A simple polynomial roots calculator script written in python.

It uses Gauss Lemma to get the potential roots of an integer coefficients polynomial. Then it does Ruffini's rule for each potential root and determine if each value is a root. If a root is found the quotient polynomial is evaluated with the root just found to get double, triple, etc roots and not loose solutions.

Remember that a n grade polynomial must have n number of roots, so if the roots that the script finds are less than the grade of the polynomial, assume complex roots (which cannot be found using Gauss Lemma & Ruffini)

• python >=3.6 download here
• pyenv install it now

$ pipenv install

• Meant to be used for real coefficients polynomials (complex polynomials are not supported by design, since Gauss Lemma only gets potential roots for integer coefficients polynomials)
• It uses the Gauss Lemma for finding the polynomials roots, so you need to input integer coefficients. If your polynomial has rational / irrationals coefficients try multiplying the whole polynomial by an integer that gets rid of the denominators. The resulting polynomial will share roots with the original one. Example:

P(x) = (3/2)(x^4) + (5/2)(x^3) - 2(x^2) + (3/2)x + (9/2)
2P(x) = 3(x^4) + 5(x^3) - 2(x^2) + 3x + 9   <-- Shares roots with P(x)

• Rational display of floats ('0.33333333333' will be displayed as '1/3')
• Square root display of irrational floats (sqrt(2) = √2)
• Support for any degree polynomial
• Support for nth (double, triple, etc) roots (will be displayed n number of times)
• Partial support for complex roots (conjugate ones only)

To perform a run, prompt:

$ python3 roots.calculator.py