Convert a polynomial w(z) to w((1-z)/(1+z))

Question

I am writing a code which takes a "code" (Coding Theory) as an input and I have calculated the weight enumerator of it. I want to find the weight enumerator of dual code using MacWilliams Identity.

I have W(z), the weight enumerator of the code, and I want to convert it to W((1-z)/(1+z)) using python.

Answer 1

If you are going to be working with polynomials in an extended fashion, you should be working with a proper computer algebra system (CAS). sympy is great for manipulations like these. For example:

from sympy import poly
from sympy.abc import x,z

W1 = poly(x**2 + 3*x)

# Evaluate the polynomial at x=(1-z)/(1+z)
W2 = W1((1-z)/(1+z))

print W1
print W2

>>> Poly(x**2 + 3*x, x, domain='ZZ')
>>> (-2*z**2 - 2*z + 4)/(z**2 + 2*z + 1)

You can simplify any answer with sympy.simplify and .expand for example:

import sympy

expr = (4*x**2 - 4*x + 4)*(x**3 + 3*x**2 + 3*x + 1)/(4*(x**2 + 2*x + 1))
print sympy.simplify(sympy.expand(expr))
>>> x**3 + 1