Using Python’s Math, Science, and Engineering Libraries

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In this section, we will deal with the functions that are used with number theory as well as representation theory such as finding the factorial of a number. We will discuss these numerical functions along with examples and use-cases. Now it’s time to start applying what you learned to real-life situations. If you have any questions or comments, then please leave them in the comments section below.

The math Module Constants

Theano was a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays. It has support for nearly all data types found in Numpy, including support for converting other datatypes into Numpy arrays. Though further improvements to this library have been halted, it remains a popular and efficient choice for a lot of developers who work with multi-dimensional arrays. SciPy is a comprehensive Python library that is widely used in the scientific community for scientific and engineering applications. It is built on top of the NumPy library and provides a wide range of functions and tools for optimizing performance, performing complex calculations, and analyzing data.

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You can use iterables such as arrays, tuples, or lists as input and the function returns the sum of the values. A built-in function called sum() lets you calculate the sum of iterables as well, but fsum() is more accurate than sum(). The Python math module has many useful functions for mathematical calculations, and this article only covered a few of them in depth. In this section, you will briefly learn about some of the other important functions available in the math module. It’s an open-source python module that provides a comprehensive set of tools for statistical analysis of data sets.

… install scientific Python packages?¶

In this code snippet, we use the math.sinh() function to calculate the hyperbolic sine of x, where x is a given value (in this case, 2.3). The result is then printed, showing the value of the hyperbolic sine at x. One practical example is in physics, particularly in the study of vibrating strings. The shape of a vibrating string can be described using hyperbolic cosine functions, allowing us to understand the behavior of standing waves and harmonics. In this example, we calculate the time required for radioactive decay using the inverse hyperbolic cosine function. The tangent function, along with other trigonometric functions, was developed to solve problems involving right triangles.

The math.remainder() function finds applications in various scientific, engineering, and computational fields, especially those involving mathematics, computer science, and financial calculations. The “math.nextafter(x, y)” function provides a mathematical tool to navigate between floating-point numbers accurately. “math.fmod(x, y)” is a function provided by the math library in Python. Unlike the modulo operator (%), math.fmod() returns a float value that represents the precise remainder. The math.fmod() function finds applications in various fields such as mathematics, physics, and engineering. The power and logarithmic functions section are responsible for exponential calculations, which is important in many areas of mathematics, engineering, and statistics.

To convert a given angle from radians to degrees, use the math.degrees(), and to convert a given angle from degrees to radians, use math.radians(x). This tutorial will explore python math libraries the common constants and functions implemented in the math module — and how to use them. The functions of the Python math module aren’t equipped to handle complex numbers.

But first, you’re going to see how to use scipy.linalg to build models using least squares. You may notice that the value of the determinant is zero, which means that the system doesn’t have a unique solution. This also means that the inverse of the coefficients matrix doesn’t exist.

The Python math module provides a function called math.gcd() that allows you to calculate the GCD of two numbers. You can give positive or negative numbers as input, and it returns the appropriate GCD value. Euler’s number (e) is a constant that is the base of the natural logarithm, a mathematical function that is commonly used to calculate rates of growth or decay. As with pi and tau, Euler’s number is an irrational number with infinite decimal places. It allows you to perform a wide range of mathematical operations, including algebraic manipulation, calculus, and equation solving, using symbolic rather than numerical techniques.

  1. The formula for calculating compound interest involves using the base “e” raised to the power of the interest rate multiplied by the time period.
  2. In the below code, the calculate_circle_properties function takes the radius of a circle as input.
  3. You can calculate matrix inverses and determinants using scipy.linalg.inv() and scipy.linalg.det().
  4. By dividing the final value by the initial value and taking the logarithm, we obtain a measure that quantifies the percentage change in the investment.

In this code snippet, we use the math.lgamma() function to calculate the natural logarithm of the absolute value of the gamma function of x, where x is a given value (in this case, 4.5). The result is then printed, showing the value of the logarithm of the gamma function at x. “erf(x)” is a mathematical function known as the error function, commonly used in various branches of mathematics, statistics, and scientific computing. It is defined as the integral of the Gaussian (normal) distribution from zero to x. The error function provides a way to quantify the deviation between a random variable and its expected value. It is particularly useful in probability theory, statistics, and the analysis of experimental data.

In this example, we use the math.sqrt() function to calculate the speed of an object in freefall based on the given height and acceleration due to gravity. By taking the square root of the product of 2, gravity, and height, we obtain the speed of the object. This calculation is essential in understanding the behavior of objects in freefall and in designing safety measures. In this example, we use the math.pow() function to calculate the power dissipated by an electrical device based on the given voltage and current values.

Int.bit_length() returns the number of bits necessary to representan integer in binary, excluding the sign and leading zeros. For float and mixed int/float inputs, the intermediate productsand sums are computed with extended precision. This function isintended specifically for use with numeric values and may rejectnon-numeric types. The IEEE 754 special values of NaN, inf, and -inf will behandled according to IEEE rules.