The Sympy Python library

1 - What is Sympy?

SymPy is a Python library for symbolic computing. It provides computer algebra functionality as a stand-alone application, as a library for other applications, or live on the web as SymPy Live or SymPy Gamma. SymPy is easy to install and inspect as it is written entirely in Python with few dependencies. SymPy includes functionalities ranging from basic symbolic arithmetic to calculus, algebra, discrete mathematics and quantum physics ... The Sympy library is able to format the result of calculations as LaTeX code.

2 - Installation of the SymPy library

to install the Sympy library, just use the pip utility with the command:

pip install sympy

3 - Identify the installed version of Sympy

To find the version of Sympy installed, just type the commands:

>>> import sympy
>>> sympy .__ version__
    '1.4'

4 - Use of Symbols

The SymPy library can be used in any environment where Python is available. In order to be able to use it, we must first import it:

>>> from sympy import *

We will see a first use of symbols. To define an x ​​symbol, we use the command:

>>> x = Symbol ('x') # note the S in uppercase
>>> x
x

To define several symbols at the same time, we use the command:

>>> x, y, z = symbols ('x y z') # note the lowercase 's'
>>> x, y, z
( X Y Z )

5 - Use of sympy expressions

A sympy expression is obtained by combining a number of symbols using functions and classical operators of addition, multiplication ...

Example

expr = 2 * sin (x) + y

Example

from sympy import *
x = symbols ('x')
expr = (x + 1) ** 7
print (expr)

#Which displays after execution:
#(x + 1) ** 7

You can also do operations on expressions. Here is an example with the expand() method

from sympy import *
x = symbols ('x')
expr = (x + 1) ** 7
print (expr.expand ())

#Which displays after execution:
#x ** 7 + 7 * x ** 6 + 21 * x ** 5 + 35 * x ** 4 + 35 * x ** 3 + 21 * x ** 2 + 7 * x + 1

Example (simplify() method)

from sympy import *
x = Symbol ('x')
expr1 = (x + 1) ** 2
expr2 = x ** 2 + 2 * x + 2
expr3 = simplify (expr2 - expr1)
print ("expr2 - expr1 =", expr3)
The output is: expr2 - expr1 = 1

Example (comparison of 2 expressios using the equals() method)

from sympy import *
x = Symbol ('x')
e1 = 2 * sin (x) * cos (x)
e2 = sin (2 * x)
print (e1.equals (e2))

#The output is : True