Suppose that in Python you want to expand an expression (x+y)2 to x2 + y2 + 2 xy, this can be done using sympy library in Python, first of all see a simple program.
from sympy import *
x = Symbol('x')
y = Symbol('y')
z=(x + y)**2
print(expand(z))
Output:- x**2 + 2*x*y + y**2
How is it happening,
Actually statement x = Symbol(‘x’) is not defining x as a numerical value instead it is defining by a symbol x , i.e x is referring to x.
The same way
Statement y = Symbol(‘y’) is not defining y as a numerical value instead it is defining by a symbol y , i.e y is referring to y.
And z is referring to (x + y)**2 and expand(z) statement expand it as x**2 + 2*x*y + y**2.
sympy is not just limited to expanding expressions, using diff() and integrate() functions of sympy differentiation and integration coefficients of functions can be computed, see below.
from sympy import *
x = Symbol('x')
y = Symbol('y')
dy=diff(x**3+3*x, x)
I=integrate(x**3+3*x, x)
print(expand(dy))
print(expand(I))
Outputs
3*x**2 + 3
x**4/4 + 3*x**2/2
