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feat(data/polynomial/root_isolation): root_parity_in_range_of_evals #14916

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feat(data/polynomial/root_isolation): root_parity_in_range_of_evals #14916

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@BoltonBailey BoltonBailey commented Jun 24, 2022 •
edited by alexjbest
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A PR to prove that the parity of the number of roots of a real polynomial in a range depends on the signs of the evaluations of the polynomial on either side of the range. Perhaps useful for Descartes rule of signs.

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@BoltonBailey BoltonBailey added help-wanted The author needs attention to resolve issues WIP Work in progress labels Jun 24, 2022
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Jun 24, 2022
@BoltonBailey BoltonBailey mentioned this pull request Jun 25, 2022
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@BoltonBailey BoltonBailey removed help-wanted The author needs attention to resolve issues WIP Work in progress labels Jun 26, 2022
@BoltonBailey BoltonBailey added awaiting-review The author would like community review of the PR and removed awaiting-review The author would like community review of the PR labels Jul 3, 2022
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Jul 4, 2022
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@BoltonBailey BoltonBailey added the awaiting-review The author would like community review of the PR label Jul 4, 2022
urkud
urkud reviewed Jul 8, 2022
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src/data/polynomial/root_isolation.lean Outdated
open polynomial multiset

lemma opposite_signs_of_roots_filter_mem_Ioo_empty (a b : ℝ) (hab : a ≤ b) (p : polynomial ℝ)
(ha : p.eval a ≠ 0) (hb : p.eval b ≠ 0) (hr : (p.roots.filter (∈ set.Ioo a b)) = ∅) :
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IMHO, a more readable assumption is ∀ x ∈ Icc a b, p.eval x ≠ 0.

@BoltonBailey BoltonBailey added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Jul 8, 2022
@BoltonBailey BoltonBailey added the help-wanted The author needs attention to resolve issues label Nov 27, 2022
@semorrison semorrison added the too-late This PR was ready too late for inclusion in mathlib3 label Jul 16, 2023
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