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Context: I am testing 8 different root finding algorithms on their efficiency on finding roots of different polynomials. However, on its own, random polynomials (meaning degree and coefficients are random) doesn't appear to have many practical applications.

Motivation: I want to bring in some practical usability in my program and some real world implications.

Previous Research: I heard that there are polynomials used in cryptography and finance but I actually can't find a format for these and in general what these polynomials are.

Question: What type of polynomials have practical applications. I am hoping for something beyond just degree or number of terms, but some properties with coefficients.

  • Edit: Clarification, I am looking for univariate polynomials that can have complex roots!
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  • $\begingroup$ The most commonly used polynomials are the families of so-called orthogonal polynomials : Legendre, Chebyshev T and U, Jacobi, etc. $\endgroup$ Commented Dec 3 at 20:18
  • $\begingroup$ Sorry this completely slipped by! Good thing you mentioned orthogonal polynomials . I did some more research and these do look amazing! Thank you so much! $\endgroup$ Commented Dec 5 at 22:59

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