Using sympy for proofs in Jupyter

[CM]

Sympy can be good for proofs, because you can avoid making transcription and algebra errors.
  There is a bit of an art to making computer algebra packages represent solutions in a usable way, so this method isn't for everyone.
  I am attaching a heavily-commented notebook for E4.7b, in part for my own reference.  If anyone knows better ways to do some of these steps, feel free to  comment.

[Jay Wang]

Thanks for posting a beautifully crafted code. It shows some very useful sympy tricks.

One can use subscripts to make it look neater, e.g. to print $r_{max}$, set

rmax = symbols('r_{max}')

Added:

One can also use inequality solvers to do simple proofs, for instance, the von Neumann analysis of waves in Ch. 6, Eq. (6.78) to (6.81) (see attached code, or link http://www.faculty.umassd.edu/j.wang/p521/inequal.ipynb):

from sympy import *
from sympy.solvers.inequalities import solve_univariate_inequality
x = symbols('x', real=True)

# x = beta^2*s^2 per Eq. (6.78)--(6.81)
print (solve_univariate_inequality(abs(1-2*x**2)>1, x))
print (solve_univariate_inequality(abs(1-2*x**2)<=1, x))