Sympy module in pythonSymPy is a symbolic computation Python package that is opensource. It may be used as a standalone program, a library for other applications, or as a live online application called SymPy Live or SymPy Gamma. Because SymPy is written purely in Python and has minimal dependencies, it is straightforward to install and investigate. SymPy is a computer algebra system with a low entry barrier thanks to its simplicity of use and a simple and extendable codebase written in a wellknown language. From elementary symbolic arithmetic through calculus, algebra, discrete mathematics, and quantum physics, SymPy has it all. It has the ability to format the results of computations into LaTeX code. To begin with, SymPy is entirely free. It is opensource and released under the permissive BSD license, allowing you to change and even sell the source code. This stands out from popular commercial systems such as Maple or Mathematica, which cost hundreds of dollars in software, and licenses. SymPy is opensource software released under the New BSD license. Ondrej Ertk and Aaron Meurer are the principal developers. It was founded by Ondrej Erik in 2005. Symbolic computing is concerned with the symbolic calculation of mathematical objects. This implies that mathematical objects are represented precisely rather than roughly and that mathematical equation with unevaluated variables are left in symbolic form. Second, SymPy is written in Python. The vast majority of computer algebra systems create their own language. Not with SymPy. SymPy is fully written in Python and is totally run in Python. This implies that if you already know Python, getting started with SymPy is significantly easier because you already know the syntax (and if you don't, Python is quite simple to learn). Python is already a welldesigned and battletested language. The developers of SymPy feel confident in their skills to write mathematical software, but designing computer languages is a whole different matter. We may concentrate on the important aspects of mathematics by utilizing an existing language. Sage is another computer algebra system that employs Python as its programming language. Sage, on the other hand, is big, requiring a download of over a gigabyte. SymPy has the benefit of being lightweight. It is not only tiny, but it also has no dependencies other than Python, allowing it to be used practically everywhere. Furthermore, the aims of Sage and SymPy are not the same. Sage aspires to be a fullfeatured mathematics system, combining all of the main opensource mathematical systems into a single package. When you use a Sage function, such as integrate, it uses one of the opensource packages that it provides. SymPy is, in fact, included in Sage. SymPy, on the other hand, aspires to be a selfcontained system with all functionality implemented within the framework. SymPy may also be used as a library, which is a significant feature. Many computer algebra systems are designed to be used in interactive situations, but automating or extending them is challenging. You may use SymPy in an interactive Python environment or import it into your own Python program with ease. SymPy also has APIs that allow it simple to add your own custom functions. Some key features:
Now let us have a look at the code of the sympy module in python. Code:Output: please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 1 enter the integer whose square root you want to calculate 7 ?7??7 equals to 7 To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 2 enter the expression(linear) that you want to form with two variables 2*x + 5*y  18*x + 34*y Expression is 16*var1 + 39*var2 To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 3 The trigno expression is exp(var1)*sin(var1) The differential expression is exp(var1)*sin(var1) + exp(var1)*cos(var1) To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 4 The trigno expression is exp(var2)*sin(var2) + exp(var2)*cos(var2) The integration expression is 2*exp(var2)*cos(var2) To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 5 Enter the values for the 2X2 matrix Enter values for the first row 3 8 Enter values for the second row 5 9 Matrix is Matrix([[3, 8], [5, 9]]) Eigenvalues of the matrix are {13: 1, 1: 1} To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 5 Enter the values for the 2X2 matrix Enter values for the first row 1 9 Enter values for the second row 4 2 Matrix is Matrix([[1, 9], [4, 2]]) Eigenvals of the matrix are {3/2  sqrt(145)/2: 1, 3/2 + sqrt(145)/2: 1} To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 1 enter the integer whose square root you want to calculate 98 7??2?7??2 equals to 98 To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivative of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 5 Enter the values for the 2X2 matrix Enter values for the first row 500 600 Enter values for the second row 700 800 Matrix is Matrix([[500, 600], [700, 800]]) Eigenvals of the matrix are {650  50*sqrt(177): 1, 650 + 50*sqrt(177): 1} To continue with code execution, type [y] otherwise [n]. y please choose any one of the operations from the listed below the list of operations:: 1. To use the sympy module for calculation of the square root. 2. To use the sympy module for generating dynamic expressions. 3. To use the sympy module to calculate the derivate of the trigonometric expressions. 4. To use the sympy module to calculate the integration of the trigonometric expressions. 5. To use the sympy module to calculate the eigenvalues of a matrix. 6. To exit from the code execution. 6 In the abovewritten code, we have called the different functions which we have written each of which is representing a different use case scenario of this module provided by Python The user is asked for the input wherever a particular input is required from the user side and then some operations are performed on that input data provided by the user and the resultant data is printed to the user as a return type or resulted value of that particular function the operation which is performed on the input data provided by the user depends upon the type of operation for which that data has been taken as an input. Advantages:
So, in this article, we have understood the usage of the Sympy module in python and understood the use cases where we can use this module to perform various mathematical operations.
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