Johnathan Johnathan - 19 days ago 10
Python Question

Python: my polynomial coefficients are off by a factor of 10

I am learning scientific computing with python. In the exercise, I am supposed to generate a polynomial by using its roots with this formula:

enter image description here

Here is my implementation:

def poly(x,roots): #Pass real and/or complex roots

x = symbols(x)
f = 1
for r in roots:
f = f*(x - r)

return expand(f)


When I test it:

from sympy import expand
poly('x',[(-1/2), 5, (21/5), (-7/2) + (1/2)*sqrt(73), (-7/2) - (1/2)*sqrt(73)])


I get:

x**5 - 1.7*x**4 - 50.5*x**3 + 177.5*x**2 - 24.8999999999999*x - 63.0


But I should get:

10*x**5 - 17.0*x**4 - 505.0*x**3 + 1775.0*x**2 - 248.999999999999*x - 630.0


Hence, everything is off by a factor of 10. If I set
f = 10
, it works, but I don't see why I should do that. Am I making an obvious mistake? Thank you!

Answer

While 10x**5 + ... is correct, that is 10 * p(x), which isn't really what is needed. The answer you are getting is fine right now as well and you can test that as for each r in roots, p(r) is 0.