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 |
|---|---|---|---|---|---|
23,946 | lean_file_chunk | d2726fb6a0b4b7934c8454b612defb9a91744bae2a120300c411ed176a648a5f | lean_source_file | lean_pool_source_file_chunks | * ((μ.map U).real {u} * (μ.map X).real {x} * (μ.map Y).real {y})) * (μ.map Z).real {z}
= ((μ.map (fun ω => (X ω, Y ω, Z ω))).real {(x, y, z)}
* (μ.map (fun ω => (X ω, U ω))).real {(x, u)}
* (μ.map (fun ω => (Y ω, U ω))).real {(y, u)}) * (μ.map Z).real {z} := by
have h_lhs : (phat... |
23,964 | lean_file_chunk | fa0f635ce47c05fe8baefb8a55e84c9fca294684032ba0ef07eb2907950f1470 | lean_source_file | lean_pool_source_file_chunks | (h_proj_embed : ∀ d, proj (embed d) = c)
(h_extract_embed : ∀ d, extract (embed d) = d)
(h_embed_extract : ∀ t, proj t = c → embed (extract t) = t) :
(∑ t ∈ (Finset.univ : Finset (S₁ × S₂ × S₃ × S₄)).filter
(fun t => proj t = c), ptilde X Y Z U μ t)
= ∑ d : δ, ptilde X Y Z U μ (embed d) := by
... |
4,391 | lean_file_chunk | ac4db037b21e77cf7b06dcf463c4ffa27abefae79f5a503f06592858ae2eb18c | lean_source_file | lean_pool_source_file_chunks | have h_YZU_le_Y := measureReal_map_pair_le_map_fst hY (hZ.prodMk hU) μ y (z, u)
have h_ZU_le_Z := measureReal_map_pair_le_map_fst hZ hU μ z u
have h_ZU_le_U := measureReal_map_pair_le_map_snd hZ hU μ z u
have hXZU_nn : 0 ≤ (μ.map (fun ω => (X ω, Z ω, U ω))).real {(x, z,
u)} := measureReal_nonneg
h... |
10,514 | lean_file_chunk | 85f1bd4a6e787e64aa16e5cee37cbadd75eaca2689750068dd80d78ef3fd09da | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.CopyLemma
import LeanPool.ZhangYeungInequality.Delta
import LeanPool.ZhangYeungInequality.Prelude
/-!
# The Zhang-Yeung i... |
23,986 | lean_file_chunk | ffa0614e7e352c9a234ff7485cd49910d5e3cbdbecbcda7b375fece0f8512cd5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.EntropyRegion
import LeanPool.ZhangYeungInequality.Theorem3
/-!
# Theorem 4: Shannon incompleteness at `n = 4`
Theorem 4... |
23,990 | lean_file_chunk | d86f6dad23428c965f07785e62d9ca42e48e1c80b56db14f072c7160aed6d19a | lean_source_file | lean_pool_source_file_chunks | the joint tuple is constant, and its entropy is zero.
-/
lemma entropyFn_empty : entropyFn X μ ∅ = 0 := by
simp only [entropyFn, entropyFnN]
have : IsEmpty {j : Fin 4 // j ∈ (∅ : Finset (Fin 4))} :=
⟨fun ⟨j, hj⟩ => Finset.notMem_empty j hj⟩
have : Nonempty Ω := nonempty_of_isProbabilityMeasure μ
have h_eq :... |
589 | lean_file_chunk | 371945b9a0f4b89f47bdc4505894482b405a9e555260e6cc4892e6424e02a9c4 | lean_source_file | lean_pool_source_file_chunks | almost-entropic
realization back down to the first four coordinates and applying the `n = 4` exclusion.
-/
theorem _root_.ZhangYeung.theorem4_ge_four (n : ℕ) (hn : 4 ≤ n) :
∃ F : Finset (Fin n) → ℝ,
F ∈ shannonRegionN n ∧ F ∉ almostEntropicRegionN.{u} n := by
refine ⟨FWitnessN hn, shannonCone_of_witness_n h... |
19,893 | lean_file_chunk | e83e3be35867e8bc3afdedb2b952b098b2c6d4aab5a0ad4984978546d90599bb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.CopyLemma
import LeanPool.ZhangYeungInequality.Delta
import LeanPool.ZhangYeungInequality.EntropyRegion
import LeanPool.Zh... |
827 | lean_file_chunk | 6c60c237fd7236cdd3d6e3f2cc762665c1463a4f7e3bbb7e1d2065709a2985d7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.CopyLemma
import LeanPool.ZhangYeungInequality.Delta
import LeanPool.ZhangYeungInequality.EntropyRegion
import LeanPool.Zh... |
1,143 | lean_file_chunk | f5c2fe940f30a1a2e1176da224a282e6a1a65d471b6761fa77f2e0a9bf34eaa7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 The FLT Project. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: The FLT Project, √2
-/
import LeanPool.Odlyzko
/-!
# Solution: Odlyzko bound for root discriminants
Challenge: `odlyzko-root-discriminant-bound` (`Challenge.Odlyzko`)
Proves: `Chal... |
3,763 | lean_file_chunk | 0820e6b651cc9b53d08acffff89e9433543d1c4a95f3f4e031ca6386c11b4d0f | 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.Mathematics.VariationalCalculus.IsTestFunction
/-!
# Admissible local variations
## i. Overview
This module ... |
1,258 | lean_file_chunk | bb3fae7f9c22a77ee800159cbae7463886b8af96ab7e76d6e237b1a854eed9f4 | 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
/-!
# A. Classical mechanics
Classical mechanics describes the motion of physical systems using trajectories, forces,
energies, and variational prin... |
23,976 | lean_file_chunk | 98e9efced7d64204aa3ea87c1d215ae20d66c13497bc47341722756fc7124896 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicola Bernini. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicola Bernini, Florian Wiesner
-/
module
public import Physlib.ClassicalMechanics.HarmonicOscillator.Basic
/-!
# The damped harmonic oscillator
## i. Overview
The damped harmonic ... |
185 | lean_file_chunk | 60673ec0d5fe73b7d8a88599996150fa1ce631529a278c6b3b81f165710e2032 | lean_source_file | physlib_source_file_chunks | refine forall_congr' fun t => ?_
simp only [Pi.zero_apply, smul_eq_zero, Real.exp_ne_zero, false_or, sub_eq_zero]
exact eq_comm
end DampedHarmonicOscillator
end ClassicalMechanics |
23,970 | lean_file_chunk | d27d3662b8de5f0d05eb330f324b15d3bd7de1c77438de66bcd111e262b7fc2d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge, Florian Wiesner
-/
module
public import Physlib.ClassicalMechanics.DampedHarmonicOscillator.Basic
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivH... |
52 | lean_file_chunk | 287b832dc461d3a0a888cee561773955ffcf88f413387c4df0ef0d818d4ada7c | lean_source_file | physlib_source_file_chunks | end DampedHarmonicOscillator
end ClassicalMechanics |
3,603 | lean_file_chunk | 5667f097a405e51a1d2f4cd042b56187988e74ac7082dd9373b8db50ff049c4b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Tomas Skrivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Skrivan, Joseph Tooby-Smith
-/
module
public import Physlib.Mathematics.VariationalCalculus.HasVarGradient
public import Physlib.SpaceAndTime.Time.Derivatives
/-!
# A. Euler–Lag... |
6,809 | lean_file_chunk | 0548b449483b322b6c7a70278b2cd2b877582a09d9406bce931ff51066375317 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Pranav Magdum. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pranav Magdum
-/
module
public import Physlib.SpaceAndTime.Time.Derivatives
public import Mathlib.Analysis.Calculus.MeanValue
/-!
# The Free Particle
## i. Overview
The free particle... |
3,875 | lean_file_chunk | 95e4ea1b697d0ae9f640f2312a93cb32bca23258a33245306448b50c1037c8cc | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Tomas Skrivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomas Skrivan, Joseph Tooby-Smith
-/
module
public import Physlib.Mathematics.VariationalCalculus.HasVarGradient
public import Physlib.SpaceAndTime.Time.Derivatives
/-!
# Hamilton's e... |
23,941 | lean_file_chunk | 1d194dc07621965b82c7e0dcfe01c21af4615c97fb6073d3cae8d58a12bab501 | 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, Lode Vermeulen
-/
module
public import Physlib.ClassicalMechanics.EulerLagrange
public import Physlib.ClassicalMechanics.HamiltonsEquations
public import Mathl... |
2,411 | lean_file_chunk | 5764e4b3e031b288cd8bfd04547e05c7bf865016f03724aefc496df0d6243477 | lean_source_file | physlib_source_file_chunks | hamilton's equations between the momentum and position. -/
noncomputable def hamiltonEqOp (p : Time → EuclideanSpace ℝ (Fin 1))
(q : Time → EuclideanSpace ℝ (Fin 1)) :=
ClassicalMechanics.hamiltonEqOp (hamiltonian S) p q
/-!
### G.5. Equation of motion if and only if Hamilton's equations
We show that the equat... |
11,634 | lean_file_chunk | a8f055b3cdcaec86e65d22f1f299b1409826eb334bf2bc9307842bab95fc1a0a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicola Bernini. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicola Bernini, Nathaneal Sajan
-/
module
public import Physlib.SpaceAndTime.Space.Basic
public import Mathlib.Geometry.Manifold.Diffeomorph
public import Mathlib.Geometry.Manifold.Ve... |
8,667 | lean_file_chunk | a46a4cfe05015839a61bd880158a81b0e21add2ea393868897ae406d6a1e5a4e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nathaneal Sajan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaneal Sajan
-/
module
public import Physlib.ClassicalMechanics.HarmonicOscillator.Basic
public import Physlib.ClassicalMechanics.HarmonicOscillator.Geometric.Basic
public import ... |
6,849 | lean_file_chunk | 83070b6b4ac69471f1ef32a8e4a9b933cb34ceb0b5dbbcd48a80d956170429be | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nathaneal Sajan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaneal Sajan
-/
module
public import Physlib.ClassicalMechanics.HarmonicOscillator.Geometric.Basic
public import Physlib.SpaceAndTime.Time.Derivatives
public import Mathlib.Geomet... |
23,963 | lean_file_chunk | 13461c03723e51bf1a63388cce5512f4041ed25b591e163ba159d316efd8523d | 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: Nathaneal Sajan, Joseph Tooby-Smith, Lode Vermeulen
-/
module
public import Physlib.ClassicalMechanics.HarmonicOscillator.Basic
public import Mathlib.Analysis.SpecialFunctions.Com... |
20,546 | lean_file_chunk | 03d6d5d2256942439de6eb25b02ccd041eb4bf1d88b3325a0c356aa186bd3171 | lean_source_file | physlib_source_file_chunks | linear_combination (IC.vT₀.ofLp i) * cos_sq_add_sin_sq (S.ω * IC.t₀.val)
/-- The energy of the trajectory at time `t₀` equals the energy computed from the
initial conditions at `t₀`. -/
lemma toInitialConditions_energy_at_t₀ (S : HarmonicOscillator)
(IC : InitialConditionsAtTime) :
S.energy ((IC.toInitialCon... |
16,025 | lean_file_chunk | 13e7eabe9203271b99894af41fbd573d4c467072a7d15364a9a1f09e1c6145e3 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Rein Zustand. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rein Zustand
-/
module
public import Physlib.Mathematics.InnerProductSpace.Basic
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Physlib.SpaceAndTime.Time.Derivative... |
6,092 | lean_file_chunk | 51ce7882cf6689e3ba8b5432968ba96f44e86a91caad0f7a0795e8943940174e | 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.RCLike.Basic
/-!
# Units on Mass
A unit of mass corresponds to a choice of translationally-invariant
metric on the ma... |
1,412 | lean_file_chunk | 6ea7f847168559ea3d2698d15e5925fcc465c8995bd4ae9a56117cc8bbbc0d17 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Hannah Dawe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hannah Dawe
-/
module
public import Mathlib.Analysis.Real.Sqrt
/-!
# Circular Orbit Vis Viva
The vis-viva equation relates the speed of an orbiting body to its position
and the mass of... |
4,960 | lean_file_chunk | 670089a2eaf2556475c118c627cb88b512ef82fec042c9eb78af5314d5bc34bc | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Shlok Vaibhav Singh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shlok Vaibhav Singh
-/
module
/-!
# Miscellaneous Pendulum Pivot Motions
### Tag: LnL_1.5.3
## Source:
* Textbook: Landau and Lifshitz, Mechanics, 3rd Edition
* Chapter 1 The Equ... |
2,133 | lean_file_chunk | 3562004fd0c72877ec4aa7bfaaab3e3f6fd2a204403d9083258f541edfaf7167 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Shlok Vaibhav Singh. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shlok Vaibhav Singh
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle
/-!
# Sliding Pendulum
### Tag: LnL_1.5.2
## Source:
* Textbook: Landau and Lifs... |
2,555 | lean_file_chunk | 54cd808b66ff21d2df5e448cb0c851820e8cae46281cbddd2a89c570c72fc109 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Sorge. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge
-/
module
public import Physlib.ClassicalMechanics.RigidBody.Basic
public import Physlib.Mathematics.CrossProduct
/-!
# Angular momentum of a rigid body
For a rigid b... |
13,911 | lean_file_chunk | 6ba77c193cc42984f901dd5813089fdeb143e13536d02dd8257ad1ec4cd8ffe0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Sorge. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge
-/
module
public import Physlib.ClassicalMechanics.RigidBody.Motion
public import Physlib.Mathematics.CrossProductMatrix
public import Physlib.SpaceAndTime.Time.MatrixD... |
16,582 | lean_file_chunk | ff5af0d9be133449e047e9aec96964ff6223f1bacc37017a8f541d8bfe0fee2a | 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.Module
public import Physlib.Meta.Informal.Basic
public import Mathlib.Geometry.Manifold.Algebra.SmoothFuncti... |
10,581 | lean_file_chunk | 663e32bd8fd21040689adacf50b1f0a1d15e585e072eb4e6b82010dee1a8ca9b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Sorge. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge
-/
module
public import Physlib.ClassicalMechanics.RigidBody.AngularMomentum
public import Physlib.ClassicalMechanics.RigidBody.AngularVelocity
public import Physlib.Ma... |
14,475 | lean_file_chunk | c2fe2625b258297d1366722c762dc7bddf1ae846722ba740d4f5e593c3d53274 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Sorge. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge
-/
module
public import Physlib.ClassicalMechanics.RigidBody.Basic
public import Physlib.SpaceAndTime.Time.Derivatives
public import Physlib.SpaceAndTime.Time.MatrixDer... |
437 | lean_file_chunk | 7aadd836c28a54b8bda406967fd487906e4711bbdc019b4375fcbf8e4593d989 | 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
/-!
# Scattering off a perfectly rigid sphere
## References
- Landau and Lifshitz, Mechanics, page 50, Sectio... |
463 | lean_file_chunk | 69ae6d14e918c3621507cbf9937d6d2df2f2f1d37b970d5dc3d35d04ff835319 | 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
/-!
# Vibrations of a symmetric linear triatomic molecule
## References
- Landau and Lifshitz, Mechanics, pag... |
15,341 | lean_file_chunk | cddaeaa0902868ddc83eba59b207ca678ff495a50565e13f97596a826c2a3b11 | 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
-/
module
public import Physlib.SpaceAndTime.Space.CrossProduct
public import Physlib.SpaceAndTime.Space.Derivatives.Laplacian
/-!
# Wave equation
## i. Overview
In this... |
3,330 | lean_file_chunk | a907f390d5d76f753fa30e9a9fb38eed2905178413e25a62e0fea49b5e120cf8 | 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
-/
module
public import Physlib.ClassicalMechanics.WaveEquation.Basic
/-!
# Harmonic Wave
Time-harmonic waves.
Note TODO `EGU3E` may require considerable effort to be ma... |
431 | lean_file_chunk | 16b11593e5f01e8bb974a9d91c66cb1a1136e36c0819ad9ad2af46f7362bac45 | 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
/-!
# Condensed Matter
This directory is currently a place holder.
Please feel free to contribute!
Some directories which are NOT currently place h... |
7,242 | lean_file_chunk | 0d896d75f9ad5a04ad99493256c2ff147aba6c0c9080b2c91a32a1e09db1debc | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Barbalinardo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Barbalinardo
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Tactic.Ring
public import Mathlib.Tactic.Positivity
/-!
# Thermoelectric figure of ... |
18,440 | lean_file_chunk | bbcdb2db1d50db6295db3c4b0edca76d2e3d96811f43400b58ba16e2f5f8de27 | 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.QuantumMechanics.HilbertSpaces.FiniteTarget.Basic
/-!
# The tight binding chain
## i. Overview
The tight binding chain corres... |
424 | lean_file_chunk | 9e4c61c6666ab47da72da5e4c6d2a9980d659ede42f2b8ac11ed64290bf079fb | 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
/-!
# Cosmology
This directory is currently a place holder.
Please feel free to contribute!
Some directories which are NOT currently place holders ... |
1,294 | lean_file_chunk | 4d7fdd2fe13f4aceac81a64b0f4c9afa8fde89e5de6da2212e34ee09d24d529c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Conformal time in FLRW cosmology
Placeholder file collecting TODO items for the conformal time and the conformal
Hubbl... |
1,363 | lean_file_chunk | c1080b812d5eb8d6a4de3afc27a1d130a7fd7c447578e413ab0f31521fe45e08 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Density parameters and the standard cosmological model
Placeholder file collecting TODO items for the critical density... |
1,826 | lean_file_chunk | fca3276a60001cde899791f0ec521fad492bc352a070f52245e3ad01030d0fc8 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Distances and redshift in FLRW cosmology
Placeholder file collecting TODO items for the notions of distance used in
co... |
1,922 | lean_file_chunk | c26e6964e1fcd297efd4df2da47c4f9d4951a978950866f4edd17101116e08e4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Dynamical criteria for FLRW cosmology
Placeholder file collecting TODO items for the qualitative consequences of the
F... |
1,499 | lean_file_chunk | 960a99e29801a1629286be3152fa720383c89e2a3a26336d51d6b5e5056449fe | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Matter content of FLRW cosmology
Placeholder file collecting TODO items for the matter content of a
Friedmann-Lemaître... |
1,410 | lean_file_chunk | dda1aa5a0faabf29e20d23428c59ddd3fd97b1235f53fe7c8bcf1307f44f3bdf | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Jinzheng Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jinzheng Li
-/
module
public import Physlib.Meta.TODO.Basic
/-!
# Exact solutions of the Friedmann equations
Placeholder file collecting TODO items for the standard closed-form solutio... |
2,925 | lean_file_chunk | 1faa0096b93a0d6da7915e0467e7af112a4a1e35f36ad18ddf2b59e646b6df64 | 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.SpaceTime.Basic
/-!
# A. Electromagnetism
Electromagnetism describes electric and magnetic fields, their potentia... |
4,406 | lean_file_chunk | e02b0d727e9fadc4e2ae49445c9ab70454105c06d35ea361d2fce338f6ab05f1 | 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.RCLike.Basic
/-!
# The units of charge
A unit of charge corresponding to a choice of translationally-invariant
metric... |
1,077 | lean_file_chunk | 3e342734ed13a48df437e0038298b504ff545fc8235972c3b8399cfb620af849 | 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
/-!
# The electrostatics of a circular coil
## i. Overview
This module is currently a stub, but will eventuall... |
9,040 | lean_file_chunk | 3244fafb8655efa5a1fb81c296460599bc32b63469bda0a638ae19ca6e947d18 | 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.Electromagnetism.Distributional.Dynamics.IsExtrema
public import Physlib.SpaceAndTime.Space.Norm.Basic
public import Physlib.Spa... |
6,944 | lean_file_chunk | 5364348ec43ba869c67f04eb49aa2f04e3d6b8d09438717dd0bfceeba06db99f | 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.TimeAndSpace.ConstantTimeDist
public import Physlib.Mathematics.VariationalCalculus.HasVarAdjDeriv
public import Ph... |
2,386 | lean_file_chunk | 2001d8bbaaffd5e577dbe3b80f099e0b1001a9c4c47a54a4ddda0ef953bece44 | 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.SpaceTime.TimeSlice
/-!
# The Lorentz Current Density
## i. Overview
In this module we define the Lorentz curren... |
9,321 | lean_file_chunk | 7618aca45da74ccb455e7c10215076678d912abaaa072f26faf93e3a2a2ee57a | 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.Electromagnetism.Distributional.Dynamics.Lagrangian
/-!
# Extrema of the Lagrangian density
## i. Overview
In this module we ... |
8,853 | lean_file_chunk | be82f6ddb657920b5aeb128e5c6fd4ed12eb6b620f9335d2c4a1cddc627bc825 | 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.Electromagnetism.Distributional.MagneticField
public import Physlib.Electromagnetism.Dynamics.Basic
public import Physlib.Mathem... |
7,791 | lean_file_chunk | 63ae2fac3e8ddc5b20ac2545a6f2fe9dea40dfbf654ecfe6044c772df642e198 | 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.Electromagnetism.Distributional.Dynamics.CurrentDensity
public import Physlib.Electromagnetism.Distributional.Dynamics.KineticTe... |
3,277 | lean_file_chunk | b06b702152291de9195c7eac53321dc9a4b1a404b9a089724e7530fabef5b7e3 | 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.Electromagnetism.Distributional.VectorPotential
public import Physlib.Electromagnetism.Distributional.ScalarPotential
public imp... |
11,388 | lean_file_chunk | a439b4d02d6627eb9e77afebabd55a4b992bf301903e1a815a8e224a883fcaa1 | 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.Electromagnetism.Distributional.Basic
public import Physlib.Relativity.Tensors.RealTensor.Metrics.Basic
public import Mathlib.Al... |
5,731 | lean_file_chunk | 9a278a984929789696e62f11256b73d233ccb227e91eddcbeb7f779c48b93a7e | 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.Electromagnetism.Distributional.ElectricField
/-!
# The Magnetic Field
## i. Overview
In general dimensions we define the mag... |
1,805 | lean_file_chunk | ec9ad2ebced1e62eea16095a54501631e0b63b97f96a21018a8b91398e3a3867 | 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.Electromagnetism.Distributional.Basic
public import Mathlib.Algebra.Order.Archimedean.Real.Hom
/-!
# The Scalar Potential
## i... |
1,796 | lean_file_chunk | b0b2d7cedd3f02bd4d13cdad80c8174d897301213193fdcc067c4ad37395033c | 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.Electromagnetism.Distributional.Basic
public import Mathlib.Algebra.Order.Archimedean.Real.Hom
/-!
# The vector Potential
## i... |
2,241 | lean_file_chunk | 59d8519f3251b2cf776fa5126be8aff1e94c0f3e6234cd5ba81f54e373738467 | 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.SpeedOfLight
public import Mathlib.Analysis.Real.Sqrt
/-!
# Free space
## i. Overview
In this module we define a t... |
7,766 | lean_file_chunk | 6b99dec071953fa2fdcbd0f3ed862f7ee327f43363837fd78d704e80b0716e90 | 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.SpaceTime.TimeSlice
/-!
# The Lorentz Current Density
## i. Overview
In this module we define the Lorentz curren... |
8,959 | lean_file_chunk | 148b525fc69261cc9217b83bb74cd5e9b5f3eb3e8fac70d939b90d41c02d28e6 | 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.Electromagnetism.Dynamics.Lagrangian
/-!
# The Hamiltonian in electromagnetism
## i. Overview
In this module we define the ca... |
19,663 | lean_file_chunk | aa398c4d8548565c48baffb1e2ad931d9a7a93c9cf81e377b691276b48ea15fe | 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.Electromagnetism.Dynamics.Lagrangian
/-!
# Extrema of the Lagrangian density
## i. Overview
In this module we define what it ... |
23,937 | lean_file_chunk | ecad0834caf10819f9c660ec6a3de11ac4b8aaebae6f5b1262c0dac651a9e7ce | 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.Electromagnetism.Kinematics.MagneticField
public import Physlib.Electromagnetism.Dynamics.Basic
public import Physlib.Mathematic... |
5,482 | lean_file_chunk | 909f7e818f06d7c5a7959b0c59e76c91895d09766390f9a8da5f8c436a15fcfb | lean_source_file | physlib_source_file_chunks | lemma gradKineticTerm_eq_electric_magnetic_three {𝓕 : FreeSpace} (A : ElectromagneticPotential)
(x : SpaceTime) (ha : ContDiff ℝ ∞ A) :
A.gradKineticTerm 𝓕 x =
(1/(𝓕.μ₀ * 𝓕.c) * Space.div (A.electricField 𝓕.c (x.time 𝓕.c)) x.space) •
Lorentz.Vector.basis (Sum.inl 0) +
∑ i, (𝓕.μ₀⁻¹ * (1 / 𝓕... |
14,299 | lean_file_chunk | c7b2e3394da416038699912936f99cdc3256d021f0915b383527768990ab9fa3 | 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.Electromagnetism.Dynamics.CurrentDensity
public import Physlib.Electromagnetism.Dynamics.KineticTerm
public import Physlib.Relat... |
6,240 | lean_file_chunk | 152eb8578e412e06053e2cf00bb598ff66f5bbc2a375abec5ed406ddceb08363 | 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.Electromagnetism.Kinematics.MagneticField
public import Physlib.SpaceAndTime.SpaceTime.Boosts
/-!
# Boosts on the electric and ... |
23,024 | lean_file_chunk | 88eca3fc833b4b3756c45fadc851ee984769f800db06f4a432a7d94c2b297cdb | 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.Mathematics.VariationalCalculus.HasVarAdjDeriv
public import Physlib.SpaceAndTime.SpaceTime.TimeSlice
public import Physlib.Math... |
13,164 | lean_file_chunk | c74e90ec32d75ce63086e0196405344014a71d927088682a1f700a4cd827f1a9 | 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.Electromagnetism.Kinematics.ScalarPotential
public import Physlib.Electromagnetism.Kinematics.FieldStrength
public import Physli... |
23,998 | lean_file_chunk | 9cbb29e503a635795b8c954e2262aa24b87ea7cb05d21385a980599523d13766 | 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.Electromagnetism.Kinematics.EMPotential
public import Physlib.Relativity.Tensors.RealTensor.Metrics.Basic
public import Mathlib.... |
2,117 | lean_file_chunk | 50a2e79915cf348b108f2fce3804817e2942db5f2593ffe86955bd4b3c416e83 | lean_source_file | physlib_source_file_chunks | lemma toFieldStrength_add {d} (A1 A2 : ElectromagneticPotential d)
(x : SpaceTime d) (hA1 : Differentiable ℝ A1) (hA2 : Differentiable ℝ A2) :
toFieldStrength (A1 + A2) x = toFieldStrength A1 x + toFieldStrength A2 x := by
apply (Lorentz.CoVector.basis.tensorProduct Lorentz.Vector.basis).repr.injective
ext ... |
17,712 | lean_file_chunk | 7c84b6fdf6dfe010e9002fed4a0c62f4848f4390f532fa4d875997f1d87e8d92 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Justin Findlay. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justin Findlay
-/
module
public import Physlib.Electromagnetism.Kinematics.FieldStrength
/-!
# Gauge Transformations of the Electromagnetic Potential
## i. Overview
In this module ... |
18,009 | lean_file_chunk | e7d7ff49a511beced5a22a3e4f08ed778a485162a45f863a29343c17c02b3fdf | 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.Electromagnetism.Kinematics.ElectricField
/-!
# The Magnetic Field
## i. Overview
In 3-spatial dimensions from the electromag... |
6,953 | lean_file_chunk | 2ca7504681091c7f1faa35b47eeb4e04a53ecb6fcf6cc40a29bd2440282c0707 | 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.Electromagnetism.Kinematics.VectorPotential
/-!
# The Scalar Potential
## i. Overview
The electromagnetic potential is given ... |
11,530 | lean_file_chunk | 98c0973df02bb14a90c357738b43443755a3829b8b215f9439be972607735524 | 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.Electromagnetism.Kinematics.EMPotential
public import Mathlib.Algebra.Order.Archimedean.Real.Hom
/-!
# The vector Potential
##... |
8,775 | lean_file_chunk | 07e1eac733579f8f38adcf493edafd415f1da6049445bf2004659f4e03490862 | 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.Electromagnetism.Distributional.Dynamics.IsExtrema
public import Physlib.SpaceAndTime.Space.Norm.Basic
public import Physlib.Spa... |
10,833 | lean_file_chunk | 8643f892717b7bc14a3e494ce0c0399dd12e92307e62f6c57dfa0591ce0ae018 | 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.Electromagnetism.Distributional.Dynamics.IsExtrema
public import Physlib.SpaceAndTime.Space.Norm.Basic
public import Physlib.Spa... |
1,606 | lean_file_chunk | 3b3398923959bf2788b4ddde90fffb53402c892396865a1a5b9b60f47e8ae25c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Zhi Kai Pong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong
-/
module
public import Physlib.Electromagnetism.Kinematics.MagneticField
/-!
# Three-Dimensional Electromagnetism
This directory provides a three-dimensional, vector-cal... |
3,554 | lean_file_chunk | d6f4dc84e359419abf02d05b785cc50ddb86b4af94c47325d0dfa4156c276159 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Zhi Kai Pong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong
-/
module
public import Physlib.Electromagnetism.ThreeDimension.Basic
public import Physlib.Electromagnetism.Dynamics.IsExtrema
/-!
# A. Maxwell's equations in three dimen... |
6,609 | lean_file_chunk | 48534e190bf930bbfeaecf8a9efab72300355bcc90e3cd32a55d08f8e9f6ba7c | 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.Electromagnetism.Dynamics.IsExtrema
/-!
# The constant electric and magnetic fields
## i. Overview
In this module we define t... |
21,078 | lean_file_chunk | 0b2bc70c6c9e4c6eb29d0ac7fb55777c108959fc13635cd8752356b73fa34a6a | 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 Physlib.Electromagnetism.Vacuum.IsPlaneWave
/-!
# Harmonic Wave in Vacuum
## i. Overview
In this module we define the electro... |
19,965 | lean_file_chunk | d17287e376d9565951269bbfc91906a6b9e7005c663c5a18df195d732c459339 | 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 Physlib.ClassicalMechanics.WaveEquation.Basic
public import Physlib.Electromagnetism.Dynamics.IsExtrema
/-!
# Electromagnetic w... |
1,835 | lean_file_chunk | e538210416df1a06c236d37d9658783cc68a4a42e4ef82aea0ee18a1b3d52451 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 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.Basic
public import Physlib.SpaceAndTime.Time.Basic
/-!
# Basic field types for fluid dynamics
## i. Overview
Th... |
2,186 | lean_file_chunk | 2740f626885edf175c5a6daf285437c7d99bf1651b2daa89610f439ebb48a36e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.FluidFlow.Basic
/-!
# Basic API for Cauchy flows
## i. Overview
This module defines `CauchyFlow`, the momentum-balanc... |
1,412 | lean_file_chunk | 2b25a3873b521339259bd2fab7e2ebe2315fe05edca8b17df882beee790e33d8 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner, Michał Mogielnicki
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.Grad
/-!
# Body-force predica... |
2,471 | lean_file_chunk | 22c0f1a32d0c9bab5bae72e5168b5e6e9ec42882d3d6919857434993f19de82a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner, Michał Mogielnicki
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.MatrixDiv
/-!
# Inviscid stre... |
4,073 | lean_file_chunk | 7630d5dbc40fb22e9b607d1783e4ddfe889a87b37225cdbf28b1ba25bcaa5f4d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Basic
public import Physlib.FluidDynamics.FluidFlow.Momentum
/-!
# Cauchy momentum equations
## i. Overview... |
3,683 | lean_file_chunk | 2a784f5f7588df56ccd8da5aff3fc61b562c105b51c3d82a72355a617422ddd1 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Momentum
public import Physlib.FluidDynamics.CauchyFlow.Newtonian
/-!
# The Navier-Stokes equations
## i. O... |
1,111 | lean_file_chunk | ecffa9810a3f59961a003150358a2ec43cbee36b585ac3ee6333b279760c20f0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Basic
public import Physlib.FluidDynamics.FluidFlow.Newtonian
/-!
# Newtonian stress law for Cauchy flows
#... |
3,046 | lean_file_chunk | 5d4f86afe347258a1f434143a31a186b1d6d0b844bf48899e4a1c594505e3bf0 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner, Michał Mogielnicki
-/
module
public import Physlib.FluidDynamics.CauchyFlow.Inviscid
public import Physlib.FluidDynamics.CauchyFlow.Momentum
/-!
# Euler equation fo... |
1,763 | lean_file_chunk | 8f84cd184204f7e4bcac67f1319552f7c65e3d6f4a6b49e120651a8a37f91ac2 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.Basic
/-!
# Basic API for fluid flows
## i. Overview
This module defines `FluidFlow`, the kinematic and mass-transpor... |
3,002 | lean_file_chunk | 647c20d9e8be7d02f5e9ccea6d5b6dcd7a97166f53413eb2bb180776f50fce93 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.FluidFlow.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.Div
public import Physlib.SpaceAndTime.Time.Derivat... |
2,384 | lean_file_chunk | d29c9c8c96b923e8af3ebfa504854153743c6a48d4a383e0a3ca95c110dd71d1 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner, Michał Mogielnicki
-/
module
public import Physlib.FluidDynamics.FluidFlow.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.Div
/-!
# Incompressible fluid... |
1,442 | lean_file_chunk | 3724997762fab39ba0dbf5913b169801bfdf95eb4755f06ac4afc5cd611b0cc4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.FluidFlow.Basic
public import Physlib.SpaceAndTime.Space.Derivatives.Grad
public import Physlib.SpaceAndTime.Time.Deriva... |
7,420 | lean_file_chunk | 6707b4e7dcdc585c8e94c04a1742e2c37c3e408a632beefb277be286193b1ff7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Florian Wiesner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florian Wiesner
-/
module
public import Physlib.FluidDynamics.FluidFlow.Continuity
public import Physlib.SpaceAndTime.Space.Derivatives.MatrixDiv
/-!
# Momentum fields for fluid flo... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.