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 |
|---|---|---|---|---|---|
1,574 | lean_file_chunk | 6c60b3d61f46d5be0f95062fb40647f032fb63975a51111e2d7a3ec2040c30f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Group.ULift
public import Mathlib.Algebra.Regular.SMul
/-!
# Results about `IsRegular` and `ULift`
-/
public section
universe u v
... |
2,070 | lean_file_chunk | d5ab0869eec9ce8afb5d4e63badc5880f9ae8f932691f394d2fab4cd341b8290 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Notation.Defs
/-!
# Regular elements
We introduce left-regular, right-regular and regular elements, along with their `to_additiv... |
1,007 | lean_file_chunk | f2da4d2636c3be02e5b83f155b9935ded8b2988b7396df444fbea8755ef12866 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Yunzhou Xie
-/
module
public import Mathlib.Algebra.Central.Defs
public import Mathlib.Data.Matrix.Basis
/-!
# The matrix algebra is a central algebra
-/
@[expose] publi... |
3,375 | lean_file_chunk | 781ddd8f3aa30fef8a746622c1b8fc245129190562ae1311b99d9812a2d8b315 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Yunzhou Xie
-/
module
public import Mathlib.Algebra.Central.Basic
public import Mathlib.RingTheory.Flat.Basic
public import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
#... |
2,883 | lean_file_chunk | d17600bff4be87f7d0661102856318765ad6aceeb25e14a4967d02ccfcc47101 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Jujian Zhang, Yunzhou Xie
-/
module
public import Mathlib.Algebra.Central.Defs
import Mathlib.Algebra.Module.Torsion.Field
/-!
# Central Algebras
In this file, we prov... |
3,091 | lean_file_chunk | 68b2dc40cdcf86590dd13efcfd6a9aae618db9956182bd0ffb8ca100fc511102 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Algebra.Central.Basic
public import Mathlib.LinearAlgebra.FreeModule.Basic
/-!
# `Module.End R M` is a central algebra
This file shows that ... |
2,535 | lean_file_chunk | a903c97a5bf66bbc0c459c47304704a7dabcd3511161d7d91a5e5a5cf07e0cf7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.Algebra.Algebra.Subalgebra.Lattice
/-!
# Central Algebras
In this file we define the predicate `Algebra.IsCentral K D` where `K` is a comm... |
23,972 | lean_file_chunk | 43bda044f43fbde7d2652c90b35c637b1cd675a3bfd401350fdb105cc6273c2f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser, Antoine Chambert-Loir, María-Inés de Frutos-Fernández
-/
module
public import Mathlib.Algebra.BigOperators.GroupWithZero.Action
public import Mathlib.Algebra.GroupW... |
16,590 | lean_file_chunk | 51eb90c3eb6ad157998ec8a238169984d18cfd24fc7f788b38d27abeac85518a | lean_source_file | pkg_mathlib_source_file_chunks | variable [AddCommGroup M] [Semiring R] [Module Rᵐᵒᵖ M] [Module R M]
/-- `x.fst : R` is invertible when `x : tzre R M` is. -/
abbrev invertibleFstOfInvertible (x : tsze R M) [Invertible x] : Invertible x.fst where
invOf := (⅟x).fst
invOf_mul_self := by rw [← fst_mul, invOf_mul_self, fst_one]
mul_invOf_self := by ... |
1,298 | lean_file_chunk | f232a9658ebac6dbcb68e4c79b88641351943486b7be9fa8f31eed326993a0cc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Antoine Chambert-Loir, María-Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María-Inés de Frutos-Fernández
-/
module
public import Mathlib.Algebra.TrivSqZeroExt.Basic
public import Mathlib.RingTheo... |
6,194 | lean_file_chunk | 609b6e640ee3c660b847aa021dc0fd4595614c9308051da380527254be109b45 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Defs
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.Ring.Parity
/-!
# Lemmas about ... |
11,593 | lean_file_chunk | 7c2441cc32e6f56ccacbdfdc9b6e34a305de301387de87566f9b70822c0d7452 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Data.Nat.Multiplicity
public import Mathlib.Data.Nat.Choose.Sum
/-!
# Char... |
2,631 | lean_file_chunk | a2deebd78dacadabb5bad4b28d314fe37cfb58372b29983b37939545af505ad4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.IsPrimePow
public import Mathlib.Data.Nat.Factorization.Basic
public import Mathlib.RingTheor... |
14,081 | lean_file_chunk | 13b5587a21851dfe764c98c40530494cb5d548b2d91b787767cad2665759bcfc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.IsPrimePow
public import Mathlib.RingTheory.Ideal.... |
1,176 | lean_file_chunk | ee4ca79e242a37c5a8af0aa746388e2b5a194a0c2a25e0b6fd2aa6f7f9f5ff69 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.Algebra.CharP.Algebra
public import Mathlib.FieldTheory.IntermediateField.Basic
/-!
# Characteristic of intermediate fields
This file contains some c... |
4,618 | lean_file_chunk | 1763fc62e7839475cdbab5f1238912e6ced62edcd63284224485e3a461867581 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Algebra.GroupWithZ... |
924 | lean_file_chunk | f2513f4c1786166cfab601b8255e3f020392456f3eef60730c639f871728a3ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.Ring.Pi
/-!
# Characteristic of semirings of functions
-/
@[expose] public section
universe u... |
1,539 | lean_file_chunk | 819df7b66a79bafb7be4be881549faac4fa6495c1ab2cc2bc2d550da66838be7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.CharP.Algebra
/-!
# Characteristic of subrings
-/
@[expose] public section
universe u v
namespace CharP
instance subsemiring (R : Ty... |
7,923 | lean_file_chunk | a007e49cb0297a225b21721b2d5fdb68cf6dbe290545f097b29924e0c013c6ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.Group.Fin.Basic
public import Mathlib.Algebra.Ring.ULift
public imp... |
5,970 | lean_file_chunk | 6bffc609deb6ecda48803bc070c15595a76ae39cf29d28a75f6e8f27bf2b4b01 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.CharP.Lemmas
/-!
### The Frobenius endomorphism
## Tags
Frobenius endomorphism
... |
2,917 | lean_file_chunk | 623fe36d51fb6aa6dec79e570fdc42ebab9979b979d7095a14f2e4c34a107a4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
module
public import Mathlib.GroupTheory.OrderOfElement
public import Mathlib.RingTheory.Ideal.Maps
public import Mathlib.RingTheory.Ideal.Nonunits
public import ... |
16,033 | lean_file_chunk | 6f0768288b535c567175cc495339cc28ff0dc71080cb111897fc76b750b03120 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
module
public import Mathlib.Data.Nat.Cast.Basic
public import Mathlib.Data.Nat.Find
public import Mathlib.Data.Nat.Prime.Defs
public import Math... |
9,299 | lean_file_chunk | 765b45f4a7212176c648919ef5bee473cafade7e723b2d92ee48c822b3142bc1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Eric Wieser
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.FreeAlgebra
public import Mathlib.RingTheory.Localization.FractionRing
public im... |
2,359 | lean_file_chunk | 176642b46b5ce4f08a582b06e70a283be7a2c6cb9d7646c91ff243c214b25b60 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Wanyi He. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wanyi He, Huanyu Zheng
-/
module
public import Mathlib.Algebra.CharP.Algebra
public import Mathlib.Algebra.Module.Torsion.Basic
/-!
# Characteristic of the ring of linear Maps
This file c... |
3,731 | lean_file_chunk | 1e2f4b85edbb59551b4f06f9cc9bc2d58676ba2a5ae2a8c6f74fc1ce03239b74 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.CharP.Basic
public import Mathlib.Algebra.CharP.Lemmas
public import Mathlib.GroupTheory.Perm.Cycle.Type
public import Mathlib.Rin... |
1,417 | lean_file_chunk | 9159aff57a795018df10d5425a413ce2ba89136866b24bcfa959e54e5bf16fe4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
module
public import Mathlib.Algebra.CharP.Frobenius
/-!
# Results about characteristic p reduced rings
-/
public section
open Finset
sectio... |
297 | lean_file_chunk | f4679116ffe8ad3fd070c2b2efa58d139280ffcaa496f289f9084a3208c6d3e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module -- shake: keep-all
public import Mathlib.Tactic.Common
public import Mathlib.Util.CompileInductive
deprecated_module (since := "2026-01-19") |
1,176 | lean_file_chunk | 949bcebf650b5aa027ca864d0ece5177c41c0c81e917920b2c4740cbb5b9f0cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yaël Dillies
-/
module
public import Mathlib.Algebra.NoZeroSMulDivisors.Defs
public import Mathlib.Algebra.Group.Action.Pi
/-!
# Pi instances for NoZeroSMulDivisors
This f... |
1,034 | lean_file_chunk | 2b27c63735de2e7ad320ac99649931920a85a8bc1d364b41886874603fc7a23a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yury Kudryashov, Joseph Myers, Heather Macbeth, Kim Morrison, Yaël Dillies
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Units
public import Mathlib.Alge... |
3,322 | lean_file_chunk | 5e0319006f8c39f09eb27cb660916f22934535a62a265091e75e7b93419b5592 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yury Kudryashov, Joseph Myers, Heather Macbeth, Kim Morrison, Yaël Dillies
-/
module
public import Mathlib.Algebra.Module.Torsion.Free
public import Mathlib.Tactic.Cont... |
9,324 | lean_file_chunk | c50215f4da338c16f56b19b93c85617ba5c79794f087ffbeea6886e549fd2fbc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Finset
public import Mathlib.GroupTheory.QuotientGroup.Defs
public import Mathlib.Order.ConditionallyComplete... |
23,997 | lean_file_chunk | 16aa0453ff9a564de297da9cf7a65010b4a3f36d027de7fe17a60c6b708383f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Field.IsField
public import Mathlib.Algebra.Polynomial.Inductions
public import Mathli... |
11,606 | lean_file_chunk | fd211aa5018922d53b1fea996a68a1f6367b44dbc201bc3c9b0b59797ccdd636 | lean_source_file | pkg_mathlib_source_file_chunks | theorem X_sub_C_dvd_sub_C_eval : X - C a ∣ p - C (p.eval a) := by
rw [dvd_iff_isRoot, IsRoot, eval_sub, eval_C, sub_self]
-- TODO: generalize this to Ring. In general, 0 can be replaced by any element in the center of R.
theorem modByMonic_X (p : R[X]) : p %ₘ X = C (p.eval 0) := by
rw [← modByMonic_X_sub_C_eq_C_ev... |
7,058 | lean_file_chunk | 0a22b6ef93200ba6bafff58ed8937d849ca6304977a380df619e5350815aa081 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.Algebra.Polynomial.Degree.Defs
public import Mathlib.Algebra.Polynomial.EraseLead
public import Mathlib.Data.List.Range
/-!
# A list of coe... |
5,490 | lean_file_chunk | 1c56df310abb0714117b0aeadc3a5ed9e28a167db94790183bbb3ec3db9d49c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Algebra.Algebra.Operations
public import Mathlib.Algebra.Polynomial.Div
public import Mathlib.RingTheory.Ideal.Spa... |
5,278 | lean_file_chunk | 2747443a84ab3a17a58ce11b93cf805ae8b063dea32e5d97ada76b404a9edfdf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Richard M. Hill
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Derivative
public import Mathlib.Algebra.Polynomia... |
13,574 | lean_file_chunk | c3de3e7772dacecdfeb5d470e1793dce3652f844ec87c411f4eefe4cac301a89 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Polynomial.Degree.TrailingDegree
public import Mathlib.Algebra.Polynomial.EraseLead
/-!
# Reverse of a univariate polynomial
The... |
20,818 | lean_file_chunk | ed4ee47631681f6c8fff6a42348f46e9676d01f80c1a601e177ce39099ec385a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.Algebra.Polynomial.CoeffList
public import Mathlib.Algebra.Polynomial.Monic
public import Mathlib.Algebra.Polynomial.Roots
public import Mat... |
2,572 | lean_file_chunk | d13b99fbdd01ca4c96a931257d24ac0a5db42b82999083b67bc6c016f746727c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
module
public import Mathlib.Algebra.Polynomial.Roots
public import Mathlib.Algebra.Polynomial.FieldDivision
/-!
# Polynomials of specific degree
Facts abo... |
12,206 | lean_file_chunk | 2bb74a9c1a1211ed085c60fd307e51e75f67a0775280436c5d3b26eb9e805a63 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
module
public import Mathlib.Algebra.Group.NatPowAssoc
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Eval.SMul
/-!
# ... |
11,830 | lean_file_chunk | 75ee03f06bfc07571ea287578fdd706e1a9182c203acae9c4be96b3a05cf8e78 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Concordance Inc. dba Harmonic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.Finsupp.Notation
public import Mathlib.RingTheory.MvPolynomial.Homogeneous
/-!
# Homogenize a univariate polynomia... |
12,811 | lean_file_chunk | f005df235751d47e7c5601db716e2404f8d5f82867f1f7b32e01efa2a6f6f6ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.CharP.Frobenius
public import Mathlib.Algebra.Polynomial.Derivative
public import Mathlib.Algebra.Polynomial.RingDivision
public import Ma... |
8,209 | lean_file_chunk | 55b8e8aaced779aaaedb97ef502e625b05aad86875efecba4d740017a8400ec1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.BigOperators.NatAntidiagonal
public import Mathlib.Algebra.Polynomial.Reverse
/-!
# "Mirror" of a univariate polynomial
In t... |
23,957 | lean_file_chunk | 5dc1f7aa65c748665dc59b27ec650de759c191ff90b1a5b61e959a3bf75d1356 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Reverse
public import Mathlib.Algebra.Polynomial.Inductions
public ... |
2,314 | lean_file_chunk | 82e6a0b50ebe2d7edb64671da7b3e6564b7258459a0aaf8dfb7fb21527d57c8d | lean_source_file | pkg_mathlib_source_file_chunks | /-- Evaluate a Laurent polynomial at a unit, using scalar multiplication. -/
def smeval : S := Finsupp.sum f fun n r => r • (x ^ n).val
theorem smeval_eq_sum : f.smeval x = Finsupp.sum f fun n r => r • (x ^ n).val := rfl
theorem smeval_congr : f = g → x = y → f.smeval x = g.smeval y := by rintro rfl rfl; rfl
set_opt... |
13,633 | lean_file_chunk | 0c34499bb4cfef41c14f945fd36e5b80fd1e76d3cb4e9de2db71e5f3ace8e128 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.RingTheory.AdjoinRoot
public import Mathlib.Algebra.MvPolynomial.PDeriv
public import Mathlib.RingTheory.Derivation.MapCoeffs
/-!
# Bivariate pol... |
146 | lean_file_chunk | 18013459723f4c4047e70c76b55df18c31b19909e0c0b8878a6ae16b35cc8247 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Tactic.NormNum
public import Mathlib.Tactic.Positivity
deprecated_module (since := "2025-12-16") |
2,452 | lean_file_chunk | b85166b458ff2f36923d878d7a7a5504e2d17da043a14b0ec3f4d759a967c628 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Group.Nat.Hom
public import Mathlib.Algebra.Polynomial.Basic
/-!
# Univariate monomia... |
23,981 | lean_file_chunk | f6a662e6b3c97bdc45c33d24bdba96d8d0436ac5f637a229a90df189b6939481 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Algebra.Pi
public import Mathlib.Algebra.Algebra.Prod
public import Mathlib.Algebra.Al... |
4,551 | lean_file_chunk | fca5e967d62ccdcaf1f32623ef2719752f05a2b10e316a7ade65dde68791774f | lean_source_file | pkg_mathlib_source_file_chunks | convert (map_dvd_iff <| algEquivAevalXAddC t).symm using 2
simp [C_eq_algebraMap]
lemma comp_X_add_C_eq_zero_iff : p.comp (X + C t) = 0 ↔ p = 0 :=
EmbeddingLike.map_eq_zero_iff (f := algEquivAevalXAddC t)
lemma comp_X_add_C_ne_zero_iff : p.comp (X + C t) ≠ 0 ↔ p ≠ 0 := comp_X_add_C_eq_zero_iff.not
lemma dvd_comp... |
11,756 | lean_file_chunk | 1032e63cf5a285ba151439374b4d66efccd308d89672ca8e023e596fa07abdfa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.BigOperators
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
pub... |
9,179 | lean_file_chunk | 11946087b6f81d055c145c73445724ab9df1c02472d04e17c3175154633e9003 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Julian Berman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Hill, Julian Berman, Austin Letson, Matej Penciak
-/
module
public import Mathlib.Algebra.Polynomial.Monic
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.R... |
23,968 | lean_file_chunk | 31a4422073a3d134c19c01451385c6fe2cf442c7dd572e7cff71d1b25b7fb730 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Group.AddChar
public import Mathlib.Algebra.Group.Submonoid.Operations
public import M... |
18,682 | lean_file_chunk | 99f486b4d01d1567e479ed0344791cf547d8cbd2292af4a05ee239a698a8301e | lean_source_file | pkg_mathlib_source_file_chunks | (h : ∀ n, f.comp (monomial n).toAddMonoidHom = g.comp (monomial n).toAddMonoidHom) : f = g :=
addHom_ext fun n => DFunLike.congr_fun (h n)
@[ext high]
theorem lhom_ext' {M : Type*} [AddCommMonoid M] [Module R M] {f g : R[X] →ₗ[R] M}
(h : ∀ n, f.comp (monomial n) = g.comp (monomial n)) : f = g :=
LinearMap.toAd... |
23,961 | lean_file_chunk | 07b0034a236e086bf58de6e830d3b4bf1a9fba1d12897232e47614561febad1a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Polynomial.Degree.Domain
public import Mathlib.Algebra.Polynomial.Degree.Support
publi... |
6,378 | lean_file_chunk | 433d1a493751c3fac86b65d3c7a5762e09c21f8703e796a193bc98ceff37af41 | lean_source_file | pkg_mathlib_source_file_chunks | Multiset.sum_cons, Multiset.erase_cons_head, mul_comm (derivative (f i))]
congr
rw [h, ← AddMonoidHom.coe_mulLeft, (AddMonoidHom.mulLeft (f i)).map_multiset_sum _,
AddMonoidHom.coe_mulLeft]
simp only [Function.comp_apply, Multiset.map_map]
refine congr_arg _ (Multiset.map_congr rfl fun j hj => ?_)
rw [← m... |
14,551 | lean_file_chunk | 4e76e1edba96fdac3f1730bf07869c1ec202855e40484fded902d4d0abcf4e97 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Polynomial.Mirror
public import Mathlib.Data.Int.Order.Units
public import Mathlib.RingTheory.Coprime.Basic
/-!
# Unit Trinom... |
8,935 | lean_file_chunk | 726bd6b9c89aca43a8986f0ad0910f13034035045e04fdfc45816abe75385f2a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Eval.Subring
public import Mathlib.Algebra.Polynomial.Monic
/-... |
7,595 | lean_file_chunk | 893e5fb4e000ce86e27a6c6ea6980927c142e569b4aa0856ea62e97ee6d54426 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
public import Mathlib.Algebra.Polynomial.Eval.SMul
... |
12,579 | lean_file_chunk | e0fce51725aa802cbe84b514907741139f435395fad705c693c444230e621b94 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker, Johan Commelin
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Div
pub... |
2,727 | lean_file_chunk | 24a17a3492eafcf9a34d1fd54875d5c21f4737498bae7878d62e3e65c8b68efe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
public import Mathlib.Tactic.ComputeDegree
/-!
# Cancel the leading terms of two polynomials
## Defin... |
16,335 | lean_file_chunk | 5fbfbf7f3c34250862eb063503c6ac4cd178f33b8faf47a21373fd9c75978be9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.Polynomial.Monic
public import Mathlib.LinearAlgebra.LinearIndependent.D... |
4,865 | lean_file_chunk | 24f50e0638a3f19eca7ee6904b03c8114a723fbcbbdc38c24611b16b2c9a1b75 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Monic
public import Mathlib.Algebra.Ring.Action.Basic
public import Mathlib... |
23,984 | lean_file_chunk | 739e4b0b39fdd73d64276ca667cf148fef37307621c61d501b360dd50ece0914 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Sidharth Hariharan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Sidharth Hariharan, Aaron Liu
-/
module
public import Mathlib.Algebra.Algebra.Basic
public import Mathlib.Algebra.Polynomial.Div
public import Mathlib.RingTheory.Co... |
4,775 | lean_file_chunk | 000caf58e60496df6cf68e33986bba2fd9e43a5620c64a9e4eaa1707243175ff | lean_source_file | pkg_mathlib_source_file_chunks | inv_mul_cancel₀ (by simpa using (hg i hi).ne_zero)
obtain ⟨q, r, hr, hf⟩ := mul_prod_pow_inverse_eq_quo_add_sum_rem_mul_pow_inverse
f hg hcop (fun _ => 1) hgi
refine ⟨q, fun i => r i 0, fun i hi => hr i hi 0, ?_⟩
simp_rw [Fin.sum_univ_one, Fin.val_zero, zero_add, pow_one, Finset.prod_inv_distrib] at hf
simp... |
21,939 | lean_file_chunk | 60ad426e8a0225bb31be5e6969ffb8769de2a0d12e7dc363730cf6b31698efb1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Polynomial.Reverse
public import Mathlib.Algebra.Regular.SMul
/-!
# Theory of monic p... |
9,332 | lean_file_chunk | 248f0adbee292ac60cf7295287bdcbc8abafe6452d912b84ad09a1bfe960f1be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Polynomial.BigOperators
public import Mathlib.Algebra.Polynomial.Derivative
public import Mathlib.Data.Nat.Choose.Cast
public im... |
23,990 | lean_file_chunk | ed3a372015ebbf91718bf36f7f5a8a9d9d0e8f0592da1593f06f77ae90611d99 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Chris Hughes
-/
module
public import Mathlib.Algebra.Order.SuccPred.WithBot
public import Mathlib.Algebra.Polynomial.FieldDivision
public import Mathlib.Algebra.Polynom... |
11,106 | lean_file_chunk | e8c82bd9a0b8b21de124a60188f84f0701ee9e697685c4318b90fcf246634946 | lean_source_file | pkg_mathlib_source_file_chunks | rw [natDegree_C_mul (mt inv_eq_zero.mp ha), natDegree_X_sub_C]
theorem splits_iff_comp_splits_of_degree_eq_one {f g : R[X]} (hg : g.degree = 1) :
f.Splits ↔ (f.comp g).Splits :=
splits_iff_comp_splits_of_natDegree_eq_one (natDegree_eq_of_degree_eq_some hg)
theorem Splits.degree_eq_one_of_irreducible {f : R[X]} ... |
3,943 | lean_file_chunk | 973deff9200d7d57b03a25f43e2ac02bd63467d74a83631cb50050a62f34ce71 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
module
public import Mathlib.Algebra.BigOperators.Fin
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
public import Mathlib.Data.List.ToFinsupp
public i... |
13,898 | lean_file_chunk | c94d90cd94a57b10316c765b5b950ed7935a805fc1849156cc9298eec67ceea3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Algebra.MonoidAlgebra.Support
public import Mathlib.A... |
731 | lean_file_chunk | 39cab06cb54c337462d554d671b85b21fa02927aa43947a2a6a97a1a7d200642 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.Algebra.Polynomial.Basic
public import Mathlib.LinearAlgebra.Basis.Defs
/-!
# Basis of a polynomial ring
-/
@[expose] public section
open Module
u... |
3,927 | lean_file_chunk | d58e9068d186dc47033079a5c1c8e957e3a01c93d03ebf77873311a9bf2a3bb5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Polynomial.Derivative
public import Mathlib.Tactic.LinearCombination
public import Mat... |
978 | lean_file_chunk | 3ac91400a2548383e950f20185a89d4a38c04fb043e2b49c96b50821078adfd8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
module
public import Mathlib.Algebra.Polynomial.Basic
public import Mathlib.SetTheory.Cardinal.Finsupp
/-!
# Cardinality of Polynomial Ring
The r... |
7,852 | lean_file_chunk | 8b366eaeee8cca69bbc6c3729e12e5b1ad34b3c1b834f9120f76534b8232f2d4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Damiano Testa, Jens Wagemaker
-/
module
public import Mathlib.Algebra.MonoidAlgebra.Division
public import Mathlib.Algebra.Polynomial.Degree... |
23,979 | lean_file_chunk | 15899903f0aaaa29105fb88ae892db85e243f152589924483f878f331eb3504e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Order.Group.Finset
public import Mathlib.Algebra.Polynomial.Derivative
public import M... |
8,164 | lean_file_chunk | 6727ae64c5ec812514a8f83e1009706b40b112f59f27aea60bdcb3fdb78d6fe5 | lean_source_file | pkg_mathlib_source_file_chunks | by_cases hq : q = 0
· simp [hq]
rw [div_def, leadingCoeff_mul, leadingCoeff_C,
leadingCoeff_divByMonic_of_monic (monic_mul_leadingCoeff_inv hq) _, mul_comm,
div_eq_mul_inv]
rwa [degree_mul_leadingCoeff_inv q hq]
theorem div_C_mul : p / (C a * q) = C a⁻¹ * (p / q) := by
by_cases ha : a = 0
· simp [ha]... |
23,981 | lean_file_chunk | 748c94ed69c5c804aafe6025a97b7024c99b7a73c29707fb0d52120aac20f370 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker, Johan Commelin
-/
module
public import Mathlib.Algebra.Polynomial.BigOperators
public import Mathlib.Algebra.Polynomial.RingD... |
17,390 | lean_file_chunk | 218aab3f0ebb1c095e84055726cc8d0586e0664e42e6baec00d0b721f03b278e | lean_source_file | pkg_mathlib_source_file_chunks | theorem preimage_eval_singleton (hp : p ≠ C a) : p.eval ⁻¹' {a} = (p - C a).rootSet R := by
ext; simp [mem_rootSet_of_ne (sub_ne_zero.mpr hp), sub_eq_zero]
theorem Monic.mem_rootSet {p : T[X]} (hp : Monic p) {S : Type*} [CommRing S] [IsDomain S]
[Algebra T S] {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 := by
sim... |
20,708 | lean_file_chunk | fb9451cb34d2d88dbedfa72dda770aad8d55d7b437ddbb51a0f23dae871ad6fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Alex Meiburg
-/
module
public import Mathlib.Algebra.BigOperators.Fin
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
public import Mathlib.Algebra.Polynomial.Deg... |
4,583 | lean_file_chunk | d41e41c1d827215a7d373ecda7394ffc73617516479ed3cf1214db8af2336a13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Algebra.Basic
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Algebra.Polynomial.EraseLead
/-!
# Denominators ... |
7,056 | lean_file_chunk | c3fcd3d4d82382c1544b54c1167bf0ee584e84c84b7e45d157a6e8150798274b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Divisibility.Hom
public import Mathlib.Algebra.Group.Irreducible.Lemmas
public import Mathlib.Algebra.GroupWithZ... |
5,057 | lean_file_chunk | 73618d9bce278e48db1f1f1d197609659d693ed08a1db6d516faa05981b7b443 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
module
public import Mathlib.Algebra.Group.Irreducible.Defs
public import Mathlib.Algebra.GroupWithZero.Divisibility
/-!
# Prime elements
In this f... |
12,082 | lean_file_chunk | 92401236712adc92bf3360798d96f89874da60641c8f13f7b7d155fb02f27082 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.RingTheory.Coprime.Lemmas
public import Mathlib.RingTheory.Nilpotent.Basic
public import Mathlib.RingTheory.UniqueFactorizationDomain.GC... |
12,283 | lean_file_chunk | 983659b73b1bc20d2ea4e4c188f5ffa3e7d24c33a352449a7100ad0026fa2e60 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.Exact
public import Mathlib.CategoryTheory.ComposableArrows.Basic
/-!
# Exact sequences
A sequence of `n` composab... |
6,722 | lean_file_chunk | dd438a5abed988e757bc0fd95713caaad27123f96350260d921e34d4c9eeaa42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Opposite
public import Mathlib.Algebra.Homology.Embedding.Restriction
/-!
# Opposite categories of cochain complexes
We constru... |
7,595 | lean_file_chunk | 0653741420c6a8c251aea3ac4ec74779280219acc1f82040d1aeedac237bcac5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Basic
public import Mathlib.Algebra.GroupWithZero.Indicator
public import Mathlib.Algebra.Homology.ShortComplex.Hom... |
10,179 | lean_file_chunk | 9f78c1b3707f7f845ef381832134c6a6f306cebae315d0e20f17c569dc899426 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
public import Mathlib.Algebra.Module.BigOperators
public import Mathlib.AlgebraicTopology.Ext... |
16,251 | lean_file_chunk | 8a8ab3da239ac3316e91126d8cdca15d5ad3f75f20087ab39e7bf47c0c701bb2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Amelia Livingston, Joël Riou
-/
module
public import Mathlib.CategoryTheory.Abelian.Opposite
public import Mathlib.Algebra.Homology.Additive
public import Mathlib.A... |
14,069 | lean_file_chunk | 793863de8d8f3a0fa7359b9f3b389773474ae739af5514d5e3dcc9e759dbcab4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Bifunctor
public import Mathlib.Algebra.Homology.TotalComplexShift
public import Mathlib.CategoryTheory.Shift.CommShiftTwo
/-!
#... |
10,350 | lean_file_chunk | 2ae45274f34ccfe70445fcc45b1e91dd9fb30dac11d0aff3989ddcb295d62d03 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Homology.Single
/-!
# Augmentation and truncation of `ℕ`-indexed (co)chain complexes.
-/
@[expose] public section
noncomputable ... |
7,216 | lean_file_chunk | 7897a76540f04b0a9520b853113d14c95f5ccb62d763a06d91bc2c657f07891f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Defs
public import Mathlib.Logic.Relation
public import Mathlib.Logic.Function.Basic
public import Mathlib.Tac... |
10,390 | lean_file_chunk | 5ef1dcfcf79133c408eb9602da56242f2316f4d61e98b4b41814b56724bbdd4f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Pi.Basic
public import Mathlib.Algebra.Homology.Single
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
#... |
13,376 | lean_file_chunk | 2b4a5dd54d700552be35e39e9e5500df30bfa3c41c502ee6677eb37d834a71c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Homotopy
public import Mathlib.Algebra.Homology.ShortComplex.Retract
public import Mathlib.CategoryTheory.Morphi... |
2,121 | lean_file_chunk | 91c50c679cb697450f12eb68ea3d691343eda4609c99135aaba03373ce76762c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant
public import Mathlib.Algebra.Homology.HomologicalComplexLimits
public import Mathlib.Algeb... |
12,922 | lean_file_chunk | 18a885f3376885d14e938477c4b6cf065f9ef3fd4bdaf931e4a94176ac11bbe8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Kim Morrison
-/
module
public import Mathlib.Algebra.Homology.BifunctorAssociator
public import Mathlib.Algebra.Homology.Single
public import Mathlib.CategoryTheory.GradedObject... |
23,976 | lean_file_chunk | 53bbb88a5cf5c09b3bae2003808997acd38b07b64a6787987cce109a1e38f59d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison
-/
module
public import Mathlib.Algebra.Homology.ComplexShape
public import Mathlib.CategoryTheory.Subobject.Limits
public import Mathlib.CategoryTheory.Gra... |
10,609 | lean_file_chunk | 5e45d353c24252c7581d04eecb378e4ddb484604e658e54771bf3ebb7e8c1dc9 | lean_source_file | pkg_mathlib_source_file_chunks | (mkXIso X₀ X₁ X₂ d₀ d₁ s succ n).hom ≫ (succ
(ShortComplex.mk _ _ ((mk X₀ X₁ X₂ d₀ d₁ s succ).d_comp_d (n + 2) (n + 1) n))).2.1 := by
have eq := mk_congr_succ_d₂ succ
(mkAux_eq_shortComplex_mk_d_comp_d X₀ X₁ X₂ d₀ d₁ s succ n)
rw [eqToHom_refl, comp_id] at eq
refine Eq.trans ?_ eq
dsimp only [mk, of... |
10,457 | lean_file_chunk | 668d2833a18b38b5b0955236c7af5c26f555671d4c511031fb5dee0aa47f79bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Emily Witt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emily Witt, Kim Morrison, Jake Levinson, Sam van Gool
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Colimits
public import Mathlib.Algebra.Category.ModuleCat.Projective
publi... |
5,229 | lean_file_chunk | 4a223fc5d3f5c3fbb129f70b332c9c8d3885fe31aafae84be5f2c90b260d6dcd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Homology.Embedding.CochainComplex
public import Mathlib.Algebra.Homology.HomotopyCategory.Shift
public import Mathlib.CategoryTheory.Objec... |
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