mathlib
91f8e687 - feat(src/ring_theory/polynomial/cyclotomic): cyclotomic polynomials (#4914)

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5 years ago
feat(src/ring_theory/polynomial/cyclotomic): cyclotomic polynomials (#4914) I have added some basic results about cyclotomic polynomials. I defined them as the polynomial, with integer coefficients, that lifts the complex polynomial ∏ μ in primitive_roots n ℂ, (X - C μ). I proved that the degree of cyclotomic n is totient n and the product formula for X ^ n - 1. I plan to prove the irreducibility in the near future. This was in [4869](https://github.com/leanprover-community/mathlib/pull/4869) before I splitted that PR. Compared to it, I added the definition of `cyclotomic n R` for any ring `R` (still using the polynomial with coefficients in `ℤ`) and some easy lemmas, especially `cyclotomic_of_ring_hom`, `cyclotomic'_eq_X_pow_sub_one_div` `cyclotomic_eq_X_pow_sub_one_div`, and `cycl_eq_cycl'`.
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