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Commit 2022-09-14 11:13 e1452ef2

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chore(number_theory/legendre_symbol/): move zmod.{legendre|jacobi}_sym to other namespaces (#16461) This PR moves legendre_sym and jacobi_sym (and qr_sign) to the root namespace. It also moves definitions and lemmas named legendre_sym_... to the legendre_sym namespace and analogous for jacobi_sym_... and qr_sign_.... We change names like jacobi_sym_two to jacobi_sym.at_two. This mostly affects the files number_theory.legendre_symbol.quadratic_reciprocity and number_theory.legendre_symbol.jacobi_symbol. Note that names like exists_sq_eq_neg_one_iff have been left in zmod. We prefix quadratic_reciprocity* by legendre_sym to disambiguate with the versions for the Jacobi symbol. (The links in docs/100.yaml and docs/overview.yaml are updated accordingly.) We also move the results in number_theory.legendre_symbol.gauss_eisenstein_lemmas from the legendre_symbol namespace to the zmod namespace. See this Zulip thread and the comments at [#16395](https://github.com/leanprover-community/mathlib/pull/16395) for discussion.

Estimated changes

added theorem jacobi_sym.at_neg_one
added theorem jacobi_sym.at_neg_two
added theorem jacobi_sym.at_two
added theorem jacobi_sym.eq_zero_iff
added theorem jacobi_sym.mod_left'
added theorem jacobi_sym.mod_left
added theorem jacobi_sym.mod_right'
added theorem jacobi_sym.mod_right
added theorem jacobi_sym.mul_left
added theorem jacobi_sym.mul_right'
added theorem jacobi_sym.mul_right
added theorem jacobi_sym.ne_zero
added theorem jacobi_sym.neg
added theorem jacobi_sym.one_left
added theorem jacobi_sym.one_right
added theorem jacobi_sym.pow_left
added theorem jacobi_sym.pow_right
added theorem jacobi_sym.sq_one'
added theorem jacobi_sym.sq_one
added theorem jacobi_sym.trichotomy
added theorem jacobi_sym.value_at
added theorem jacobi_sym.zero_left
added theorem jacobi_sym.zero_right
added def jacobi_sym
added theorem qr_sign.eq_iff_eq
added theorem qr_sign.mul_left
added theorem qr_sign.mul_right
added theorem qr_sign.neg_one_pow
added theorem qr_sign.sq_eq_one
added theorem qr_sign.symm
added def qr_sign
deleted def zmod.jacobi_sym
deleted theorem zmod.jacobi_sym_mod_left'
deleted theorem zmod.jacobi_sym_mod_left
deleted theorem zmod.jacobi_sym_mod_right
deleted theorem zmod.jacobi_sym_mul_left
deleted theorem zmod.jacobi_sym_mul_right
deleted theorem zmod.jacobi_sym_ne_zero
deleted theorem zmod.jacobi_sym_neg
deleted theorem zmod.jacobi_sym_neg_one
deleted theorem zmod.jacobi_sym_neg_two
deleted theorem zmod.jacobi_sym_one_left
deleted theorem zmod.jacobi_sym_one_right
deleted theorem zmod.jacobi_sym_pow_left
deleted theorem zmod.jacobi_sym_pow_right
deleted theorem zmod.jacobi_sym_sq_one'
deleted theorem zmod.jacobi_sym_sq_one
deleted theorem zmod.jacobi_sym_two
deleted theorem zmod.jacobi_sym_value
deleted theorem zmod.jacobi_sym_zero_left
deleted def zmod.qr_sign
deleted theorem zmod.qr_sign_eq_iff_eq
deleted theorem zmod.qr_sign_mul_left
deleted theorem zmod.qr_sign_mul_right
deleted theorem zmod.qr_sign_neg_one_pow
deleted theorem zmod.qr_sign_sq_eq_one
deleted theorem zmod.qr_sign_symm
added theorem legendre_sym.at_one
added theorem legendre_sym.at_two
added theorem legendre_sym.at_zero
added theorem legendre_sym.eq_pow
added def legendre_sym.hom
added theorem legendre_sym.mod
added theorem legendre_sym.mul
added theorem legendre_sym.sq_one'
added theorem legendre_sym.sq_one
added def legendre_sym
deleted def zmod.legendre_sym
deleted theorem zmod.legendre_sym_eq_pow
deleted theorem zmod.legendre_sym_mod
deleted theorem zmod.legendre_sym_mul
deleted theorem zmod.legendre_sym_neg_one
deleted theorem zmod.legendre_sym_neg_two
deleted theorem zmod.legendre_sym_one
deleted theorem zmod.legendre_sym_sq_one'
deleted theorem zmod.legendre_sym_sq_one
deleted theorem zmod.legendre_sym_two
deleted theorem zmod.legendre_sym_zero