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committedAug 7, 2023
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‎Mathlib.lean

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@@ -2494,7 +2494,6 @@ import Mathlib.NumberTheory.Multiplicity
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import Mathlib.NumberTheory.NumberField.Basic
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import Mathlib.NumberTheory.NumberField.CanonicalEmbedding
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import Mathlib.NumberTheory.NumberField.ClassNumber
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import Mathlib.NumberTheory.NumberField.Discriminant
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import Mathlib.NumberTheory.NumberField.Embeddings
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import Mathlib.NumberTheory.NumberField.Norm
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import Mathlib.NumberTheory.NumberField.Units

‎Mathlib/NumberTheory/NumberField/Discriminant.lean

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‎Mathlib/RingTheory/Discriminant.lean

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@@ -3,9 +3,9 @@ Copyright (c) 2021 Riccardo Brasca. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Riccardo Brasca
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-/
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import Mathlib.NumberTheory.NumberField.Basic
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import Mathlib.RingTheory.Trace
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import Mathlib.RingTheory.Norm
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import Mathlib.NumberTheory.NumberField.Basic
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#align_import ring_theory.discriminant from "leanprover-community/mathlib"@"3e068ece210655b7b9a9477c3aff38a492400aa1"
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end Field
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section Int
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end Int
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/-- Two (finite) ℤ-basis have the same discriminant. -/
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theorem discr_eq_discr [Fintype ι] (b : Basis ι ℤ A) (b' : Basis ι ℤ A) :
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Algebra.discr ℤ b = Algebra.discr ℤ b' := by
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convert Algebra.discr_of_matrix_vecMul b' (b'.toMatrix b)
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· rw [Basis.toMatrix_map_vecMul]
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· suffices IsUnit (b'.toMatrix b).det by
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rw [Int.isUnit_iff, ← sq_eq_one_iff] at this
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rw [this, one_mul]
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rw [← LinearMap.toMatrix_id_eq_basis_toMatrix b b']
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exact LinearEquiv.isUnit_det (LinearEquiv.refl ℤ A) b b'
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end Discr
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end Algebra

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