path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Data\Stream\Init.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Stream.Defs
import Mathlib.Logic.Function.Basic
import Mathlib.Init.Data.List.Basic
import Mathlib.Data.List.Basic
/-!
# Streams a.k.a.... |
Data\String\Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Lex
import Mathlib.Data.Char
import Mathlib.Tactic.AdaptationNote
import Mathlib.Algebra.Order.Group.Nat
/-!
# Strings
Supplementary theore... |
Data\String\Defs.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Keeley Hoek, Floris van Doorn, Chris Bailey
-/
import Batteries.Data.String.Basic
import Batteries.Tactic.Alias
/-!
# Definitions for `String`
This file defines a bunch of ... |
Data\String\Lemmas.lean | /-
Copyright (c) 2021 Chris Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Bailey
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Data.String.Defs
import Mathlib.Tactic.Basic
/-!
# Miscellaneous lemmas about strings
-/
namespace String
lemma congr_a... |
Data\Sum\Basic.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury G. Kudryashov
-/
import Mathlib.Logic.Function.Basic
import Mathlib.Tactic.MkIffOfInductiveProp
import Batteries.Data.Sum.Lemmas
/-!
# Additional lemmas about sum... |
Data\Sum\Interval.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Sum
import Mathlib.Data.Sum.Order
import Mathlib.Order.Interval.Finset.Defs
/-!
# Finite intervals in a disjoint union
This file provides the... |
Data\Sum\Lattice.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Sum.Order
import Mathlib.Order.Hom.Lattice
/-!
# Lexicographic sum of lattices
This file proves that we can combine two lattices `α` and `β` into a ... |
Data\Sum\Order.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Hom.Basic
/-!
# Orders on a sum type
This file defines the disjoint sum and the linear (aka lexicographic) sum of two orders and
provides relation ... |
Data\Sym\Basic.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Multiset.Basic
import Mathlib.Data.Vector.Basic
import Mathlib.Data.Setoid.Basic
import Mathlib.Tactic.ApplyFun
/-!
# Symmetric powers
This file defin... |
Data\Sym\Card.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta, Huỳnh Trần Khanh, Stuart Presnell
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Finset.Sym
import Mathlib.Data.Fintype... |
Data\Sym\Sym2.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Sym2.Init
import Mathlib.Data.SetLike.Basic
/-!
# The symmetric square
This file def... |
Data\Sym\Sym2\Init.lean | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Aesop
/-!
# Sym2 Rule Set
This module defines the `Sym2` Aesop rule set. Aesop rule sets only become
visible once the file in which they're declared is impo... |
Data\Sym\Sym2\Order.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.Sym.Sym2
import Mathlib.Order.Lattice
/-!
# Sorting the elements of `Sym2`
This files provides `Sym2.sortEquiv`, the forward direction of which is som... |
Data\Tree\Basic.lean | /-
Copyright (c) 2019 mathlib community. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Wojciech Nawrocki
-/
import Batteries.Data.RBMap.Basic
import Mathlib.Data.Nat.Notation
import Mathlib.Tactic.TypeStar
import Mathlib.Util.CompileInductive
/-!
# Bi... |
Data\Tree\Get.lean | /-
Copyright (c) 2019 mathlib community. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Wojciech Nawrocki
-/
import Mathlib.Data.Num.Basic
import Mathlib.Data.Tree.Basic
/-!
# Binary tree get operation
In this file we define `Tree.indexOf`, `Tree.get`... |
Data\Vector\Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Data.Vector.Defs
import Mathlib.Data.List.Nodup
import Mathlib.Data.List.OfFn
import Mathlib.Data.List.I... |
Data\Vector\Defs.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Init.Data.List.Lemmas
import Mathlib.Tactic.Common
/-!
The type `Vector` represents lists with fixed length.
-/
namespace Mathlib
assert_no... |
Data\Vector\MapLemmas.lean | /-
Copyright (c) 2023 Alex Keizer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Keizer
-/
import Mathlib.Data.Vector.Basic
import Mathlib.Data.Vector.Snoc
/-!
This file establishes a set of normalization lemmas for `map`/`mapAccumr` operations on vectors
-/
... |
Data\Vector\Mem.lean | /-
Copyright (c) 2022 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import Mathlib.Data.Vector.Basic
/-!
# Theorems about membership of elements in vectors
This file contains theorems for membership in a `v.toList` for a vector `v`.
Having ... |
Data\Vector\Snoc.lean | /-
Copyright (c) 2023 Alex Keizer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Keizer
-/
import Mathlib.Data.Vector.Basic
/-!
This file establishes a `snoc : Vector α n → α → Vector α (n+1)` operation, that appends a single
element to the back of a vector.... |
Data\Vector\Zip.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Data.Vector.Basic
/-!
# The `zipWith` operation on vectors.
-/
namespace Mathlib
namespace Vector
section ZipWith
variable {α β γ : Type*} {n : ℕ}... |
Data\W\Basic.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Logic.Equiv.List
/-!
# W types
Given `α : Type` and `β : α → Type`, the W type determined by this data, `WType β`, is the
inductively defined type of t... |
Data\W\Cardinal.lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.W.Basic
import Mathlib.SetTheory.Cardinal.Ordinal
/-!
# Cardinality of W-types
This file proves some theorems about the cardinality of W-types. The ... |
Data\W\Constructions.lean | /-
Copyright (c) 2015 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Hua
-/
import Mathlib.Data.W.Basic
/-!
# Examples of W-types
We take the view of W types as inductive types.
Given `α : Type` and `β : α → Type`, the W type determined by this dat... |
Data\ZMod\Algebra.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Algebra.Defs
/-!
# The `ZMod n`-algebra structure on rings whose characteristic divides `n`
-/
namespace ZMod... |
Data\ZMod\Basic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Ring.Prod
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
/-!
# Integers mod `n`
Definit... |
Data\ZMod\Coprime.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.RingTheory.Int.Basic
import Mathlib.RingTheory.PrincipalIdealDomain
/-!
# Coprimality and vanishing
We show that for pri... |
Data\ZMod\Defs.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.NeZero
import Mathlib.Data.Nat.ModEq
import Mathlib.Data.Fintype.Card
/-!
# Definition of `ZMod n` + ba... |
Data\ZMod\Factorial.lean | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Data.Nat.Factorial.BigOperators
import Mathlib.Data.ZMod.Basic
/-!
# Facts about factorials in ZMod
... |
Data\ZMod\IntUnitsPower.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Data.Int.Order.Units
import Mathlib.Data.ZMod.Basic
/-!
# The power operator on `ℤˣ` by `ZMod 2`, `ℕ`, and... |
Data\ZMod\Module.lean | /-
Copyright (c) 2023 Lawrence Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lawrence Wu
-/
import Mathlib.Algebra.Module.Submodule.Lattice
import Mathlib.Data.ZMod.Basic
import Mathlib.Order.OmegaCompletePartialOrder
/-!
# The `ZMod n`-module structure on Abelia... |
Data\ZMod\Parity.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Data.ZMod.Basic
/-!
# Relating parity to natural numbers mod 2
This module provides lemmas relating `ZMod 2` to `Even... |
Data\ZMod\Quotient.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Group.Equiv.TypeTags
import Mathlib.Data.ZMod.Basic
import Mathlib.GroupTheory.GroupAction.Quotient
import Mathlib.RingTheory.Ideal.QuotientOperation... |
Data\ZMod\Units.lean | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching, Ashvni Narayanan, Michael Stoll
-/
import Mathlib.Algebra.BigOperators.Associated
import Mathlib.Data.ZMod.Basic
import Mathlib.Data.Nat.PrimeFin
import Mathlib.Rin... |
Deprecated\Group.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.TypeTags
import Mathlib.Algebra.Group.Units.Hom
import Mathlib.Algebra.Ring.Hom.Defs
/-!
# Un... |
Deprecated\Ring.lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Deprecated.Group
/-!
# Unbundled semiring and ring homomorphisms (deprecated)
This file is deprecated, and is no longer imported by anything in mathl... |
Deprecated\Subfield.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Deprecated.Subring
/-!
# Unbundled subfields (deprecated)
This file is deprecated, and is no longer imported b... |
Deprecated\Subgroup.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Deprecated.Submonoid
/-!... |
Deprecated\Submonoid.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Submonoid.Basic
import Mathlib... |
Deprecated\Subring.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Deprecated.Subgroup
import Mathlib.Deprecated.Group
import Mathlib.Algebra.Ring.Subring.Basic
/-!
# Unbundled subrings (deprecated)
This file is depr... |
Dynamics\Flow.lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Logic.Function.Iterate
/-!
# Flows and invariant sets
This file defines a flow on a topological space `α` by a topologi... |
Dynamics\Minimal.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.Topology.Algebra.ConstMulAction
/-!
# Minimal action of a group
In this file we define an action... |
Dynamics\Newton.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, Oliver Nash
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Algebra.Polynomial.Identities
import Mathlib.RingTheory.Nilpotent.Lemmas
import Mathlib.R... |
Dynamics\OmegaLimit.lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import Mathlib.Dynamics.Flow
import Mathlib.Tactic.Monotonicity
/-!
# ω-limits
For a function `ϕ : τ → α → β` where `β` is a topological space, we
define the ω-limit under `ϕ` of... |
Dynamics\PeriodicPts.lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.Algebra.Ring.Divisibility.Basic
import Mathlib.Data.List.Cycle
import Mathlib.Data.Nat.Prime.Basic... |
Dynamics\BirkhoffSum\Average.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Dynamics.BirkhoffSum.Basic
import Mathlib.Algebra.Module.Basic
/-!
# Birkhoff average
In this file we define `birkhoffAverage f g n x` to be
$$
\fr... |
Dynamics\BirkhoffSum\Basic.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Dynamics.FixedPoints.Basic
/-!
# Birkhoff sums
In this file we define `birkhoffSum f g n x` to be ... |
Dynamics\BirkhoffSum\NormedSpace.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.RCLike.Basic
import Mathlib.Dynamics.BirkhoffSum.Average
/-!
# Birkhoff average in a normed space
In this file we prove some lemmas about ... |
Dynamics\Circle\RotationNumber\TranslationNumber.lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Order.Iterate
import Mathlib.Order.SemiconjSup
import... |
Dynamics\Ergodic\AddCircle.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Data.Set.Pointwise.Iterate
import Mathlib.Dynamics.Ergodic.Ergodic
import Mathlib.MeasureTheory.Covering.DensityTheorem... |
Dynamics\Ergodic\Conservative.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.Combinatorics.Pigeonhole
/-!
# Conserv... |
Dynamics\Ergodic\Ergodic.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Dynamics.Ergodic.MeasurePreserving
/-!
# Ergodic maps and measures
Let `f : α → α` be measure preserving with respect to a measure `μ`. We say `f` is ergod... |
Dynamics\Ergodic\Function.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Dynamics.Ergodic.Ergodic
import Mathlib.MeasureTheory.Function.AEEqFun
/-!
# Functions invariant under (quasi)ergodic map
In this file we prove tha... |
Dynamics\Ergodic\MeasurePreserving.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.AEMeasurable
/-!
# Measure preserving maps
We say that `f : α → β` is a measure preserving map w.r.t. measures `μ : Measure α... |
Dynamics\FixedPoints\Basic.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Set.Function
import Mathlib.Logic.Function.Iterate
import Mathlib.GroupTheory.Perm.Basic
/-!
# Fixed points of a self-map
In this file we defi... |
Dynamics\FixedPoints\Topology.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hölzl
-/
import Mathlib.Dynamics.FixedPoints.Basic
import Mathlib.Topology.Separation
/-!
# Topological properties of fixed points
Currently this file cont... |
FieldTheory\AbelRuffini.lean | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.GroupTheory.Solvable
import Mathlib.FieldTheory.PolynomialGaloisGroup
import Mathlib.RingTheory.RootsOfUnity.Basic
/-... |
FieldTheory\AbsoluteGaloisGroup.lean | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import Mathlib.FieldTheory.KrullTopology
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.Topology.Algebra.Group... |
FieldTheory\Adjoin.lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.Algebra.Algebra.Subalgebra.Directed
import Mathlib.FieldTheory.IntermediateField
import Mathlib.FieldTheory.Separable
imp... |
FieldTheory\AxGrothendieck.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.MvPolynomial.Basic
import Mathlib.Data.Fintype.Card
import Mathlib.RingTheory.Algebraic
/-!
# Ax-Grothendieck for algebraic extensions of `ZMod p`... |
FieldTheory\Cardinality.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.Field.ULift
import Mathlib.Algebra.MvPolynomial.Cardinal
import Mathlib.Data.Nat.Factorization.PrimePow
import Mathlib.Data.Rat.Denumerable
imp... |
FieldTheory\ChevalleyWarning.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.FieldTheory.Finite.Basic
/-!
# The Chevalley–Warning theorem
This file contains a proof of the Chevalley–Warning theorem.
Throughout most of this fil... |
FieldTheory\Extension.lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.FieldTheory.Adjoin
/-!
# Extension of field embeddings
`IntermediateField.exists_algHom_of_adjoin_splits'` is the main result: if E/L/F is a tower ... |
FieldTheory\Finiteness.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# A module over a d... |
FieldTheory\Fixed.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Polynomial.GroupRingAction
import Mathlib.Algebra.Ring.Action.Field
import Mathlib.Algebra.Ring.Action.Invariant
import Mathlib.FieldTheory.Normal
import... |
FieldTheory\Galois.lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.FieldTheory.Fixed
import Mathlib.FieldTheory.NormalClosure
import Mathlib.FieldTheory.PrimitiveElement
import Mathlib.Gro... |
FieldTheory\IntermediateField.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.Tower
import Mathlib.RingTheory.Algebraic
import Mathlib.FieldTheory.Minpoly.Basic
/-!
# Intermediate fields
Let `L / K` be a field extension, ... |
FieldTheory\IsPerfectClosure.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.PurelyInseparable
import Mathlib.FieldTheory.PerfectClosure
/-!
# `IsPerfectClosure` predicate
This file contains `IsPerfectClosure` which asserts that ... |
FieldTheory\IsSepClosed.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.FieldTheory.Galois
/-!
# Separably Closed Field
In this file we define the typeclass for separably closed fie... |
FieldTheory\KrullTopology.lean | /-
Copyright (c) 2022 Sebastian Monnet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Monnet
-/
import Mathlib.FieldTheory.Galois
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.OpenSubgroup
import Mathlib.Tactic.ByContra
/-!
# K... |
FieldTheory\KummerExtension.lean | /-
Copyright (c) 2023 Andrew Yang, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.RootsOfUnity.Basic
import Mathlib.RingTheory.AdjoinRoot
import Mathlib.FieldTheory.Galois
import Mathlib.LinearAlgebra.Eigenspace.Mi... |
FieldTheory\Laurent.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Polynomial.Taylor
import Mathlib.FieldTheory.RatFunc.AsPolynomial
/-!
# Laurent expansions of rational functions
## Main declarations
* `R... |
FieldTheory\MvPolynomial.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
import Mathlib.RingTheory.MvPolynomial.Basic
/-!
# Multivaria... |
FieldTheory\Normal.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import Mathlib.FieldTheory.Extension
import Mathlib.FieldTheory.SplittingField.Construction
import Mathlib.GroupTheory.Solvable
/-!
# Normal fie... |
FieldTheory\NormalClosure.lean | /-
Copyright (c) 2023 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.FieldTheory.Normal
import Mathlib.Order.Closure
/-!
# Normal closures
## Main definitions
Given field extensions `K/F` and `L/F`, the predicate `I... |
FieldTheory\Perfect.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.FieldTheory.Separable
import Mathlib.FieldTheory.SplittingField.Construction
import Mathlib.Algebra.CharP.Reduced
/-!
# Perfect fields and rings
In this f... |
FieldTheory\PerfectClosure.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.FieldTheory.Perfect
/-!
# The perfect closure of a characteristic `p` ring
## Main definitions
- `PerfectClosure`: the perfect closure of a ... |
FieldTheory\PolynomialGaloisGroup.lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.FieldTheory.Galois
/-!
# Galois Groups of Polynomials
In this file, we introduce the Galois group of a polynomial `p` o... |
FieldTheory\PrimitiveElement.lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.RingTheory.IntegralDomain
/-!
# Primitive Element Theorem
In th... |
FieldTheory\PurelyInseparable.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.SeparableClosure
import Mathlib.Algebra.CharP.IntermediateField
/-!
# Purely inseparable extension and relative perfect closure
This file contains basic... |
FieldTheory\Separable.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Polynomial.Expand
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.Algebra.Squarefree.Basic
import Mathlib.FieldTheory.Minpoly.Field
import Mathli... |
FieldTheory\SeparableClosure.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.SeparableDegree
import Mathlib.FieldTheory.IsSepClosed
/-!
# Separable closure
This file contains basics about the (relative) separable closure of a fie... |
FieldTheory\SeparableDegree.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.SplittingField.Construction
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.FieldTheory.Separable
import Mathlib.FieldTheory.NormalC... |
FieldTheory\Tower.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.RingTheory.AlgebraTower
import Mathlib.LinearAlgebra.FiniteDimensional.Defs
import Mathlib.LinearAlgebra.FreeModule.Finite.Mat... |
FieldTheory\Finite\Basic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Joey van Langen, Casper Putz
-/
import Mathlib.FieldTheory.Separable
import Mathlib.RingTheory.IntegralDomain
import Mathlib.Algebra.CharP.Reduced
import Mathlib.Tactic.App... |
FieldTheory\Finite\GaloisField.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Alex J. Best, Johan Commelin, Eric Rodriguez, Ruben Van de Velde
-/
import Mathlib.Algebra.CharP.Algebra
import Mathlib.Data.ZMod.Algebra
import Mathlib.FieldTheory.Fin... |
FieldTheory\Finite\Polynomial.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.MvPolynomial.Expand
import Mathlib.FieldTheory.Finite.Basic
import Mathlib.LinearAlgebra.FiniteDimensional
import Mathlib.RingTheory.MvPolynomi... |
FieldTheory\Finite\Trace.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.RingTheory.Trace.Basic
import Mathlib.FieldTheory.Finite.GaloisField
/-!
# The trace map for finite fields
We state the fact that the trace map from a ... |
FieldTheory\IsAlgClosed\AlgebraicClosure.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.DirectLimit
import Mathlib.Algebra.CharP.Algebra
import Mathlib.FieldTheory.IsAlgClosed.Basic
import Mathlib.FieldTheory.SplittingField.Construction
/-!... |
FieldTheory\IsAlgClosed\Basic.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.FieldTheory.Normal
import Mathlib.FieldTheory.Perfect
import Mathlib.RingTheory.Localization.Integral
/-!
# Algebraically Closed Field
In this file we define t... |
FieldTheory\IsAlgClosed\Classification.lean | /-
Copyright (c) 2022 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Polynomial.Cardinal
import Mathlib.Algebra.MvPolynomial.Cardinal
import Mathlib.Data.ZMod.Algebra
import Mathlib.FieldTheory.IsAlgClosed.Basic
impo... |
FieldTheory\IsAlgClosed\Spectrum.lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Spectrum
import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Spectrum mapping theorem
This file develops proves the spectral mapping the... |
FieldTheory\Minpoly\Basic.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johan Commelin
-/
import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic
/-!
# Minimal polynomials
This file defines the minimal polynomial of an element `x` of an `A... |
FieldTheory\Minpoly\Field.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.FieldTheory.Minpoly.Basic
import Mathlib.RingTheory.Algebraic
/-!
# Minimal polynomia... |
FieldTheory\Minpoly\IsIntegrallyClosed.lean | /-
Copyright (c) 2019 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Paul Lezeau, Junyan Xu
-/
import Mathlib.RingTheory.AdjoinRoot
import Mathlib.FieldTheory.Minpoly.Field
import Mathlib.RingTheory.Polynomial.GaussLemma
/-!
# Minimal... |
FieldTheory\Minpoly\MinpolyDiv.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed
import Mathlib.FieldTheory.PrimitiveElement
import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Results about `minpoly... |
FieldTheory\RatFunc\AsPolynomial.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.FieldTheory.RatFunc.Basic
import Mathlib.RingTheory.EuclideanDomain
import Mathlib.RingTheory.DedekindD... |
FieldTheory\RatFunc\Basic.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.RatFunc.Defs
import Mathlib.RingTheory.EuclideanDomain
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.RingTheory.Polynomial.C... |
FieldTheory\RatFunc\Defs.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.Algebra.Polynomial.RingDivision
/-!
# The field of rational functions
Files in this folder define the f... |
FieldTheory\RatFunc\Degree.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.RatFunc.AsPolynomial
import Mathlib.RingTheory.EuclideanDomain
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.RingTheory.Poly... |
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