[Merged by Bors] - feat(number_theory/quadratic_reciprocity): change type of a in API lemmas to int
#13393
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…emmas to `int` (#13393) This is step 2 in the overhaul of number_theory/qudratic_reciprocity. The only changes are that the argument `a` is now of type `int` rather than `nat` in a bunch of statements. This is more natural, since the corresponding (now second) argument of `legendre_symnbol` is of type `int`; it therefore makes the API lemmas more easily useable.
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Apr 12, 2022
| legendre_sym p a = 1 ↔ (∃ b : zmod p, b ^ 2 = a) := | ||
| begin | ||
| rw [euler_criterion p ha0, legendre_sym, int.cast_coe_nat, if_neg ha0], | ||
| rw [euler_criterion p ha0, legendre_sym, if_neg ha0], | ||
| split_ifs, | ||
| { simp only [h, eq_self_iff_true] }, | ||
| { simp only [h, iff_false], tauto } | ||
| end | ||
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| lemma eisenstein_lemma [fact (p % 2 = 1)] {a : ℕ} (ha1 : a % 2 = 1) (ha0 : (a : zmod p) ≠ 0) : |
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Should this become an integer too?
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I have left this, since the proof does not seem to be easily adaptable. The result is used for proving quadratic reciprocity, wheere the arguments are (natural) prime numbers, and there is probably not much use outside of this.
YaelDillies
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a in API lemmas to inta in API lemmas to int
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Pull request successfully merged into master. Build succeeded: |
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a in API lemmas to inta in API lemmas to int
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This is step 2 in the overhaul of
number_theory/quadratic_reciprocity.The only changes are that the argument
ais now of typeintrather thannatin a bunch of statements.This is more natural, since the corresponding (now second) argument of
legendre_symnbolis of typeint; it therefore makes the API lemmas more easily useable.