Lecturer: Vince Knight
Office hours: Thursday 1400-1600
What you have learnt this week:
Using Sympy to study symbolic mathematics.
Your next assessment is the individual coursework, this is due 1300 Thursday of Week 11 (December 8th).
Equality of expressions
Sympy expressions specifically keep track of their form.
For example, the following is just two ways of writing the same thing:
If we consider these in Python:
>>> import sympy as sym >>> x = sym.symbols('x') >>> exp2 = x ** 2 + x >>> exp2 x**2 + x >>> exp1 = x *(1 + x) >>> exp1 x*(x + 1)
If we check that these two expressions are the same, we get that they are not:
>>> exp1 == exp2 False
This is because they’re not exactly the same expression, however, of course they compute to the same expression:
>>> exp3 = exp1 - exp2 >>> exp3 -x**2 + x*(x + 1) - x >>> exp3.expand() 0
Note that sometimes it will automatically translate the expression somewhat. For example, in question 10 of this lab sheet we were asked to verify that \(\cos(n\pi) = (-1) ^ n\).
>>> n = sym.symbols('n', integer=True) # This is an important step >>> exp1, exp2 = sym.cos(n * sym.pi), (-1) ** n >>> exp1, exp2 ((-1)**n, (-1)**n)