math

x = 7.6
y = 3.2

print(math.ceil(x))  # выведет 8
print(math.floor(y)) # выведет 3

import math

print(math.pow(5, 3))  # выведет 125.0

import math

x = 25

print(math.sqrt(x)) # выведет 5.0

import math

print(math.fabs(-50))  # выведет 50.0

import math

x = 15
y = 30

print(math.gcd(x, y))  # выведет 15

import math

mylist = [1, 0.1, 0.2, 0.3, 3]
result = math.fsum(mylist)

print(result) # выведет 4.6

import math

x = math.exp(1)

print(x)  # выведет 2.718281828459045

import math

x = math.radians(45)

print(x)   # выведет 7853981633974483
print(math.sin(x))   # выведет 0.7071067811865476
print(math.cos(x))   # выведет 0.7071067811865476
print(math.tan(x))   # выведет 0.9999999999999999
print(math.asin(x))   # выведет 0.9033391107665127
print(math.acos(x))   # выведет 0.6674572160283838
print(math.atan(x))   # выведет 0.6657737500283538
print(math.degrees(x))   # выведет 45.0

import math

print(math.pi)  # выведет 3.141592653589793
print(math.e)   # выведет 2.718281828459045

log(x, base) = frac{ln(x)}{ln(base)}

import math

x = 10

print(math.log(x))  # выведет 2.302585092994046
print(math.log(x, 2))  # выведет 3.3219280948873626
print(math.log10(x))  # выведет 1.0 (логарифм по основанию 10)

Содержание

1. Функции представления чисел
2. ceil() и floor() — целая часть числа
3. Функция fabs() — модуль числа
4. factorial() — функция факториала
5. Функция fmod() — остаток от деления
6. Функция frexp()
7. Функция fsum() — точная сумма float
8. Функции возведения в степень и логарифма
9. Функция exp()
10. Функция expm1()
11. Функция log() — логарифм числа
12. Функция log1p()
13. Функция log10()
14. Функция pow() — степень числа
15. Функция sqrt() — квадратный корень числа
16. Тригонометрические функции
17. Функция преобразования углов
18. Математические константы

from math import floor, ceil

float_var = 3.14
first_int_var = floor(float_var)
second_int_var = ceil(float_var)
print(f'Число {float_var} имеет тип {type(float_var)}')
print(f'Округляем число {float_var} вниз и получаем {first_int_var}')
print('С типом', type(first_int_var))
print(f'Округляем число {float_var} вверх и получаем {second_int_var}')
print('С типом', type(second_int_var))
# Вывод:
Число 3.14 имеет тип <class 'float'>
Округляем число 3.14 вниз и получаем 3
С типом <class 'int'>
Округляем число 3.14 вверх и получаем 4
С типом <class 'int'>
  

from math import fabs

var = -3
first_int_var = abs(var)
second_int_var = fabs(var)
print(f'Число {var} имеет тип {type(float_var)}')
print(f'Модуль числа {var}, полученный функцией abs: {first_int_var}')
print('С типом', type(first_int_var))
print(f'Модуль числа {float_var}, полученный функцией fabs: {second_int_var}')
print('С типом', type(second_int_var))
print(abs(complex(1, 2)))
print(fabs(complex(1, 2)))
# Вывод:
Число -3 имеет тип <class 'int'>
Модуль числа -3, полученный функцией abs: 3
С типом <class 'int'>
Модуль числа -3, полученный функцией fabs: 3.0
С типом <class 'float'>
2.23606797749979
Traceback (most recent call last):
File "C:UsersivandAppDataRoamingJetBrainsPyCharm2021.2scratchesscratch.py", line 12, in
print(fabs(complex(1, 2)))
TypeError: can't convert complex to float
  

from math import factorial

var = 3
first_int_var = factorial(var)
print(f'Число {var} имеет тип {type(var)}')
print(f'Факториал числа {var}, полученный функцией factorial: {first_int_var}')
print('С типом', type(first_int_var))
# Вывод:
Число 3 имеет тип <class 'int'>
Факториал числа 3, полученный функцией factorial: 6
С типом <class 'int'>
  

from math import factorial

var = -3
first_int_var = factorial(var)
print(f'Число {var} имеет тип {type(var)}')
print(f'Факториал числа {var}, полученный функцией factorial: {first_int_var}')
print('С типом', type(first_int_var))
# Вывод:
Traceback (most recent call last):
File "C:UsersivandAppDataRoamingJetBrainsPyCharm2021.2scratchesscratch.py", line 4, in
first_int_var = factorial(var)
ValueError: factorial() not defined for negative values
from math import factorial

  

var = 3.14
first_int_var = factorial(var)
print(f'Число {var} имеет тип {type(var)}')
print(f'Факториал числа {var}, полученный функцией factorial: {first_int_var}')
print('С типом', type(first_int_var))
# Вывод:
C:UsersivandAppDataRoamingJetBrainsPyCharm2021.2scratchesscratch.py:4: DeprecationWarning: Using factorial() with floats is deprecated
first_int_var = factorial(var)
Traceback (most recent call last):
File "C:UsersivandAppDataRoamingJetBrainsPyCharm2021.2scratchesscratch.py", line 4, in
first_int_var = factorial(var)
ValueError: factorial() only accepts integral values
  

from math import fmod

var = 3.14
print('fmod(var, 2)', fmod(var, 2))
print('fmod(2, var)', fmod(2, var))
print('fmod(var, 1)', fmod(var, 1))
print('fmod(var, 3.14)', fmod(var, 3.14))
print('fmod(var, 50)', fmod(var, 50))
# Вывод:
fmod(var, 2) 1.1400000000000001
fmod(2, var) 2.0
fmod(var, 1) 0.14000000000000012
fmod(var, 3.14) 0.0
fmod(var, 50) 3.14
  

from math import frexp

var = 3.14
print('frexp(var)', frexp(var))
# Вывод:
frexp(var) (0.785, 2)
  

from math import fsum

var_list = [1/i for i in range(1, 10)]
print(f'Сумма элементов последовательностиn{var_list}nравна', fsum(var_list))
# Вывод:
Сумма элементов последовательности
[1.0, 0.5, 0.3333333333333333, 0.25, 0.2, 0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111]
равна 2.828968253968254
  

from math import exp

var_list = 3.14
print(f'exp(3.14):', exp(var_list))
# Вывод:
exp(3.14): 23.103866858722185
  

from math import exp, expm1

var_list = 3.14
print(f'exp(3.14) - 1:', exp(var_list) - 1)
print(f'expm1(3.14):', expm1(var_list))
# Вывод:
exp(3.14) - 1: 22.103866858722185
expm1(3.14): 22.103866858722185
  

from math import log

var_list = 3.14
print(f'log(3.14):', log(var_list))
# Вывод:
log(3.14): 1.144222799920162
  

from math import log, log1p

var_list = 3.14
print(f'log(3.14 + 1):', log(var_list + 1))
print(f'log1p(3.14):', log1p(var_list))
# Вывод:
log(3.14 + 1): 1.420695787837223
log1p(3.14): 1.420695787837223
  

from math import log10

var_list = 3.14
print(f'log10(3.14):', log10(var_list))
# Вывод:
log10(3.14): 0.49692964807321494
  

from math import pow

var_list = 3.14
print(f'pow(3.14, 10):', pow(var_list, 10))
print(f'pow(10, 3.14):', pow(10, var_list))
print(f'pow(10, 10):', pow(10, 10))
# Вывод:
pow(3.14, 10): 93174.3733866435
pow(10, 3.14): 1380.3842646028852
pow(10, 10): 10000000000.0
  

from math import sqrt

var_list = 3.14
print(f'sqrt(3.14):', sqrt(var_list))
print(f'sqrt(93174.3733866435):', sqrt(93174.3733866435))
print(f'sqrt(10000000000):', sqrt(10000000000))
# Вывод:
sqrt(3.14): 1.772004514666935
sqrt(93174.3733866435): 305.2447761824001
sqrt(10000000000): 100000.0

from math import sin, cos, tan, acos, atan, sinh, acosh, atanh, asin

var = 0.5
print('sin(var):', sin(var))
print('cos(var):', cos(var))
print('tan(var):', tan(var))
print('acos(var):', acos(var))
print('asin(var):', asin(var))
print('atan(var):', atan(var))
print('sinh(var):', sinh(var))
print('acosh(3.14):', acosh(3.14))
print('atanh(var):', atanh(var))
# Вывод:
sin(var): 0.479425538604203
cos(var): 0.8775825618903728
tan(var): 0.5463024898437905
acos(var): 1.0471975511965979
asin(var): 0.5235987755982989
atan(var): 0.4636476090008061
sinh(var): 0.5210953054937474
acosh(3.14): 1.810991348900196
atanh(var): 0.5493061443340549
  

from math import degrees, radians

var_1 = 3.14
var_2 = 4.13
print('degrees(var_1):', degrees(var_1))
print('radians(var_2):', radians(var_2))
# Вывод:
degrees(var_1): 179.9087476710785
radians(var_2): 0.07208209810736581
  

import math

# вывод значения PI
print("значение PI", math.pi)

# вывод значения e
print("значение e", math.e)
Вывод:
значение PI 3.141592653589793
значение e 2.718281828459045