[Merged by Bors] - feat: add MultilinearMap.dfinsuppFamily and MultilinearMap.piFamily#17881
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eric-wieser wants to merge 21 commits intomasterfrom
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[Merged by Bors] - feat: add MultilinearMap.dfinsuppFamily and MultilinearMap.piFamily#17881eric-wieser wants to merge 21 commits intomasterfrom
MultilinearMap.dfinsuppFamily and MultilinearMap.piFamily#17881eric-wieser wants to merge 21 commits intomasterfrom
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PR summary 44c1065481Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…lly our helper lemmas are very similar
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urkud
reviewed
Oct 19, 2024
MultilinearMap.dfinsuppFamily and MultilinearMap.piFamily
eric-wieser
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Oct 19, 2024
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| /-- | ||
| Given a family of indices `κ` and a multilinear map `f p` for each way `p` to select one index from | ||
| each family, map a family of functions `x` into a function from each selection. | ||
| -/ | ||
| @[simps] | ||
| def piFamily (f : Π (p : Π i, κ i), MultilinearMap R (fun i ↦ M i (p i)) (N p)) : | ||
| MultilinearMap R (fun i => Π j : κ i, M i j) (Π t : Π i, κ i, N t) where | ||
| toFun x := fun p => f p (fun i => x i (p i)) | ||
| map_add' {dec} m i x y := funext fun p => by | ||
| cases Subsingleton.elim dec (by infer_instance) | ||
| dsimp | ||
| simp_rw [Function.apply_update (fun i m => m (p i)) m, Pi.add_apply, (f p).map_add] | ||
| map_smul' {dec} m i c x := funext fun p => by | ||
| cases Subsingleton.elim dec (by infer_instance) | ||
| dsimp | ||
| simp_rw [Function.apply_update (fun i m => m (p i)) m, Pi.smul_apply, (f p).map_smul] |
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@urkud, I added this one to make the naming question slightly easier; dfinsupp was really a distraction, and the same underlying function works on pi types too.
I'm happy to split the pi and dfinsupp parts into separate PRs if that's useful.
Co-authored-by: FR <zhao.yu-yang@foxmail.com>
jcommelin
reviewed
Oct 26, 2024
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| Given a family of indices `κ` and a multilinear map `f p` for each way `p` to select one index from | ||
| each family, map a family of finitely-supported functions `x` into a finitely-supported function | ||
| from each selection. |
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I have trouble parsing this sentence.
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Maybe
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| Given a family of indices `κ` and a multilinear map `f p` for each way `p` to select one index from | |
| each family, map a family of finitely-supported functions `x` into a finitely-supported function | |
| from each selection. | |
| Given a family of indices `κ` and a multilinear map `f p` for each way `p` to select one index from | |
| each family, `dfinsuppFamily f` maps a family of finitely-supported functions (one for each index `κ i`) | |
| into a finitely-supported function on the selection families `Π i, κ i`. |
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Yes, that definitely helped me.
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| Given a family of indices `κ` and a multilinear map `f p` for each way `p` to select one index from | ||
| each family, map a family of functions `x` into a function from each selection. |
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bors d+ |
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✌️ eric-wieser can now approve this pull request. To approve and merge a pull request, simply reply with |
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bors merge |
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…y` (#17881) This is the analog to `Fintype.piFinset` Since this is computable and rather confusing, I've included a test with a concrete evaluation. Co-authored-by: Eric Wieser <efw@google.com>
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Pull request successfully merged into master. Build succeeded: |
MultilinearMap.dfinsuppFamily and MultilinearMap.piFamilyMultilinearMap.dfinsuppFamily and MultilinearMap.piFamily
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This is the analog to
Fintype.piFinsetSince this is computable and rather confusing, I've included a test with a concrete evaluation.