-
Notifications
You must be signed in to change notification settings - Fork 297
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
chore(algebra/ring/equiv): split out results about big operators (#17750
- Loading branch information
1 parent
35da8bd
commit 5cd3c25
Showing
3 changed files
with
54 additions
and
32 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,45 @@ | ||
/- | ||
Copyright (c) 2018 Johannes Hölzl. All rights reserved. | ||
Released under Apache 2.0 license as described in the file LICENSE. | ||
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov | ||
-/ | ||
|
||
import algebra.big_operators.basic | ||
import algebra.ring.equiv | ||
|
||
/-! | ||
# Results about mapping big operators across ring equivalences | ||
-/ | ||
|
||
namespace ring_equiv | ||
|
||
open_locale big_operators | ||
|
||
variables {α R S : Type*} | ||
|
||
protected lemma map_list_prod [semiring R] [semiring S] (f : R ≃+* S) (l : list R) : | ||
f l.prod = (l.map f).prod := map_list_prod f l | ||
|
||
protected lemma map_list_sum [non_assoc_semiring R] [non_assoc_semiring S] (f : R ≃+* S) | ||
(l : list R) : f l.sum = (l.map f).sum := map_list_sum f l | ||
|
||
/-- An isomorphism into the opposite ring acts on the product by acting on the reversed elements -/ | ||
protected lemma unop_map_list_prod [semiring R] [semiring S] (f : R ≃+* Sᵐᵒᵖ) (l : list R) : | ||
mul_opposite.unop (f l.prod) = (l.map (mul_opposite.unop ∘ f)).reverse.prod := | ||
unop_map_list_prod f l | ||
|
||
protected lemma map_multiset_prod [comm_semiring R] [comm_semiring S] (f : R ≃+* S) | ||
(s : multiset R) : f s.prod = (s.map f).prod := map_multiset_prod f s | ||
|
||
protected lemma map_multiset_sum [non_assoc_semiring R] [non_assoc_semiring S] | ||
(f : R ≃+* S) (s : multiset R) : f s.sum = (s.map f).sum := map_multiset_sum f s | ||
|
||
protected lemma map_prod [comm_semiring R] [comm_semiring S] (g : R ≃+* S) (f : α → R) | ||
(s : finset α) : g (∏ x in s, f x) = ∏ x in s, g (f x) := | ||
map_prod g f s | ||
|
||
protected lemma map_sum [non_assoc_semiring R] [non_assoc_semiring S] | ||
(g : R ≃+* S) (f : α → R) (s : finset α) : g (∑ x in s, f x) = ∑ x in s, g (f x) := | ||
map_sum g f s | ||
|
||
end ring_equiv |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters