[Tutor] Complex roots

Tim Peters tim.peters at gmail.com
Mon Dec 13 05:37:52 CET 2004

[Dick Moores]
>>> Actually, I'm trying to write a Python script that computes all 3
>>> roots of a cubic equation. Do you happen to have one tucked
>>> away in your store of wisdom and tricks? (One for real coefficients
>>> will do).

[Tim Peters]
>> I don't, no.  You can code one for cubics from Cardano's formula, e.g.,
>>     http://mathworld.wolfram.com/CubicFormula.html
>> but it's rarely worth the bother -- it's complicated and doesn't
>> generalize.

> I accept this challenge to write a complicated script of little value.

Cool!  If it's just for fun, it's fun.

>> In practice, roots for polynomials beyond quadratics are
>> usually obtained by numerical approximation methods that don't care
>> much about the polynomial's degree.

> Are these "numerical approximation methods" pythonically possible?

Of course, but coding general-purpose root finders-- even if "general"
is limited to just polynomials --requires mathematical and numeric
expertise.  If it interests you, there are book-length treatments of
the subject, and there's really no easy reliable approach.  Good
online sources for numeric algorithms include:


Just Googling on

    polynomial roots Python

will point you to


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