Elementary Functions

Examples for elementary functions in SymPy are trigonometric functions and their inverses. The following example shows how simplify acts on expression which include elementary function:

x = symbols('x')
simplify(cos(x)**2 + sin(x)**2)  # returns 1

Here is another example for the use of elementary functions:

atan(x).diff(x) - 1./(x**2+1)  # returns 0

If you use SciPy and SymPy together, we strongly recommend that you use them in different namespaces:

import scipy as sp
import sympy as sym
# working with numbers
x=3
y=sp.sin(x)
# working with symbols
x=sym.symbols('x')
y=sym.sin(x)   

Lambda - functions

In section Anonymous functions of Chapter 7, Functions, we saw how to define so-called anonymous functions in Python. The counterpart in SymPy is done by the Lambda command. Note the difference; lambda is a keyword while Lambda is a constructor.

The command Lambda takes two arguments, the symbol of the function's independent variable...