path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Lean\Exception.lean | /-
Copyright (c) 2022 E.W.Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: E.W.Ayers
-/
import Lean.Exception
/-!
# Additional methods for working with `Exception`s
This file contains two additional methods for working with `Exception`s
* `successIfFail`, a gene... |
Lean\Expr.lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis, Floris van Doorn
-/
import Mathlib.Lean.Expr.Basic
import Mathlib.Lean.Expr.ReplaceRec
|
Lean\GoalsLocation.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Lean.Meta.Tactic.Util
import Lean.SubExpr
/-! This file defines some functions for dealing with `SubExpr.GoalsLocation`. -/
namespace Lean.SubExpr.GoalsL... |
Lean\Json.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Lean.Data.Json.FromToJson
/-!
# Json serialization typeclass for `PUnit` & `Fin n` & `Subtype p`
-/
universe u
namespace Lean
deriving instance FromJson, ToJso... |
Lean\LocalContext.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 Lean.LocalContext
/-!
# Additional methods about `LocalContext`
-/
namespace Lean.LocalContext
universe u v
variable {m : Type u → Type v} [Monad m] [Altern... |
Lean\Message.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Lean.Message
/-!
# Additional operations on MessageData and related types
-/
open Lean Std MessageData
instance {α β : Type} [ToMessageData α] [ToMessag... |
Lean\Meta.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Elab.Term
import Lean.Elab.Tactic.Basic
import Lean.Meta.Tactic.Assert
import Lean.Meta.Tactic.Clear
import Batteries.CodeAction -- to enable the hole cod... |
Lean\Name.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Lean.Meta.Match.MatcherInfo
import Lean.Meta.Tactic.Delta
import Std.Data.HashMap.Basic
/-!
# Additional functions on `Lean.Name`.
We provide `allNames` and ... |
Lean\Thunk.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Batteries.Data.Thunk
/-!
# Basic facts about `Thunk`.
-/
namespace Thunk
@[simp] theorem get_pure {α} (x : α) : (Thunk.pure x).get = x := rfl
@[simp] theorem get_... |
Lean\Elab\Term.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Lean.Elab.SyntheticMVars
/-!
# Additions to `Lean.Elab.Term`
-/
namespace Lean.Elab.Term
/-- Fully elaborates the term `patt`, allowing typeclass inference failur... |
Lean\Elab\Tactic\Basic.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jon Eugster
-/
import Mathlib.Lean.Meta
/-!
# Additions to `Lean.Elab.Tactic.Basic`
-/
open Lean Elab Tactic
namespace Lean.Elab.Tactic
/-- Return expected type ... |
Lean\Expr\Basic.lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis,
Floris van Doorn, E.W.Ayers, Arthur Paulino
-/
import Lean.Meta.Tactic.Rewrite
import Batteries.Lean.Expr
im... |
Lean\Expr\ExtraRecognizers.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Set.Defs
/-!
# Additional Expr recognizers needing theory imports
-/
namespace Lean.Expr
/-- If `e` is a coercion of a set to a type, return the set... |
Lean\Expr\ReplaceRec.lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis,
Floris van Doorn, E.W.Ayers
-/
import Lean.Expr
import Mathlib.Util.MemoFix
/-!
# ReplaceRec
We define a m... |
Lean\Meta\Basic.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Lean.Meta.AppBuilder
import Lean.Meta.Basic
/-!
# Additions to `Lean.Meta.Basic`
Likely these already exist somewhere. Pointers welcome.
-/
/--
Restore the ... |
Lean\Meta\CongrTheorems.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Lean.Meta.Tactic.Cleanup
import Lean.Meta.Tactic.Cases
import Lean.Meta.Tactic.Refl
import Mathlib.Logic.IsEmpty
/-!
# Additions to `Lean.Meta.CongrTheorems`
-/
na... |
Lean\Meta\DiscrTree.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Lean.Meta.DiscrTree
/-!
# Additions to `Lean.Meta.DiscrTree`
-/
namespace Lean.Meta.DiscrTree
/--
Find keys which match the expression, or some subexpressio... |
Lean\Meta\KAbstractPositions.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Lean.HeadIndex
import Lean.Meta.ExprLens
import Lean.Meta.Check
/-!
# Find the positions of a pattern in an expression
This file defines some tools for ... |
Lean\Meta\Simp.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Gabriel Ebner, Floris van Doorn
-/
import Lean.Elab.Tactic.Simp
/-!
# Helper functions for using the simplifier.
[TODO] Needs documentation, cleanup, and possibly reu... |
Lean\PrettyPrinter\Delaborator.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Lean.PrettyPrinter.Delaborator.Basic
/-!
# Additions to the delaborator
-/
namespace Lean.PrettyPrinter.Delaborator
open Lean.Meta Lean.SubExpr SubExpr
namespace... |
LinearAlgebra\AnnihilatingPolynomial.lean | /-
Copyright (c) 2022 Justin Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justin Thomas
-/
import Mathlib.FieldTheory.Minpoly.Field
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.Algebra.Polynomial.Module.AEval
/-!
# Annihilating Ideal
Given ... |
LinearAlgebra\Basis.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
import Mathlib.Algebra.BigOperators.Finsupp
import Mathlib.Algebra.BigOperators.Finprod
import Mathlib.Data.Fintype.BigOperators
i... |
LinearAlgebra\BilinearMap.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import Mathlib.Algebra.Module.Submodule.Ker
/-!
# Basics on bilinear maps
This file provides basics on bilinear maps. The most general form considered are map... |
LinearAlgebra\Coevaluation.lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.LinearAlgebra.Contraction
/-!
# The coevaluation map on finite dimensional vector spaces
Given a finite dimensional vector space `V` over a field... |
LinearAlgebra\Contraction.lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Antoine Labelle
-/
import Mathlib.LinearAlgebra.Dual
import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Contractions
Given modules $M, N$ over a commutative ring $R$, this fil... |
LinearAlgebra\CrossProduct.lean | /-
Copyright (c) 2021 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak, Kyle Miller, Eric Wieser
-/
import Mathlib.Data.Matrix.Notation
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Math... |
LinearAlgebra\Determinant.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import Mathlib.LinearAlgebra.GeneralLinearGroup
import Mathlib.LinearAlgebra.Matrix.Reindex
import Mathlib.Tactic.FieldSimp
... |
LinearAlgebra\DFinsupp.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Data.Finsupp.ToDFinsupp
import Mathlib.LinearAlgebra.Finsupp
import Mathlib.LinearAlgebra.LinearIndependent
/-!
# Properties of the module `Π₀ i... |
LinearAlgebra\Dual.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-/
import Mathlib.LinearAlgebra.FiniteDimensional
import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
import Mathlib.LinearAlgebra.FreeModu... |
LinearAlgebra\FiniteDimensional.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.FiniteDimensional.Defs
import Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition
import Mathlib.LinearAlgebra.Dimension.DivisionRing
... |
LinearAlgebra\FiniteSpan.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.LinearAlgebra.Span
import Mathlib.Algebra.Module.Equiv.Basic
/-!
# Additional results about fin... |
LinearAlgebra\Finsupp.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.Data.Finsupp.Encodable
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Span
import Mathlib.Data.Set.Countable
/-!
# Properties of the mod... |
LinearAlgebra\FinsuppVectorSpace.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.LinearAlgebra.DFinsupp
import Mathlib.LinearAlgebra.StdBasis
/-!
# Linear structures on function with finite support `ι →₀ M`
This file contains resu... |
LinearAlgebra\FreeAlgebra.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.Basis
import Mathlib.Algebra.FreeAlgebra
import Mathlib.LinearAlgebra.FinsuppVectorSpace
import Mathlib.LinearAlgebra.FreeModule.StrongRankCond... |
LinearAlgebra\GeneralLinearGroup.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.Algebra.Module.Equiv.Basic
/-!
# The general linear group of linear maps
The general linear group is defined to be the group of invertible linear map... |
LinearAlgebra\InvariantBasisNumber.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.RingTheory.OrzechProperty
import Mathlib.RingTheory.Ideal.Quotient
import Mathlib.RingTheory.PrincipalIdealDomain
/-!
# Invariant basis ... |
LinearAlgebra\Isomorphisms.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import Mathlib.LinearAlgebra.Quotient
/-!
# Isomorphism theorems for modules.
* The Noether's first, second, and thi... |
LinearAlgebra\JordanChevalley.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Dynamics.Newton
import Mathlib.LinearAlgebra.Semisimple
/-!
# Jordan-Chevalley-Dunford decomposition
Given a finite-dimensional linear endomorphism `f`, th... |
LinearAlgebra\Lagrange.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Wrenna Robson
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.LinearAlgebra.Vandermonde
import Mathlib.RingTheory.Polynomial.Basic
/-!
# Lagrange interpolatio... |
LinearAlgebra\LinearDisjoint.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.LinearAlgebra.TensorProduct.Tower
import Mathlib.LinearAlgebra.TensorProduct.Finiteness
import Mathlib.LinearAlgebra.TensorProduct.Submodule
import Mathlib.LinearAlgeb... |
LinearAlgebra\LinearIndependent.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.LinearAlgebra.Finsupp
import Mathlib.LinearAlgebra.Prod
import Ma... |
LinearAlgebra\LinearPMap.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Moritz Doll
-/
import Mathlib.LinearAlgebra.Prod
import Mathlib.Algebra.Module.Basic
/-!
# Partially defined linear maps
A `LinearPMap R E F` or `E →ₗ.[R] F` is a l... |
LinearAlgebra\Orientation.lean | /-
Copyright (c) 2021 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.LinearAlgebra.Ray
import Mathlib.LinearAlgebra.Determinant
/-!
# Orientations of modules
This file defines orientations of modules.
## Main definitions
... |
LinearAlgebra\PerfectPairing.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.LinearAlgebra.Dual
/-!
# Perfect pairings of modules
A perfect pairing of two (left) modules may be defined either as:
1. A bilinear map `M × N → R` such ... |
LinearAlgebra\Pi.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
import Mathlib.Algebra.Group.Fin.Tuple
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.Algebra.Modu... |
LinearAlgebra\PID.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.LinearAlgebra.Trace
import Mathlib.LinearAlgebra.FreeModule.PID
import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
/-!
# Linear maps of modules with coeff... |
LinearAlgebra\PiTensorProduct.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Eric Wieser
-/
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.LinearAlgebra.Multilinear.TensorProduct
import Mathlib.Tactic.AdaptationNote
/-!
# Tensor p... |
LinearAlgebra\Prod.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Prod
import Mathlib.LinearAlgebra.Span
import Mathlib.Order.PartialSups
/... |
LinearAlgebra\Projection.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.LinearAlgebra.Quotient
import Mathlib.LinearAlgebra.Prod
/-!
# Projection to a subspace
In this file we define
* `Submodule.linearProjOfIsCompl (p ... |
LinearAlgebra\Quotient.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import Mathlib.GroupTheory.QuotientGroup
import Mathlib.LinearAlgebra.Span
import Mathlib.Algebra.Module.Equiv.Basic
... |
LinearAlgebra\QuotientPi.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Quotient
/-!
# Submodule quotients and direct sums
This file contains some results on the quoti... |
LinearAlgebra\Ray.lean | /-
Copyright (c) 2021 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Algebra.Group.Subgroup.Actions
import Mathlib.Algebra.Order.Module.Algebra
import Mathlib.LinearAlgebra.LinearIndependent
import Mathlib.Algebra.Ring.Subri... |
LinearAlgebra\Reflection.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury
-/
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.LinearAlgebra.Dual
import Mathlib.LinearAlgebra.Fin... |
LinearAlgebra\Semisimple.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.FieldTheory.Perfect
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.AnnihilatingPolynomial
import Mathlib.Order.CompleteSublattic... |
LinearAlgebra\SesquilinearForm.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.LinearAlgebra.Basis
import Mathlib.LinearAlgebra.BilinearMap
/-!
# Sesquilinear maps
This files provides properties about sesquilinear maps and f... |
LinearAlgebra\SModEq.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.Eval
import Mathlib.RingTheory.Ideal.Quotient
/-!
# modular equivalence for submodule
-/
open Submodule
open Polynomial
variable {R : Typ... |
LinearAlgebra\Span.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import Mathlib.Algebra.Module.Prod
import Mathlib.Algebra.Module.Submodule.EqLocus... |
LinearAlgebra\StdBasis.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Data.Matrix.Basis
import Mathlib.LinearAlgebra.Basis
import Mathlib.LinearAlgebra.Pi
/-!
# The standard basis
This file defines the standard basis `P... |
LinearAlgebra\SymplecticGroup.lean | /-
Copyright (c) 2022 Matej Penciak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matej Penciak, Moritz Doll, Fabien Clery
-/
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
# The Symplectic Group
This file defines the symplectic group and proves element... |
LinearAlgebra\TensorPower.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.PiTensorProduct
import Mathlib.Logic.Equiv.Fin
import Mathlib.Algebra.DirectSum.Algebra
/-!
# Tensor power of a semimodule over a commutative ... |
LinearAlgebra\Trace.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Antoine Labelle
-/
import Mathlib.LinearAlgebra.Contraction
import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
/-!
# Trace of... |
LinearAlgebra\UnitaryGroup.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.LinearAlgebra.GeneralLinearGroup
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Algebra.... |
LinearAlgebra\Vandermonde.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.Algebra.BigOperators.Fin
import Mathlib.Algebra.GeomSum
import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
impor... |
LinearAlgebra\AffineSpace\AffineEquiv.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.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.LinearAlgebra.GeneralLinearGroup
/-!
# Affine equivalences
In this file we define `AffineE... |
LinearAlgebra\AffineSpace\AffineMap.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Set.Pointwise.Interval
import Mathlib.LinearAlgebra.AffineSpace.Basic
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.LinearAlgebra.Pi
import ... |
LinearAlgebra\AffineSpace\AffineSubspace.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
/-!
# Affine spaces
This file defines affine subspaces (over modules) and the affine span of a set of points.
## M... |
LinearAlgebra\AffineSpace\Basic.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Algebra.AddTorsor
/-!
# Affine space
In this file we introduce the following notation:
* `AffineSpace V P` is an alternative notation for `AddTorsor V P... |
LinearAlgebra\AffineSpace\Basis.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.AffineSpace.Independent
import Mathlib.LinearAlgebra.AffineSpace.Pointwise
import Mathlib.LinearAlgebra.Basis
/-!
# Affine bases and barycentr... |
LinearAlgebra\AffineSpace\Combination.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Data.Fintype.BigOperators
import Mathlib.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.LinearAlgebra.Affine... |
LinearAlgebra\AffineSpace\ContinuousAffineEquiv.lean | /-
Copyright (c) 2024 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Continuous affine equivalences
In this file, we define c... |
LinearAlgebra\AffineSpace\FiniteDimensional.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Init.Core
import Mathlib.LinearAlgebra.AffineSpace.Basis
import Mathlib.LinearAlgebra.FiniteDimensional
/-!
# Finite-dimensional subspaces of affine space... |
LinearAlgebra\AffineSpace\Independent.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Sign
import Mathlib.LinearAlgebra.AffineSpace.Combination
import Mathlib.LinearAlg... |
LinearAlgebra\AffineSpace\Matrix.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.AffineSpace.Basis
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
# Matrix results for barycentric co-ordinates
Results about the ... |
LinearAlgebra\AffineSpace\Midpoint.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.LinearAlgebra.AffineSpace.AffineEquiv
/-!
# Midpoint of a segment
## Main definitions
* `midpoint R x y`: midpoint of the segment `[x, y]`. We def... |
LinearAlgebra\AffineSpace\MidpointZero.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.Algebra.CharP.Invertible
import Mathlib.LinearAlgebra.AffineSpace.Midpoint
/-!
# Midpoint of a segment for characteristic zero
We collect lemmas th... |
LinearAlgebra\AffineSpace\Ordered.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.CharP.Invertible
import Mathlib.Algebra.Order.Invertible
import Mathlib.Algebra.Order.Module.OrderedSMul
import Mathlib.Algebra.Order.G... |
LinearAlgebra\AffineSpace\Pointwise.lean | /-
Copyright (c) 2022 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang
-/
import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace
/-! # Pointwise instances on `AffineSubspace`s
This file provides the additive action `AffineSubspace.pointwis... |
LinearAlgebra\AffineSpace\Restrict.lean | /-
Copyright (c) 2022 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace
/-!
# Affine map restrictions
This file defines restrictions of affine maps.
## Main definitions
* The domai... |
LinearAlgebra\AffineSpace\Slope.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.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Tactic.FieldSimp
/-!
# Slope of a function
In this file we define the slope of a function ... |
LinearAlgebra\Alternating\Basic.lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Zhangir Azerbayev
-/
import Mathlib.GroupTheory.Perm.Sign
import Mathlib.Data.Fintype.Perm
import Mathlib.LinearAlgebra.Multilinear.Basis
/-!
# Alternating Maps
We co... |
LinearAlgebra\Alternating\DomCoprod.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.Alternating.Basic
import Mathlib.LinearAlgebra.Multilinear.TensorProduct
import Mathlib.GroupTheory.GroupAction.Quotient
/-!
# Exterior product... |
LinearAlgebra\Basis\Bilinear.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.LinearAlgebra.Basis
import Mathlib.LinearAlgebra.BilinearMap
/-!
# Lemmas about bilinear maps with a basis over each argument
-/
namespace LinearMap
vari... |
LinearAlgebra\Basis\Flag.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
import Mathlib.LinearAlgebra.Basis
import Mathlib.LinearAlgebra.Dual
import Mathlib.Data.Fin.FlagRange
/-!
# Flag of submodules defined by a basis
... |
LinearAlgebra\Basis\VectorSpace.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
import Mathlib.LinearAlgebra.Basis
import Mathlib.LinearAlgebra.FreeModule.Basic
import Mathlib.LinearAlgebra.LinearPMap
import Ma... |
LinearAlgebra\BilinearForm\Basic.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import Mathlib.Algebra.Algebra.Tower
import Mathlib.LinearAlgebra.BilinearMap
/-!
# Bilinear form
This file defines a bilinear form over a module. ... |
LinearAlgebra\BilinearForm\DualLattice.lean | /-
Copyright (c) 2018 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.LinearAlgebra.BilinearForm.Properties
/-!
# Dual submodule with respect to a bilinear form.
## Main definitions and results
- `BilinForm.dualSubmodule`: T... |
LinearAlgebra\BilinearForm\Hom.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.LinearAlgebra.BilinearForm.Basic
import Mathlib.LinearAlgebra.Basis
import Mathlib.Algebra.Al... |
LinearAlgebra\BilinearForm\Orthogonal.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.LinearAlgebra.BilinearForm.Properties
/-!
# Bilinear form
This file defines ort... |
LinearAlgebra\BilinearForm\Properties.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import Mathlib.LinearAlgebra.BilinearForm.Hom
import Mathlib.LinearAlgebra.Dual
/-!
# Bilinear form
This file defines various properties of bilinea... |
LinearAlgebra\BilinearForm\TensorProduct.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.LinearAlgebra.Dual
import Mathlib.LinearAlgebra.TensorProduct.Tower
/-!
# The bilinear form on a tensor product
## Main definitions
* `LinearMap.BilinMap.... |
LinearAlgebra\Charpoly\Basic.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
import Mathlib.FieldTheory.Minpoly.Field
/-!
# Characteris... |
LinearAlgebra\Charpoly\ToMatrix.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.LinearAlgebra.Charpoly.Basic
import Mathlib.LinearAlgebra.Matrix.Basis
/-!
# Characteristic polynomial
## Main result
* `LinearMap.charpoly_toMat... |
LinearAlgebra\CliffordAlgebra\BaseChange.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.LinearAlgebra.QuadraticForm.TensorProduct
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import Mathlib.LinearAlgebra.TensorProduct.Opposite
import... |
LinearAlgebra\CliffordAlgebra\Basic.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Utensil Song
-/
import Mathlib.Algebra.RingQuot
import Mathlib.LinearAlgebra.TensorAlgebra.Basic
import Mathlib.LinearAlgebra.QuadraticForm.Isometry
import Mathlib.LinearAlge... |
LinearAlgebra\CliffordAlgebra\CategoryTheory.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.LinearAlgebra.CliffordAlgebra.Basic
import Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat
import Mathlib.Algebra.Category.AlgebraCat.Basic
/-! # Cat... |
LinearAlgebra\CliffordAlgebra\Conjugation.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.CliffordAlgebra.Grading
import Mathlib.Algebra.Module.Opposites
/-!
# Conjugations
This file defines the grade reversal and grade involution ... |
LinearAlgebra\CliffordAlgebra\Contraction.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
import Mathlib.LinearAlgebra.CliffordAlgebra.Fold
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import Mathlib... |
LinearAlgebra\CliffordAlgebra\Equivs.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.DualNumber
import Mathlib.Algebra.QuaternionBasis
import Mathlib.Data.Complex.Module
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import ... |
LinearAlgebra\CliffordAlgebra\Even.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.CliffordAlgebra.Fold
import Mathlib.LinearAlgebra.CliffordAlgebra.Grading
/-!
# The universal property of the even subalgebra
## Main definit... |
LinearAlgebra\CliffordAlgebra\EvenEquiv.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import Mathlib.LinearAlgebra.CliffordAlgebra.Even
import Mathlib.LinearAlgebra.QuadraticForm.Prod
import Mathlib.Ta... |
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