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feat(data/polynomial/reverse.lean): show trailing_coeff is a multiplicative homomorphism #4707

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@adomani adomani commented Oct 20, 2020

use the reflect function.
prove lemmas on trailing_degree.
add a lemma on monotone non-increasing to show that trailing_coeff and leading_coeff are exchanged under reflect.

I plan to merge the contents of the file to_finset_lattice_max_min.lean in data.finset.lattice.lean section max_min. The file contains def mon and lemma monotone_max'_min'. Feel free to suggest a better home for its content!

adomani and others added 30 commits October 13, 2020 08:24
…oefficietns. Prove that reverse is a multiplicative monoid homomorphism
… poly-reverse

pulling in order to create a PR with reverse
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Good catch!  The `N` was indeed a typo for `i`!

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
I did not realize that it was a possibility not to use \lambda!

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
This happens quite a few times: I will replace the remaining instances!

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
removed a "cyclic" import
replaced ```C_mul_X_pow_of_card_support_le_one``` with the already existing ```C_mul_X_pow_eq_self```
cleared up some module dependencies
support of cardinality at most one
@jcommelin jcommelin added the WIP Work in progress label Oct 20, 2020
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I'm marking this as WIP because we need to figure out what we want to do with the non-increasing map issue first.

@github-actions github-actions bot added the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Oct 27, 2020
@adomani adomani closed this Mar 2, 2021
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adomani commented Mar 2, 2021

I closed this pull request since the main aim of it was to prove that nat_trailing_degrees are multiplicative and this is now in mathlib: nat_trailing_degree_mul in data.polynomial.ring_division.

@YaelDillies YaelDillies deleted the poly-reverse2 branch October 19, 2021 20:44
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