Scientific Computing with Python 3

Substitutions

Let us first consider a simple symbolic expression:

x, a = symbols('x a')
b = x + a

What happens if we set x = 0 ?  We observe that b did not change. What we did was that we changed the Python variable x. It now no longer refers to the symbol object but to the integer object 0. The symbol represented by the string 'x'  remains unaltered, and so does b.

Instead, altering an expression by replacing symbols by numbers, other symbols, or expressions is done by a special substitution method which can be seen in following code:

x, a = symbols('x a')
b = x + a
c = b.subs(x,0)   
d = c.subs(a,2*a)  
print(c, d)   # returns (a, 2a)

This method takes one or two arguments:

b.subs(x,0)
b.subs({x:0})  # a dictionary as argument

Dictionaries as arguments ...