[Merged by Bors] - refactor(Data/ZMod/IntUnitsPower): generalize ZMod 2 to work for Nat and Int too#7866
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[Merged by Bors] - refactor(Data/ZMod/IntUnitsPower): generalize ZMod 2 to work for Nat and Int too#7866eric-wieser wants to merge 16 commits intomasterfrom
Nat and Int too#7866eric-wieser wants to merge 16 commits intomasterfrom
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…t` and `Int` too
Na… …t and Int tooNat and Int too
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j-loreaux
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Nov 1, 2023
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This diff is very hard to follow. Would you mind trying to minimize it by ordering things the same way if possible? I don't think there is anything to complain about here, but it's hard to make sure I've checked everything.
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Nevermind, the lemmas actually are in the same order, but the git diff isn't matching them up. |
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If you want a clear diff, I could rename the lemmas first? (edit: done in #8087) |
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This reduces a diff in a future PR (#7866).
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Well, that was a waste of time; the diff is still hard to follow, just because the statements and proofs are changing too much! |
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Thanks for doing #8087. The diff was still a bit messy, but it was just readable enough to make sense of. bors merge |
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…` and `Int` too (#7866) Instead of providing `instance : Pow ℤˣ (ZMod 2)`, this now provides `instance [Module R (Additive ℤˣ)] : Pow ℤˣ R`. It turns out that this instance already exists for `ℕ` and `ℤ`, so all we need to do is create `instance : Module (ZMod 2) (Additive ℤˣ)` and we obtain new definitions that generalize over all three types. As a result of the generalization, `z₂pow` has been renamed in lemmas to `uzpow` (`u`nits of `ℤ`). The motivation here is that I need $(-1) ^ i$ to make sense (and be lawful) for `ZMod 2` (on clifford algebras) and `ℕ` (on exterior algebras). [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Powers.20of.20.60.E2.84.A4.CB.A3.60.20by.20.60ZMod.202.60/near/397569279)
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Nat and Int tooNat and Int too
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Nov 14, 2023
Following #7866, `Int.negOnePow` is redefined as a map `ℤ → ℤˣ` rather than `ℤ → ℤ`.
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Following #7866, `Int.negOnePow` is redefined as a map `ℤ → ℤˣ` rather than `ℤ → ℤ`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Following #7866, `Int.negOnePow` is redefined as a map `ℤ → ℤˣ` rather than `ℤ → ℤ`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Following #7866, `Int.negOnePow` is redefined as a map `ℤ → ℤˣ` rather than `ℤ → ℤ`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Following #7866, `Int.negOnePow` is redefined as a map `ℤ → ℤˣ` rather than `ℤ → ℤ`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Instead of providing
instance : Pow ℤˣ (ZMod 2), this now providesinstance [Module R (Additive ℤˣ)] : Pow ℤˣ R.It turns out that this instance already exists for
ℕandℤ, so all we need to do is createinstance : Module (ZMod 2) (Additive ℤˣ)and we obtain new definitions that generalize over all three types.As a result of the generalization,
z₂powhas been renamed in lemmas touzpow(units ofℤ).The motivation here is that I need$(-1) ^ i$ to make sense (and be lawful) for
ZMod 2(on clifford algebras) andℕ(on exterior algebras).Zulip thread
ZMod 2onℤˣ#7661