ring_theory.complex
⟷
Mathlib.RingTheory.Complex
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
-import Mathbin.Data.Complex.Module
-import Mathbin.RingTheory.Norm
-import Mathbin.RingTheory.Trace
+import Data.Complex.Module
+import RingTheory.Norm
+import RingTheory.Trace
#align_import ring_theory.complex from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module ring_theory.complex
-! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Complex.Module
import Mathbin.RingTheory.Norm
import Mathbin.RingTheory.Trace
+#align_import ring_theory.complex from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
+
/-! # Lemmas about `algebra.trace` and `algebra.norm` on `ℂ`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
! This file was ported from Lean 3 source module ring_theory.complex
-! leanprover-community/mathlib commit 9015c511549dc77a0f8d6eba021d8ac4bba20c82
+! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -12,7 +12,10 @@ import Mathbin.Data.Complex.Module
import Mathbin.RingTheory.Norm
import Mathbin.RingTheory.Trace
-/-! # Lemmas about `algebra.trace` and `algebra.norm` on `ℂ` -/
+/-! # Lemmas about `algebra.trace` and `algebra.norm` on `ℂ`
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.-/
open Complex
mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9
@@ -17,6 +17,7 @@ import Mathbin.RingTheory.Trace
open Complex
+#print Algebra.leftMulMatrix_complex /-
theorem Algebra.leftMulMatrix_complex (z : ℂ) :
Algebra.leftMulMatrix Complex.basisOneI z = !![z.re, -z.im; z.im, z.re] :=
by
@@ -31,22 +32,29 @@ theorem Algebra.leftMulMatrix_complex (z : ℂ) :
zero_sub, add_zero]
fin_cases i <;> rfl
#align algebra.left_mul_matrix_complex Algebra.leftMulMatrix_complex
+-/
+#print Algebra.trace_complex_apply /-
theorem Algebra.trace_complex_apply (z : ℂ) : Algebra.trace ℝ ℂ z = 2 * z.re :=
by
rw [Algebra.trace_eq_matrix_trace Complex.basisOneI, Algebra.leftMulMatrix_complex,
Matrix.trace_fin_two]
exact (two_mul _).symm
#align algebra.trace_complex_apply Algebra.trace_complex_apply
+-/
+#print Algebra.norm_complex_apply /-
theorem Algebra.norm_complex_apply (z : ℂ) : Algebra.norm ℝ z = z.normSq :=
by
rw [Algebra.norm_eq_matrix_det Complex.basisOneI, Algebra.leftMulMatrix_complex,
Matrix.det_fin_two, norm_sq_apply]
simp
#align algebra.norm_complex_apply Algebra.norm_complex_apply
+-/
+#print Algebra.norm_complex_eq /-
theorem Algebra.norm_complex_eq : Algebra.norm ℝ = normSq.toMonoidHom :=
MonoidHom.ext Algebra.norm_complex_apply
#align algebra.norm_complex_eq Algebra.norm_complex_eq
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -20,7 +20,7 @@ open Complex
theorem Algebra.leftMulMatrix_complex (z : ℂ) :
Algebra.leftMulMatrix Complex.basisOneI z = !![z.re, -z.im; z.im, z.re] :=
by
- ext (i j)
+ ext i j
rw [Algebra.leftMulMatrix_eq_repr_mul, Complex.coe_basisOneI_repr, Complex.coe_basisOneI, mul_re,
mul_im, Matrix.of_apply]
fin_cases j
mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0
@@ -17,7 +17,6 @@ import Mathbin.RingTheory.Trace
open Complex
-/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem Algebra.leftMulMatrix_complex (z : ℂ) :
Algebra.leftMulMatrix Complex.basisOneI z = !![z.re, -z.im; z.im, z.re] :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0
@@ -17,12 +17,9 @@ import Mathbin.RingTheory.Trace
open Complex
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem Algebra.leftMulMatrix_complex (z : ℂ) :
- Algebra.leftMulMatrix Complex.basisOneI z =
- «expr!![ »
- "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
+ Algebra.leftMulMatrix Complex.basisOneI z = !![z.re, -z.im; z.im, z.re] :=
by
ext (i j)
rw [Algebra.leftMulMatrix_eq_repr_mul, Complex.coe_basisOneI_repr, Complex.coe_basisOneI, mul_re,
mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f
@@ -2,16 +2,13 @@
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module ring_theory.complex
-! leanprover-community/mathlib commit 9015c511549dc77a0f8d6eba021d8ac4bba20c82
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Complex.Module
import Mathlib.RingTheory.Norm
import Mathlib.RingTheory.Trace
+#align_import ring_theory.complex from "leanprover-community/mathlib"@"9015c511549dc77a0f8d6eba021d8ac4bba20c82"
+
/-! # Lemmas about `Algebra.trace` and `Algebra.norm` on `ℂ` -/
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file