Как поставить бесконечность в питоне
As ironic as it may seem infinity is defined as an undefined number that can either be a positive or negative value. All arithmetic operations performed on an infinite value always lead to an infinite number, say it be sum, subtraction, multiplication, or any other operation.
In the world of computer science, infinity is generally used to measure performance and optimize algorithms that perform computations on a large scale application.
Representing infinity as an Integer in python
The concept of representing infinity as an integer violates the definition of infinity itself. As of 2020, there is no such way to represent infinity as an integer in any programming language so far. But in python, as it is a dynamic language, float values can be used to represent an infinite integer. One can use float(‘inf’) as an integer to represent it as infinity. Below is the list of ways one can represent infinity in Python.
1. Using float(‘inf’) and float(‘-inf’):
As infinity can be both positive and negative they can be represented as a float(‘inf’) and float(‘-inf’) respectively. The below code shows the implementation of the above-discussed content:
math — Mathematical functions¶
This module provides access to the mathematical functions defined by the C standard.
These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don’t is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number used as a parameter, so that the programmer can determine how and why it was generated in the first place.
The following functions are provided by this module. Except when explicitly noted otherwise, all return values are floats.
Number-theoretic and representation functions¶
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.
Return the 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 (1 + x)ⁿ .
Raises TypeError if either of the arguments are not integers. Raises ValueError if either of the arguments are negative.
New in version 3.8.
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.
Return the absolute value of x.
math. factorial ( n ) ¶
Return n factorial as an integer. Raises ValueError if n is not integral or is negative.
Deprecated since version 3.9: Accepting floats with integral values (like 5.0 ) is deprecated.
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.
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.
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:
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 ( * integers ) ¶
Return the greatest common divisor of the specified integer arguments. If any of the arguments is nonzero, then the returned value is the largest positive integer that is a divisor of all arguments. If all arguments are zero, then the returned value is 0 . gcd() without arguments returns 0 .
New in version 3.5.
Changed in version 3.9: Added support for an arbitrary number of arguments. Formerly, only two arguments were supported.
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.
PEP 485 – A function for testing approximate equality
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.
Return True if x is a positive or negative infinity, and False otherwise.
Return True if x is a NaN (not a number), and False otherwise.
Return the integer square root of the nonnegative integer n. This is the floor of the exact square root of n, or equivalently the greatest integer a such that a² ≤ n.
For some applications, it may be more convenient to have the least integer a such that n ≤ a², or in other words the ceiling of the exact square root of n. For positive n, this can be computed using a = 1 + isqrt(n — 1) .
New in version 3.8.
Return the least common multiple of the specified integer arguments. If all arguments are nonzero, then the returned value is the smallest positive integer that is a multiple of all arguments. If any of the arguments is zero, then the returned value is 0 . lcm() without arguments returns 1 .
New in version 3.9.
Return x * (2**i) . This is essentially the inverse of function frexp() .
Return the fractional and integer parts of x. Both results carry the sign of x and are floats.
Return the next floating-point value after x towards y.
math.nextafter(x, math.inf) goes up: towards positive infinity.
math.nextafter(x, -math.inf) goes down: towards minus infinity.
math.nextafter(x, 0.0) goes towards zero.
math.nextafter(x, math.copysign(math.inf, x)) goes away from zero.
New in version 3.9.
Return the 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.
New in version 3.8.
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.
New in version 3.8.
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.
Return x with the fractional part removed, leaving the integer part. This rounds toward 0: trunc() is equivalent to floor() for positive x, and equivalent to ceil() for negative x. If x is not a float, delegates to x.__trunc__ , which should return an Integral value.
Return the value of the least significant bit of the float x:
If x is a NaN (not a number), return x.
If x is negative, return ulp(-x) .
If x is a positive infinity, return x.
If x is equal to zero, return the smallest positive denormalized representable float (smaller than the minimum positive normalized float, sys.float_info.min ).
If x is equal to the largest positive representable float, return the value of the least significant bit of x, such that the first float smaller than x is x — ulp(x) .
Otherwise (x is a positive finite number), return the value of the least significant bit of x, such that the first float bigger than x is x + ulp(x) .
ULP stands for “Unit in the Last Place”.
New in version 3.9.
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.
Power and logarithmic functions¶
Return the cube root of x.
New in version 3.11.
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) .
Return 2 raised to the power x.
New in version 3.11.
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:
New in version 3.2.
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) .
Return the natural logarithm of 1+x (base e). The result is calculated in a way which is accurate for x near zero.
Return the base-2 logarithm of x. This is usually more accurate than log(x, 2) .
New in version 3.3.
int.bit_length() returns the number of bits necessary to represent an integer in binary, excluding the sign and leading zeros.
Return the base-10 logarithm of x. This is usually more accurate than log(x, 10) .
Return x raised to the power y . Exceptional cases follow the IEEE 754 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.
Changed in version 3.11: The special cases pow(0.0, -inf) and pow(-0.0, -inf) were changed to return inf instead of raising ValueError , for consistency with IEEE 754.
Return the square root of x.
Trigonometric functions¶
Return the arc cosine of x, in radians. The result is between 0 and pi .
Return the arc sine of x, in radians. The result is between -pi/2 and pi/2 .
Return the arc tangent of x, in radians. The result is between -pi/2 and pi/2 .
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 .
Return the cosine of x radians.
Return the Euclidean distance between two points p and q, each given as a sequence (or iterable) of coordinates. The two points must have the same dimension.
Roughly equivalent to:
New in version 3.8.
Return the Euclidean norm, sqrt(sum(x**2 for x in coordinates)) . This is the length of the vector from the origin to the point given by the coordinates.
For a two dimensional point (x, y) , this is equivalent to computing the hypotenuse of a right triangle using the Pythagorean theorem, sqrt(x*x + y*y) .
Changed in version 3.8: Added support for n-dimensional points. Formerly, only the two dimensional case was supported.
Changed in version 3.10: Improved the algorithm’s accuracy so that the maximum error is under 1 ulp (unit in the last place). More typically, the result is almost always correctly rounded to within 1/2 ulp.
Return the sine of x radians.
Return the tangent of x radians.
Angular conversion¶
Convert angle x from radians to degrees.
Convert angle x from degrees to radians.
Hyperbolic functions¶
Hyperbolic functions are analogs of trigonometric functions that are based on hyperbolas instead of circles.
Return the inverse hyperbolic cosine of x.
Return the inverse hyperbolic sine of x.
Return the inverse hyperbolic tangent of x.
Return the hyperbolic cosine of x.
Return the hyperbolic sine of x.
Return the hyperbolic tangent of x.
Special functions¶
The erf() function can be used to compute traditional statistical functions such as the cumulative standard normal distribution:
New in version 3.2.
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.
New in version 3.2.
Return the natural logarithm of the absolute value of the Gamma function at x.
New in version 3.2.
Constants¶
The mathematical constant π = 3.141592…, to available precision.
The mathematical constant e = 2.718281…, to available precision.
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.
A floating-point positive infinity. (For negative infinity, use -math.inf .) Equivalent to the output of float(‘inf’) .
New in version 3.5.
A floating-point “not a number” (NaN) value. Equivalent to the output of float(‘nan’) . Due to the requirements of the IEEE-754 standard, math.nan and float(‘nan’) are not considered to equal to any other numeric value, including themselves. To check whether a number is a NaN, use the isnan() function to test for NaNs instead of is or == . Example:
Changed in version 3.11: It is now always available.
New in version 3.5.
CPython implementation detail: The math module consists mostly of thin wrappers around the platform C math library functions. Behavior in exceptional cases follows Annex F of the C99 standard where appropriate. The current implementation will raise ValueError for invalid operations like sqrt(-1.0) or log(0.0) (where C99 Annex F recommends signaling invalid operation or divide-by-zero), and OverflowError for results that overflow (for example, exp(1000.0) ). A NaN will not be returned from any of the functions above unless one or more of the input arguments was a NaN; in that case, most functions will return a NaN, but (again following C99 Annex F) there are some exceptions to this rule, for example pow(float(‘nan’), 0.0) or hypot(float(‘nan’), float(‘inf’)) .
Note that Python makes no effort to distinguish signaling NaNs from quiet NaNs, and behavior for signaling NaNs remains unspecified. Typical behavior is to treat all NaNs as though they were quiet.
Бесконечность в Python – Установите значение переменной Python в бесконечность
Простое число не может представлять ваш набор данных? Как насчет установки вашей переменной значения в бесконечность в Python? Сегодня мы говорим только о том, что!
- Автор записи
Простое число не может представлять ваш набор данных? Как насчет установки вашей переменной значения в бесконечность в Python? Сегодня мы говорим только о том, что!
При кодировании в Python нам часто нужно инициализировать переменную с большим положительным или большим отрицательным значением. Это очень распространено при сравнении переменных для расчета минимального или максимума в наборе.
Позитивная бесконечность В Python считается самым большим положительным значением и Отрицательная бесконечность считается самым большим отрицательным числом.
В этом руководстве мы узнаем три способа инициализации переменных с положительной и отрицательной бесконечностью. Наряду с этим мы также узнаем, как проверить, является ли переменная бесконечность или нет, а также выполняет некоторые арифметические операции на этих переменных.
Инициализация поплавок переменных с бесконечности в Python
Самый простой способ установить переменную к положительной или отрицательной бесконечности без использования каких-либо модулей, используя Float.
Вы можете установить переменную к положительной бесконечности, используя следующую строку кода:
Чтобы распечатать значение переменной использования:
Чтобы инициализировать переменную с отрицательным использованием бесконечности:
Инициализация переменных с бесконечностью, используя numpy модуль
Вы также можете использовать популярный модуль Numpy для инициализации переменных с положительной или отрицательной бесконечнойностью.
Давайте начнем, импортируя модуль Numpy.
Теперь мы можем использовать модуль для инициализации переменной к положительной бесконечности, как показано ниже:
Выход выходит как:
Чтобы инициализировать переменную с отрицательным использованием бесконечности:
Выход выходит как:
Полный код
Полный код из этого раздела приведен ниже.
Инициализация переменных с бесконечностью в Python с использованием математического модуля
Третий метод инициализации переменных до бесконечности является использованием математического модуля в Python.
Давайте начнем, импортируя модуль.
Чтобы установить переменную к положительной бесконечности, используя математический модуль, используйте следующую строку кода:
Чтобы установить переменную к отрицательной бесконечности, используя математический модуль, используйте следующую строку кода:
Помимо этого, математический модуль также дает вам метод, который позволяет проверять, установлена ли переменная на бесконечность или нет.
How to Represent an Infinite Number in Python?
Infinity is an undefined number which can be negative or positive. A number is used as infinity; sometimes, the sum of two numeric values may be a numeric but different pattern; it may be a negative or positive value.
It is used to compare the solution in algorithms for the best solution. Generally, a value set at initial may be positive or negative infinity; we have to take care that no input value is bigger or smaller.
Infinity in Python
In Python, there is no way or method to represent infinity as an integer. This matches the fundamental characteristic of many other popular programming languages. But due to python being dynamically typed language, you can use float(inf) as an integer to represent it as infinity.
Therefore in python, we cannot represent infinity, or we can say that there is no way to show the infinity as an integer. But we can use float (inf) as an integer.
In Python, positive infinity and negative infinity can be represented by:
- Positive infinity: inf
- Negative infinity: -inf
Python Program to Define Positive and Negative Infinity Number
Example
Represent Positive and Negative Infinity Using the Math Module
To determine the infinity number, you can use the python math module.
Note: This will work with only python 3.5 or higher version of python.
Syntax:
- Positive infinity: math.inf
- Negative infinity: -math.inf
Positive infinity number is greatest, and the negative infinity number is the smallest of all numbers.
In comparison, positive infinity is always bigger than every natural number.
(i.e. 0,1,2. +∞. Positive integer and +infinity.)
In comparison, negative infinity is smaller than the negative number.
(i.e., ∞-. -2,-1,0, 1,.2,3. – negative infinity and -integer.)
Python Program to Check If the Number Is Infinite
In the above example, we are using the using isinf method of math library to check if the number is infinity or not.
Represent Positive and Negative Infinity Using the Decimal Module
You can define positive and negative Infinity by using the decimal module.
Syntax:
- Positive Infinity: Decimal(‘Infinity’)
- Negative Infinity: Decimal(‘-Infinity’)
Represent Positive and Negative Infinity Using Numpy Library
You can define positive and negative Infinity by using the inf module of the NumPy library
Syntax:
- Positive Infinity: np.inf
- Negative Infinity: -np.inf
Check If Positive Infinity Number Is Equal to Negative Infinity Number
You can simple check if the positive infinity number is equal to negative infinity number using simple “==” operator, and the output is always false.
Arithmetic operations on infinity number will give an infinite number
If you perform any arithmetic operation with positive or negative infinity numbers, the result will always be an endless number.