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How do programs factor polynomials of degree greater than 4? Is it done arithmetically; if so, how?

John A.
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    Do you mean over $\mathbb{Q}$ or over $\mathbb{C}$? Over $\mathbb{C}$ computer algebra systems probably use various iterative algorithms to find the roots, e.g. Newton's method. In general see https://en.wikipedia.org/wiki/Factorization_of_polynomials. – Qiaochu Yuan Mar 17 '17 at 02:52
  • There are a few theorems that say a thing or two about factorization, and then there are some algorithm based methods to try and factor. The theorems can be made into algorithms. This is, in part, what mathematica does. – ReverseFlowControl Mar 17 '17 at 03:00

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