chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
11,033 | lean_file_chunk | 4af9c658a3ed21862ffc2537256b8e540e7ee162dbf9e3c5d7cf58c682f64561 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Basic
/-!
# Boosts in the Lorentz group
-/
@[expose] public section
noncomputable section
open Matri... |
15,453 | lean_file_chunk | 5c6d9b0cc2597759bc8acaec2199aa3be5d01c4b447249e9b4c4bb281caaf0a9 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Restricted.Basic
/-!
# Generalized Boosts
This module defines a generalization of the traditional boos... |
10,826 | lean_file_chunk | 55d656b8ff702fdb26d2873ae5d46dd103dff7633bfb5581770f40cbd237d730 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Proper
public import Physlib.Relativity.LorentzGroup.ToVector
public import Physlib.Relativity.Tensors.R... |
8,224 | lean_file_chunk | 90c839b0fd62094bf5c56936eaeb76248b822508561e35c73a3af7abc1e3da47 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Basic
public import Mathlib.Topology.Connected.PathConnected
public import Mathlib.Tactic.Cases
/-!
# Th... |
2,820 | lean_file_chunk | d993edd7ca3ca84d19736787584d67e9e7ea65a14493f215520bfac028a3356a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Meta.Informal.SemiFormal
public import Physlib.Relativity.LorentzGroup.Orthochronous.Basic
/-!
# The Restricted Lorentz Group
T... |
4,109 | lean_file_chunk | cc990fc13e92183b8ecb4f4b081040798deaed426ebb3fc015139a356864a13d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Rotations
public import Physlib.Relativity.LorentzGroup.Boosts.Generalized
/-!
# The construction of an ... |
6,872 | lean_file_chunk | 803200cb80f74a0343819f88bebe1972970465fe0a91dd0b95f470b6ad17f63b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Restricted.Basic
/-!
# Rotations
In this module we define rotations of in the Lorentz group.
-/
@[exp... |
3,566 | lean_file_chunk | 7e79c5d97eb3b7548521ae89729bd47093ca0d0ad44766bf4693a38c57f3ea97 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.MinkowskiProduct
/-!
# Vectors from Lorentz group elements
Every element of the Lorentz g... |
9,142 | lean_file_chunk | 2aed20593f1f0c5f3acdd7b688699614fe577bcd16ee8539970a46d72fb558c6 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Algebra.Lie.Classical
public import Mathlib.Analysis.Normed.Ring.Lemmas
/-!
# The Minkowski matrix
## i. Overview
The aim of ... |
9,276 | lean_file_chunk | ea9f0b2adb55862e281b2e9df2664c66f3ea80668d85d775729048acbc98bf33 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Fermions.Weyl.Two
public import Physlib.Relativity.Tensors.ComplexTensor.Vector.Pre.Basic
/-!
## Pauli matrices as a... |
6,450 | lean_file_chunk | 830cc0fcc8dc3f94993e8636b08bad807ab58bbee4d3189ca7f6adff255383d8 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.LinearAlgebra.Matrix.Trace
/-!
## Pauli matrices
The pauli matrices are defined u... |
2,239 | lean_file_chunk | d0a367c5b01a91697c3be2d5dc3c016f8ed9315d50a5d32ec0624bb22add93e4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Physlib.Relativity.PauliMatrices.Basic
public import Mathlib.LinearAlgebra.CliffordAlgebra.Basic
/-!
# The Pauli matrices, interpreted as a Clifford ... |
4,632 | lean_file_chunk | b97c1ada3a1ed950bdca53d3a8e7abed122302e7236377fb0ddb6080a0d29341 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.PauliMatrices.ToTensor
public import Physlib.Relativity.Tensors.ComplexTensor.Units.Basic
/-!
## Contraction of indi... |
19,109 | lean_file_chunk | 72180bb2fa1f687e79512178708c896a35df8e10f662648fbd406d0c977e50ad | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.PauliMatrices.Basic
public import Physlib.Relativity.MinkowskiMatrix
/-!
## Interaction of Pauli matrices with self-... |
14,640 | lean_file_chunk | e88883cbd3bc53744a73b8f29ec7fbab0a5e2ff345ee11bf3261cea36469a734 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Metrics.Basic
public import Physlib.Relativity.PauliMatrices.AsTensor
public import Physlib.Rel... |
12,749 | lean_file_chunk | 567bf5f03ba5cff1407a7f2f70f069776a2588c7098b67230781257e5e4c559c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.SL2C.SelfAdjoint
public import Mathlib.Analysis.Complex.Polynomial.Basic
public import Physlib.Relativity.LorentzGrou... |
9,516 | lean_file_chunk | dfa6fd34fdcc6b83912023846f42d291c68bbf6dff3cadc46d7e31b4b0b302e1 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Gordon Hsu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gordon Hsu
-/
module
public import Physlib.Mathematics.SchurTriangulation
public import Mathlib.LinearAlgebra.Matrix.Hermitian
/-! # Extra lemmas regarding `Lorentz.SL2C.toSelfAdjointMap`... |
1,504 | lean_file_chunk | 28b70587ed1e1572a4ac96ac02a38cd4596f443c5079bef6f11b19ee35aada87 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.SpaceTime.Basic
public import Physlib.Relativity.Tensors.RealTensor.Vector.Causality.LightLike
pu... |
4,482 | lean_file_chunk | 29b0c4e3fe86cc632ff32c0b919a13a608c2211a187489b6b5a1acf6fcab6cea | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Special.ProperTime
/-!
# Twin Paradox
The twin paradox corresponds to the following scenario:
Two twins start at th... |
1,772 | lean_file_chunk | cd15a8cd3139c68a9c91a308a2b6ac3e8218963d8b9d5f76195b5a606558427d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Data.Real.Basic
/-!
# The Speed of Light
## i. Overview
In this module we define a type for the speed of light in a vacuum,
a... |
23,992 | lean_file_chunk | 3d809a52ba3476245f401c12ef24c1ce0e0f5fddad61ea2b81bd51c7685897d7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComponentIdx.Single
public import Physlib.Relativity.Tensors.Reindexing
public import Physlib.Relativity.Tens... |
2,305 | lean_file_chunk | b936e855ccf366fa1db0a8bfdebba5597a0e1c1b7c563f097d82d4cf0ae94bef | lean_source_file | physlib_source_file_chunks | lemma permT_injective {n m : ℕ} {c : Fin n → C} {c1 : Fin m → C}
{σ : Fin m → Fin n} (h : IsReindexing c c1 σ) :
Function.Injective (permT (S := S) σ h) :=
(injective_iff_map_eq_zero' _).mpr (permT_eq_zero_iff h)
/-!
## field
-/
/-- The linear map between tensors with zero indices and the underlying field
... |
11,683 | lean_file_chunk | 7a648d55b2ebfbf527b9e63fcb37809c82252bb24616eb93df3cb9f248faf78a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith, Nikolai Kashcheev
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Metrics.Pre
public import Physlib.Relativity.Fermions.Weyl.Metric
/-!
## Co... |
906 | lean_file_chunk | 2fb552f798a21f362e2005afe5d3c1f6bef68ae3cf9fe45a6a3d242020e87b67 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Basic
/-!
## Lemmas related to complex Lorentz tensors.
-/
@[expose] public section
open Ma... |
14,901 | lean_file_chunk | 09081a59411fc9dcceadc1199d4d00e9d7c2c4ca486e8beab03fb1dc6bf0ce19 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Vector.Pre.Basic
/-!
# Tensor products of two complex Lorentz vectors
-/
@[expose] public se... |
16,083 | lean_file_chunk | 3382e2a1cb7e5bbe8c863548742d71facc1d5d55a83a80c6a9407357ed494b19 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.OfRat
/-!
## Metrics as complex Lorentz tensors
-/
@[expose] public section
open Matrix
ope... |
7,102 | lean_file_chunk | 9dfed7fbad25760dd551e2b5e0bea48c35c31abde2216680e8ab7190a505e2f1 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Metrics.Basic
public import Physlib.Relativity.Tensors.ComplexTensor.Units.Basic
/-!
## Basic ... |
6,766 | lean_file_chunk | 1ed099ae71a1a6f7ff1f509280d3240564faf982344e4c385a6230601816124c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Units.Pre
/-!
# Metric for complex Lorentz vectors
-/
@[expose] public section
noncomputable... |
6,380 | lean_file_chunk | 220002cb7818a0eada4e9bb9b75ef64c0a80cab8ac9a6a97cacc61913ad230bf | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Basic
public import Physlib.Mathematics.RatComplexNum
public import Physlib.Relativity.Tensors.... |
11,234 | lean_file_chunk | 7891f4fb1f2aa65e4692a9acbde9fb6082790572cd42757961d9458a41d1fedc | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.OfRat
/-!
## Unit tensors for complex Lorentz tensors
-/
@[expose] public section
open Matr... |
6,510 | lean_file_chunk | fd27e95826920c4d3d6bc0b4985f8c4397ecd67796a95100b88163e90c8a2cbc | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Matrix.Pre
public import Physlib.Relativity.Tensors.ComplexTensor.Vector.Pre.Contraction
/-!
#... |
1,739 | lean_file_chunk | c46e56fd6f5c85f5d477c0e354d48325fe43ba46aa3a7cbd07b509497c847b23 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Units.Basic
/-!
## Symmetry lemmas relating to units
-/
@[expose] public section
open Matri... |
8,986 | lean_file_chunk | 2d37f1b03d30cf8db098c29ef0e0f913af670e773fda2982514c984ed3c31da8 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nikolai Kashcheev, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Vector.Pre.Modules
/-!
# Complex Lorentz vectors
We define complex Lorentz... |
6,320 | lean_file_chunk | ca7a8be8ef70f2c9a50b40170ea48722614375b58cec570a878a13e85ec16e82 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Vector.Pre.Basic
/-!
# Contraction of Lorentz vectors
-/
@[expose] public section
noncomput... |
5,453 | lean_file_chunk | d6e137e0412497ba3b37752da942e9a39135eea270a717249107042b57d422ce | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nikolai Kashcheev, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.SL2C.Basic
/-!
## Modules associated with complex Lorentz vectors
We define the modules underlyi... |
2,652 | lean_file_chunk | 626d7cda7449cb971b3a7a0d4b63a67a7ccd1c3942813679e66bc8bfaf436b0b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.TensorSpecies.Basic
/-!
# Component indices
## i. Overview
For a tensor species `S` and a list of colors `... |
6,112 | lean_file_chunk | 75e144f08bf7f518ac477f5adf053a06df980d8caf07e4584ba9d78c5ea6d100 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComponentIdx.Basic
public import Physlib.Relativity.Tensors.Contraction.SuccSuccAbove
/-!
# Contractions of ... |
2,533 | lean_file_chunk | 503d4357e21fceffa516bf8382c36bfb4d2eea993b428f9ede29fb262a6ea727 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComponentIdx.Basic
/-!
# Products of component indices
## i. Overview
This file contains the component-ind... |
2,119 | lean_file_chunk | c7554eb404cd27171418197354c963bb761e3e8c11b064ec4c4b3f93553439bb | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComponentIdx.Basic
/-!
# Component indices for one-index tensors
## i. Overview
This file defines the cano... |
18,894 | lean_file_chunk | 486f36734152f855a4354464b386f2349bebd35bdbe0fe981751cd959c6a587d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Andrea Pari. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrea Pari
-/
module
public import Physlib.Relativity.Tensors.Contraction.Basic
public import Physlib.Relativity.Tensors.Contraction.Basis
public import Physlib.Mathematics.ConjModule
p... |
17,388 | lean_file_chunk | 4d2ecccbae19d62b1bc2306d6cd4a5102ef47b5260b76480f1e691a42096f44c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Contraction.Products
/-!
# Constructors of tensors.
There are a number of ways to construct explicit tensor... |
8,605 | lean_file_chunk | 97fc6b3a4e0878b854d524251fad9b803fb0551ffc40c2069489a431b31f1d84 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Contraction.Pure
/-!
# Contractions on tensors
## i. Overview
This file defines tensor contraction for an ... |
3,705 | lean_file_chunk | 3584525cf6d3a3c890d828229b0f4e21e525bbd47f253214bc4f07425e91a6c5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Contraction.Basic
public import Physlib.Relativity.Tensors.ComponentIdx.Contraction
/-!
# Contractions on ba... |
18,306 | lean_file_chunk | f7030b6db0da2843e7804b2e7bf6c3b2d7cdf5a5d6e5348cd0b928dad83b1878 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Andrea Pari. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrea Pari
-/
module
public import Physlib.Relativity.Tensors.Contraction.Products
/-!
# Cross contraction at named slots
## i. Overview
`contrT` contracts two slots of a single tens... |
7,182 | lean_file_chunk | 94f203fe96256c89c3ec195527328ca1211305ff76502547014d94fdeb04fede | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Andrea Pari. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrea Pari
-/
module
public import Physlib.Relativity.Tensors.Contraction.CrossToEnd
/-!
# Result-to-slot contraction against a rank-2 tensor
## i. Overview
`crossToEnd` deposits the... |
6,299 | lean_file_chunk | 800713a6740542ef76c9eaea11145a81a247f6ce11065087971c40e701aacd6d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Contraction.Basic
public import Physlib.Relativity.Tensors.Product
/-!
# The interaction of contractions and... |
16,012 | lean_file_chunk | 1fd0503f88c543461351dc04068ecf5c2759f24aa063b2b31e9d29c4b719a264 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Basic
/-!
# Contractions on pure tensors
-/
@[expose] public section
namespace TensorSpecies
open Module
... |
16,502 | lean_file_chunk | 0c322e6cf909d76b82ee477d5070c5beee0ed9be7b6b5ab13659dbecd5e3935a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Data.Finset.Sort
public import Mathlib.Data.Nat.SuccPred
/-!
# Defining succSuccAbove
In Mathlib there is the `Fin.succAbove` ... |
20,206 | lean_file_chunk | 10d194713e5d7dfdabb084ead7e231da32b917c2d15c2122ac17ea83e5284a03 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Andrea Pari. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrea Pari
-/
module
public import Physlib.Relativity.Tensors.Contraction.CrossToSlot
public import Physlib.Relativity.Tensors.UnitTensor
public import Physlib.Relativity.Tensors.Evalua... |
8,103 | lean_file_chunk | e7e4d575029ebe528ee8d389c234b0ca9b3ecd573859d5279dae60188b907dfd | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.MetricTensor
public import Physlib.Relativity.Tensors.Contraction.UnitTensorContraction
/-!
# Dual tensors
... |
23,952 | lean_file_chunk | de43f20a50e050f0cdaff5771de66513b41a68c63dbca4a7f45e273546bc4c54 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Dual
public import Physlib.Relativity.Tensors.Tensorial
/-!
# Elaboration of tensor expressions
- Syntax in... |
2,988 | lean_file_chunk | 0b8779621c20de9484e3047d233a434c87449f0e60f9ac556361cd9deb458482 | lean_source_file | physlib_source_file_chunks | {c1 c2 c3 : C} {u : S.Tensor ![c1, c2]} {u' : S.Tensor ![c2, c1]}
{w : S.Tensor ![c3]} {td : S.Tensor ![S.τ c1, S.τ c2]}
{M : Type} [AddCommMonoid M] [Module k M] [Tensorial S c M] (m : M)
-- A bare `S.Tensor` carries no redundant `Tensorial.toTensor` wrapper.
/-- info: t : S.Tensor c -/
#guard_msgs in
#check ... |
18,126 | lean_file_chunk | f6d997d4341b04abb4b2126b33a415fb4324e1bfaf10fb9d6720d32eae7969c2 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Product
public import Physlib.Relativity.Tensors.Contraction.Basis
public import Physlib.Meta.Sorry
/-!
# Ev... |
3,715 | lean_file_chunk | 3b8683b93055dff52ab1535acc917ad394193e13cb1c9878e75eb40763191aaa | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.UnitTensor
/-!
# The metric tensors
-/
@[expose] public section
namespace TensorSpecies
variable {k : Ty... |
1,869 | lean_file_chunk | 238e7bd49baea599b337b59542fdbaa4daecc4afc9881ac36176edf974b67951 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Basic
/-!
# Basis for tensors in a tensor species
-/
@[expose] public section
open Module
namespace Tens... |
23,491 | lean_file_chunk | b325c6eb30dfb52dbae87f9b916670f40afc197941d7cd78c70a3fb85d99a2e9 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Basic
public import Physlib.Relativity.Tensors.ComponentIdx.Product
/-!
# The product of tensors
## i. Over... |
8,323 | lean_file_chunk | ce8987c3c581483d5127f4abe760df1f242cb5bac8bc040e3713c26202912a5a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Metrics.Pre
public import Physlib.Relativity.Tensors.Contraction.Basis
public import Physlib.Relat... |
5,110 | lean_file_chunk | 53d4139b290c29e268a7017a343db8472799e91ecd8718418f73a77c11297504 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Geometry.Manifold.IsManifold.Basic
/-!
# Lorentz co vec... |
2,796 | lean_file_chunk | 0f16d69956818512da7922f782c5e5ef88c37617d48a35941f97eb2e89af3aef | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.RepresentationTheory.Basic
public import Physlib.Relativity.LorentzGroup.Basic
public import Physlib.Relativity.Tensors.RealTens... |
6,618 | lean_file_chunk | 32be30072386156cd2d43b8d7bf10700a90b7aef51e7ba376db52638d175bf46 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.CoVector.Basic
public import Physlib.Relativity.Tensors.RealTensor.Basic
public ... |
12,363 | lean_file_chunk | 188d48dae8e16fbabd225af2b1d6aef0af383c33cb45410ad9888b23b7ad3564 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Pre.Basic
public import Mathlib.LinearAlgebra.TensorProduct.Matrix
/-!
# Tensor products o... |
3,710 | lean_file_chunk | 4afebe40a7b318e57aad16b23b5dc41af97ea6d260b00441549989175d20a386 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Basic
public import Physlib.Relativity.Tensors.MetricTensor
/-!
## Metrics as real Lorentz tensor... |
8,548 | lean_file_chunk | 0dd8e808a63caef4ea71afb1a14f3355343488cdc3ec5d2c9b7289bcb4108f54 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Units.Pre
/-!
# Metric for real Lorentz vectors
-/
@[expose] public section
noncomputable secti... |
4,721 | lean_file_chunk | 4b312b598c383fcb0adec147e46576709594b9ad6f32e918e86953ba542fae94 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Representation
public import Physlib.Relativity.Tensors.RealTensor.CoVector.Representation
... |
23,961 | lean_file_chunk | c0b2b4c824708dc762cbbd67561f41045eddd4232b3ab651dd25242374806d39 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nikolai Kashcheev, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComplexTensor.Basic
/-!
# Complex Lorentz tensors from real Lorentz tensors
## i. Overvi... |
8,360 | lean_file_chunk | 2a862f14bebd6a8f0a572c9ef6d3022f56f32cd82ce57180e08abe48f1fcc1e8 | lean_source_file | physlib_source_file_chunks | /-- `τ` commutes with `colorToComplex` on the Lorentz `up/down` colors. -/
@[simp]
lemma tau_colorToComplex (x : realLorentzTensor.Color) :
(complexLorentzTensor).τ (colorToComplex x) = colorToComplex ((realLorentzTensor).τ x) := by
cases x <;> rfl
/-- `complexify` commutes with precomposition by `succSuccAbove`... |
8,103 | lean_file_chunk | e1c843d9062152237a2650b4ffc8d60cd0c2c8f90dd9313a473821616c8baee6 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Matrix.Pre
public import Physlib.Relativity.Tensors.RealTensor.Vector.Pre.Contraction
/-!
# Unit ... |
14,022 | lean_file_chunk | 1b1ff7c301bdf12a67b6d620db6e7d578695eea05477907536436fd5dceeeb1c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Geometry.Manifold.IsManifold.Basic
/-!
# Lorentz Vector... |
4,951 | lean_file_chunk | 04df051bc6523c56f0dc8ca17245fa7b3baa9e796386cd371152dde6aa9adbe4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.MinkowskiProduct
/-!
## Causality of Lorentz vectors
-/
@[expose] publ... |
2,378 | lean_file_chunk | 3465ca9757abe7256ca29ad0e1c8edb6a4de88d71b18e707156aae3d860f5066 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Causality.Basic
/-!
## Properties of light like vectors
-/
@[expose] ... |
4,388 | lean_file_chunk | 260c025615f917b68a7518acda9de0ceae13a6e198f11c566f3ec01cb0fb707d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Causality.Basic
/-!
## Properties of time like vectors
-/
@[expose] p... |
10,200 | lean_file_chunk | aec8c909e16b7dc519875b6d56e3cdcb8a68e409fadefb89bb0b7f2de0c02539 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Tensorial
public import Physlib.Relativity.Tensors.RealTensor.Metrics.Bas... |
6,325 | lean_file_chunk | 073b02552d317c84ba50039264a0e7a0ff6df1a201248bd80e65e1e699a1eead | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Pre.Modules
public import Mathlib.RepresentationTheory.Rep.Basic
/-!
# Real Lorentz vector... |
16,453 | lean_file_chunk | a2700f75585525c9c270f911e5c7feff8ed3bf2772b04a277941943911208e2a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Pre.Basic
/-!
# Contraction of Real Lorentz vectors
-/
@[expose] public section
noncomp... |
15,743 | lean_file_chunk | 7a55922614e2048ec0469410e17bd8a5f5f007be7c3687b01cc051343dc65b32 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.PauliMatrices.SelfAdjoint
public import Mathlib.RepresentationTheory.Basic
public import Physlib.Relativity.LorentzGr... |
2,474 | lean_file_chunk | 0a1ff13f7c888d3ad778119ba28e527801830d8f723cec2ed96b64eb166c8719 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.RepresentationTheory.Basic
public import Physlib.Relativity.LorentzGroup.Basic
public import Physlib.Relativity.Tensors.RealTens... |
7,156 | lean_file_chunk | c3cead121f0f5d1b74a4bdc64c9ec959b33d4a8679f7aa841aea9e319235f3f4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Basic
public import Physlib.Relativity.Tensors.RealTensor.Vector.Basic
/-!
# Te... |
5,569 | lean_file_chunk | 14bc2a2d2f930a9827755ca028fe0ff7381b13149e137952bbda6371fa5c8699 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.MinkowskiProduct
/-!
# Lorentz Velocities
In this module we define Lorentz velocities to ... |
23,915 | lean_file_chunk | be5de70ab2b30c56d708736d1c8702d9f539b652a16aff26fc6a5a64fcdf1595 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.ComponentIdx.Single
public import Physlib.Relativity.Tensors.Contraction.SuccSuccAbove
public import Mathlib.... |
2,205 | lean_file_chunk | b6793141c665a5ad5bc319a54275ca14a9dc69f3b892571fa175694a0e6c273b | lean_source_file | physlib_source_file_chunks | last one as in `append_succ_last`: the block map that lists the `i.succAbove` survivors and then
`i` itself matches `c` with the survivors of `i` followed by the surviving entry `c1 1` of a
rank-two list `c1` whose second entry is slot `i`'s colour. -/
lemma move_last {n : ℕ} {c : Fin (n + 1) → C} {c1 : Fin 2 → C} ... |
5,441 | lean_file_chunk | 40500a092948fa843a2144921a53d5f3af5e1ea26bea1866f4c591e22b4dd6e6 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.RepresentationTheory.Rep.Basic
public import Physlib.Mathematics.PiTensorProduct
public import Mathlib.Algebra.Lie.OfAssociative... |
13,684 | lean_file_chunk | 1cc7850435ef9aaa5fec26eef332a873408a3fc3fca5cf4e0abc2f7390f1190f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Product
public import Physlib.Relativity.Tensors.Evaluation
public import Mathlib.Topology.Algebra.Module.Fin... |
3,531 | lean_file_chunk | abec632199fce8c63e81ae6f4e786f181d8421f1668e5a0721b1951a252db31c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.Constructors
/-!
# The unit tensors
-/
@[expose] public section
namespace TensorSpecies
variable {k : Ty... |
10,862 | lean_file_chunk | f905376d3372bd422b8fb64580a98d7d63fadfb54a001ff9b8a7b2e7e7879934 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Rob Sneiderman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rob Sneiderman
-/
module
public import Physlib.SpaceAndTime.Space.EuclideanGroup.Basic
public import Physlib.SpaceAndTime.Space.Origin
public import Physlib.SpaceAndTime.Time.Basic
/... |
8,162 | lean_file_chunk | f043f3cbcc81af9718e32339b85bf33718d04590bdf26a0c0b9e7ed2d0265ab5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Meta.TODO.Basic
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Geometry.Manifold.Instances.Real
/-!... |
23,968 | lean_file_chunk | 8ed93f96d6be0f6e2a56b829ce17d63e79018fa14e62736e3075c29b25506ac0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.FiniteDimension
public import Physlib.SpaceAndTime.Space.Derivatives.Basic
public import Physlib.Spac... |
1,068 | lean_file_chunk | 58de982988e6582233cc19613a8fbcb78fcc723fcac2b922855e1668ae5043d6 | lean_source_file | physlib_source_file_chunks | rw [integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable]
· simp
· simp
change Integrable (fun r => fderiv ℝ (fun r => η ((slice i).symm (r, x))) r 1) volume
fun_prop
· simp
exact schwartzMap_integrable_slice_symm i η x
· fun_prop
· fun_prop
simp
lemma distDeriv_c... |
3,930 | lean_file_chunk | 43bc54807835dbe5615ff73ab651a49c160c6b6cd0749d4b208e8bc488383f86 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Zhi Kai Pong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith
-/
module
public import Mathlib.LinearAlgebra.CrossProduct
public import Physlib.SpaceAndTime.Time.Derivatives
/-!
# The cross product on Euclidean vec... |
14,988 | lean_file_chunk | 715a4845a812ce456d0d165e1c473efae0ba492de5bf4831afba14dea3775d2a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Symmetric
public import Physlib.Mathematics.Distribution.Basic
public imp... |
23,980 | lean_file_chunk | cec7d5ff0423867122f08675bfc3228815b6479da4c8648dc429f0e3763469bd | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Laplacian
public import Mathlib.MeasureTheory.Integral.CurveIntegra... |
5,826 | lean_file_chunk | 966d39f33bfa748ece149cffe5b200d2aacbd5fd9537ad1d6ae541bc18945060 | lean_source_file | physlib_source_file_chunks | induction' x using basis_induction_on with j p1 p2 h1 h2 c p1 h1
rotate_left
· simp
· simp [inner_add_right, ← h1,← h2]
· simp [inner_smul_right, ← h1]
simp only [inner_basis, basis_repr_symm_apply]
rw [← deriv_eq, ← deriv_eq]
exact deriv_comm_of_curl_zero f hf hcurl a j i
obtain ⟨g, hg⟩ :... |
2,107 | lean_file_chunk | f14ce2f45c897ddecf6bb446c2def75c619cf9da5c59adb9e697713d4305a7b7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Juan Jose Fernandez Morales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Juan Jose Fernandez Morales
-/
module
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Physlib.SpaceAndTime.Space.Derivatives.MultiIndex
/-!
# ... |
7,164 | lean_file_chunk | 0b3bfebfae419193a59555da510b2fc3068c9a1ebe626ae56194bc2963ba00f0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Grad
public import Physlib.SpaceAndTime.Space.DistOfFunction
/-!
#... |
17,463 | lean_file_chunk | c0fe561a44b9f285c1ded28ee6b44ec1bdd0dba8230c58c16563eb58856c2254 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Basic
public import Physlib.SpaceAndTime.Space.IsDistBounded
public... |
6,695 | lean_file_chunk | a86586361f9bb829049f40c1a9ac6dc32bc5357aeadea3c6890800fc1b83e47e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Juan Jose Fernandez Morales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Juan Jose Fernandez Morales
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.MultiIndex
/-!
# Ite... |
2,326 | lean_file_chunk | b009f465f94c6fefeedaecbeb4982e58ad0677971c95645605b23d85ec1790b4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Div
/-!
# The Laplacian operator on `Space d`
## i. Overview
In ... |
3,532 | lean_file_chunk | 853f1a23d3dffb057873880c1a5ef49e35d6188d98812f5fcceeab54cdeeb3f4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Div
/-!
# Matrix divergence on Space
## i. Overview
In this module we define the matrix divergence o... |
5,187 | lean_file_chunk | 78511794061871c8d16614ba76aa662a727ad1d4f14c865bf5983a453ec3ea38 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Juan Jose Fernandez Morales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Juan Jose Fernandez Morales
-/
module
public import Mathlib.Algebra.BigOperators.Fin
/-!
# Multi-indices
## i. Overview
This module defines the basic type of multi-in... |
1,784 | lean_file_chunk | 6b2707bd8c91b5fd20f941fd7c8e7f384e3b788f05f558c81504a7fbe89d21d0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Curl
/-!
# The constant distribution on space
## i. Overview
In this module we define the cons... |
5,923 | lean_file_chunk | 612feaa9950974b108a0a008a68e78b019a67aba319f0a63daa289a3f3ec4823 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.IsDistBounded
public import Physlib.SpaceAndTime.Space.Derivatives.Basic
public import Mathlib.MeasureTheory.... |
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