feat(data/matrix/companion): Companion matrix #15047
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eric-wieser
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Jun 29, 2022
vihdzp
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Jun 30, 2022
YaelDillies
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Is this meant to be labelled |
eric-wieser
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Mar 30, 2023
| /-- The companion matrix of a polynomial. -/ | ||
| def companion [ring R] (P : R[X]) : matrix (fin P.nat_degree) (fin P.nat_degree) R := | ||
| if h : P.nat_degree = 0 then 0 else | ||
| λ i j, if j = fin.last' h then -P.coeff i else if (j : ℕ) + 1 = i then 1 else 0 |
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| λ i j, if j = fin.last' h then -P.coeff i else if (j : ℕ) + 1 = i then 1 else 0 | |
| of (λ i j, if j = fin.last' h then -P.coeff i else if (j : ℕ) + 1 = i then 1 else 0) |
semorrison
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semorrison
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Defines the companion matrix of a polynomial.
companion_eq_to_matrix_lmul_rootprovides a more abstract definition, from which it should be easier to prove some stuff (e.g. minimal polynomial) about the companion matrix.Edit : minimal polynomial of the companion matrix now proved.