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 |
|---|---|---|---|---|---|
1,791 | lean_file_chunk | cc68c28d3f8acf7e6dc71314eb8c70391b38941ce807c6ffa409d8b8730e0fa5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree
public import Mathlib.NumberTheory.ClassNumber.Finite
public import Mathlib.NumberTheory.Func... |
12,959 | lean_file_chunk | b91e4583e7c49cde8f52560d75113da4a6bfaaef24d1588ebd0b6e6dcc4d26bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Polynomial.Degree.CardPowDegree
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Mathlib.NumberTheory.ClassNumbe... |
16,395 | lean_file_chunk | 223d4427e8b4064104bbb7dd94c3621171b7eba5faef35be9cefc79ba8a5b508 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.GaussSum
public import Mathlib.NumberTheory.MulChar.Lemmas
public import Mathlib.RingTheory.RootsOfUnity.Lemmas
/-!
# Jacobi... |
8,071 | lean_file_chunk | b5a7127aee660434fb0509a9fad9e458a79c7d0936f46283d272193aa925dfc7 | 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.RingTheory.Valuation.DiscreteValuativeRel
public import Mathlib.Topology.Algebra.Module.Compact
public import Mathlib.Topology.Algebra.Valued.... |
884 | lean_file_chunk | ef32e64157762e3298c6a330a7fcb223ad70db3080fe57488247179874376f5a | 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.Data.Real.Sqrt
public import Mathlib.NumberTheory.Zsqrtd.Basic
/-!
# Image of `Zsqrtd` in `ℝ`
This file defines `Zsqrtd.toReal` and related ... |
8,904 | lean_file_chunk | 8ba50e74d2236bdaed293f085dc3e83fd71f3392f8248b250490adee11d2734f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.Complex.Basic
public import Mathlib.Data.Nat.Prime.Basic
public import Mathlib.Data.Real.Archimedean
public import Mathlib.NumberTheory... |
23,942 | lean_file_chunk | c01455705d0ddbf1b394d67b2910ae135435be851ee902e4f99e8672f01f6b11 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Ring.Associated
public import Mathlib.Algebra.Star.Unitary
public import Mathlib.RingTheory.PrincipalIdealDomain
public import M... |
8,561 | lean_file_chunk | 330fb6343f55c02e9c458f8029c5fd893ed2ac394bb99b1d4a3b822e7b85a8db | lean_source_file | pkg_mathlib_source_file_chunks | (sqLe_mul.right.right.right (nonnegg_pos_neg.1 ha) (nonnegg_pos_neg.1 hb))
protected theorem mul_nonneg (a b : ℤ√d) : 0 ≤ a → 0 ≤ b → 0 ≤ a * b := by
simp_rw [← nonneg_iff_zero_le]
exact nonneg_mul
theorem not_sqLe_succ (c d y) (h : 0 < c) : ¬SqLe (y + 1) c 0 d :=
not_le_of_gt <| mul_pos (mul_pos h <| Nat.succ_... |
3,458 | lean_file_chunk | 6b415eae0a274547ea7bff645261e43a4da104fbd206acc02a1f7c24ddbce551 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.NumberTheory.Zsqrtd.GaussianInt
public import Mathlib.NumberTheory.LegendreSymbol.Basic
/-!
# Facts about the Gaussian integers relying on ... |
11,229 | lean_file_chunk | d29c9ad07bdcc06a02bd8e723ee68987997e3f67c383cf401635c7668a85debb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul van Wamelen
-/
module
public import Mathlib.Data.Nat.Factors
public import Mathlib.NumberTheory.FLT.Basic
public import Mathlib.NumberTheory.PythagoreanTriples
public import Ma... |
12,235 | lean_file_chunk | 3b68c1831ab634f69360511339326cde4f33bc95832f06bac3916171ebf25118 | 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, Yaël Dillies, Jineon Baek
-/
module
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.Algebra.GCDMonoid.Finset
public import Mathlib.Algebra.GCDMon... |
4,487 | lean_file_chunk | dedf01567bc678f7de980e953093c51d8e7b6afa50435cb3ee6b29b49d9f18e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jineon Baek and Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jineon Baek, Seewoo Lee
-/
module
public import Mathlib.RingTheory.Polynomial.Radical
/-!
# Mason-Stothers theorem
This file states and proves the Mason-Stothers theorem... |
23,951 | lean_file_chunk | 54e5a137c1a4c0158ac371dd67214e070c78a46e934c4351adb4649b65959c6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Sanyam Gupta, Omar Haddad, David Lowry-Duda,
Lorenzo Luccioli, Pietro Monticone, Alexis Saurin, Florent Schaffhauser
-/
module
public import Mathlib.NumberTheory.F... |
12,640 | lean_file_chunk | b1b58b37c4a06944ce91011f29df87d45d3bed2807c1ff562a5b0478e9338ce4 | lean_source_file | pkg_mathlib_source_file_chunks | lemma w_spec : S.c = λ ^ S.multiplicity * S.w :=
(pow_multiplicity_dvd (hζ.toInteger - 1) S.c).choose_spec
lemma lambda_not_dvd_w : ¬ λ ∣ S.w := fun h ↦ by
refine S.toSolution'.multiplicity_lambda_c_finite.not_pow_dvd_of_multiplicity_lt
(lt_add_one S.multiplicity) ?_
rw [pow_succ', mul_comm]
exact S.w_spec... |
11,801 | lean_file_chunk | 8881cd9dc2779a1052ef507eb48bc65d0a96d8611398baf70ba566ce71dce5c6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jineon Baek and Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jineon Baek, Seewoo Lee
-/
module
public import Mathlib.Algebra.Polynomial.Expand
public import Mathlib.Algebra.GroupWithZero.Defs
public import Mathlib.NumberTheory.FLT.B... |
17,420 | lean_file_chunk | 51b8351fbc7a1c031a0e4b64a1ce31dcd061f39dbee1a1810d6a98ddc152c4b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yongle Hu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yongle Hu, Jiedong Jiang
-/
module
public import Mathlib.FieldTheory.Galois.IsGaloisGroup
public import Mathlib.NumberTheory.RamificationInertia.Basic
/-!
# Ramification theory in Galois ... |
4,398 | lean_file_chunk | 879f5002efa9cc9cd09afb2c24e2c202ce1d1368bd21d699a19c84e4f6ef4ed3 | 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.NumberTheory.RamificationInertia.Basic
public import Mathlib.RingTheory.LocalRing.ResidueField.Instances
public import Mathlib.RingTheory.Unra... |
9,671 | lean_file_chunk | e2c10c0f342750b46767966c4e81f028423890e7baaaf1939e5323828727d6a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.RamificationInertia.Galois
public import Mathlib.RingTheory.Ideal.Quotient.HasFiniteQuotients
/-!
# Decomposition and Inert... |
23,997 | lean_file_chunk | 15342cc8c43cf3f5960c9c8dfc41cfcf8010d9febac8671ae516df95b7b5c309 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Dimension.DivisionRing
public import Mathlib.NumberTheory.RamificationInertia.Inertia
public import Mathlib.NumberTheory.Ramific... |
8,381 | lean_file_chunk | 7f28e5c8a7cbbb091b57127c9dd8eeec7c47ae9daacf77dd9d3187fa22b88cc7 | lean_source_file | pkg_mathlib_source_file_chunks | variable [IsDedekindDomain S]
open scoped Classical in
theorem Factors.ne_bot (P : (factors (map (algebraMap R S) p)).toFinset) : (P : Ideal S) ≠ ⊥ :=
(prime_of_factor _ (Multiset.mem_toFinset.mp P.2)).ne_zero
open scoped Classical in
instance Factors.isPrime (P : (factors (map (algebraMap R S) p)).toFinset) :
... |
7,463 | lean_file_chunk | 9619231376963108953491aee739cbbe8d2f3e4f89f18d7c091c41ab70f9d52d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.RingTheory.Finiteness.Quotient
public import Mathlib.RingTheory.Ideal.Norm.AbsNorm
/-!
# Ramification index and inertia degree
Given `P : Id... |
17,105 | lean_file_chunk | 3e87a7a31f1494490de24ae371a5a573efbbd5364ebffd72e4f643b110c4121d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.GroupWithZero.Torsion
public import Mathlib.RingTheory.DedekindDomain.Dvr
public import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas... |
5,604 | lean_file_chunk | c9b111226247ec484372378a3071078919ffe295ec16bf536f3c529b414ea869 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.GroupTheory.FiniteAbelian.Duality
public import Mathlib.NumberTheory.MulChar.Lemmas
/-!
# Duality for multiplicative characters
Let `M` ... |
9,959 | lean_file_chunk | d103e5b382cf37771a5eb01c651bac7b500ca57f9397027955b4bf9fc53ff0c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.MulChar.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
/-!
# Further Results on multiplicative characters
-/
@... |
21,419 | lean_file_chunk | 68315c64af63d6013698bad2fb18a52e581653bff5f1c185a32e4faca647af94 | 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.Data.Fintype.Units
public import Mathlib.GroupTheory.... |
1,958 | lean_file_chunk | ce8bf97e380d1af38b6fd28e6b39b1284dc8965a65811718101d7974b9ddcd1c | 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 Geißer, Michael Stoll
-/
module
public import Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries
public import Mathlib.Algebra.ContinuedFractions.Computati... |
23,997 | lean_file_chunk | 1341dcc0c43ca4cde378010f4e489fc2cf1e1df3bbac2fb41b34520c7277d9ab | 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 Geißer, Michael Stoll
-/
module
public import Mathlib.NumberTheory.Real.Irrational
public import Mathlib.RingTheory.Coprime.Lemmas
public import Mathlib.RingTheory.Int.Basic
pu... |
191 | lean_file_chunk | 042b1f7aafbf93d83e2a2a61bbcf2f6d17d5cd607b5c848eb43d7eb5c428398b | lean_source_file | pkg_mathlib_source_file_chunks | rw [(by norm_cast : (q.num / q.den : ℝ) = (q.num / q.den : ℚ)), Rat.num_div_den]
exact h.trans (by rw [← one_div, sq, one_div_lt_one_div hq₂ hq₁, ← sub_pos]; ring_nf; exact hq₀)
end Real |
10,212 | lean_file_chunk | 39ce23aaf927787211efd4e0fac1c54552c206c22d8451ec2b493aebb9789165 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.EulerProduct.ExpLog
public import Mathlib.NumberTheory.LSeries.Dirichlet
/-!
# The Euler Product for the Riemann Zeta Functi... |
18,842 | lean_file_chunk | 04fb76af20e36d23f48d85be1285bf95413d7017427c9d65c91fb137daebfd31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Normed.Ring.InfiniteSum
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.NumberTheory.ArithmeticFunctio... |
1,939 | lean_file_chunk | 915485fff71fa2b46a1b3ecff75d46097816377bab6adaf5ec97b217576ccb2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv
public import Mathlib.LinearAlgebr... |
12,482 | lean_file_chunk | e090a010034324e7869100db9c7791dca0b730e0a9e25edf428ab7065d52ec31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 María Inés de Frutos-Fernández & Xavier Généreux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Xavier Généreux
-/
module
public import Mathlib.FieldTheory.Finite.Valuation
public import Mathlib.NumberTheory.Funct... |
3,314 | lean_file_chunk | 99918f93a2491dfaf69e61fb4202dd265cd1cb0515003782cb779af459be86a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michail Karatarakis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michail Karatarakis
-/
module
public import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
/-!
# Reindexed basis
This file introduces an equivalence between the set ... |
3,266 | lean_file_chunk | 9f476a857b41de1c19cc7bd55d22c4e191cf4feeee5e7afd59bfcf77f8de5aa4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Nat
public import Mathlib.NumberTheory.LSeries.SumCoeff
public import Mathlib.NumberTheory.NumberField.Ideal.Asy... |
23,995 | lean_file_chunk | ad6ab2f81a20c38beb7c35a6184a5313117d2a06440b9f43ce4a44cf87d40868 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 X. Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.FieldTheory.Galois.Abelian
public import Mathlib.FieldTheory.Galois.IsGaloisGroup
public import Mathlib.NumberTheory.NumberField.InfinitePlace... |
518 | lean_file_chunk | 924868ad941ccb089802fcfd4a6c21ceaa562e06776fd8d918368ac1b475c7cc | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨ζ, hζ⟩ := exists_isPrimitiveRoot ℚ K hn₁ (by grind)
have : IsTotallyComplex K := by
have : IsCyclotomicExtension {n} ℚ ℚ⟮ζ⟯ := hζ.intermediateField_adjoin_isCyclotomicExtension ℚ
have : IsTotallyComplex ℚ⟮ζ⟯ := isTotallyComplex ℚ⟮ζ⟯ hn₂
exact isTotallyComplex_of_algebra ℚ⟮ζ⟯ K
have := isAbelianG... |
11,115 | lean_file_chunk | 424f88e113f95c2b89de30146efc09bf04393c948cff1f700f143f010573f06e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Riccardo Brasca, Xavier Roblot
-/
module
public import Mathlib.NumberTheory.ClassNumber.AdmissibleAbs
public import Mathlib.NumberTheory.ClassNumber.Finite
public import Mat... |
5,434 | lean_file_chunk | 0a0893d6ff42c3e4d474e6bddea60c7ec6edca4abee8877d6cdef6f501cafa6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri, María Inés de Frutos-Fernández
-/
module
public import Mathlib.Algebra.Group.Pi.Units
public import Mathlib.NumberTheory.NumberFi... |
4,812 | lean_file_chunk | 19f1876ae3e4d839d7ccbaaba45454050b1dd1a1d46378bd779f2463b4a9f5d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Eric Rodriguez
-/
module
public import Mathlib.NumberTheory.NumberField.Basic
public import Mathlib.RingTheory.Localization.NormTrace
public import Mathlib.RingTheor... |
4,774 | lean_file_chunk | 54bc3447154c8ade30265a95a07a92cdd5126fd54a0fb00e51cbfc530e1aa7ad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
module
public import Mathlib.NumberTheory.NumberField.Completion.FinitePlace
public import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
/-!
# The Prod... |
16,923 | lean_file_chunk | 631fc7026505cf89ff469e6824ea78302be5b9469d911eacb29cffee3d63f34c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, Anne Baanen
-/
module
public import Mathlib.Algebra.Algebra.Rat
public import Mathlib.Algebra.CharZero.AddMonoidHom
public import Mathlib.Algebra.Ring.Int.Parity
p... |
4,672 | lean_file_chunk | be629382d28ed904b2714420fab0e55e86eb68f78475732d706c1afee4c0da49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.NumberField.Basic
public import Mathlib.RingTheory.FractionalIdeal.Norm
public import Mathlib.RingTheory.FractionalIdeal.Oper... |
14,547 | lean_file_chunk | 9386ebf3e3e5412bf22c6784b281b6ac1c651a65b80413a71e21835dc606c779 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michail Karatarakis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michail Karatarakis
-/
module
public import Mathlib.NumberTheory.SiegelsLemma
public import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
public import Mathlib.Number... |
280 | lean_file_chunk | ba46167df3c8c881f2ce7127ad6eff57d318a684f713428aca6528ba6c21ee90 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
module
public import Mathlib.NumberTheory.NumberField.Completion.FinitePlace
deprecated_module (since := "2026-03-09") |
2,427 | lean_file_chunk | 6873ae319995c2bb117b6aff615387fc0e642a8eb8bd0e8da809c79b6927f82c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri, María Inés de Frutos-Fernández
-/
module
public import Mathlib.NumberTheory.NumberField.InfiniteAdeleRing
public import Mathlib.R... |
23,984 | lean_file_chunk | db68eb3cd6d0618b4d292b37d6f1448f4e3cfcd608ef10c797ced99f0275c149 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Matthew Robert Ballard
-/
module
public import Mathlib.NumberTheory.Divisors
public import Mathlib.NumberTheory.Padics.PadicVal.Defs
public import Mathlib.Data.Nat.M... |
6,625 | lean_file_chunk | 91386cf8124fc672eeb1fdd56cc175f6065df632706449bd1a6d37fb1953a876 | lean_source_file | pkg_mathlib_source_file_chunks | padicValNat_eq_zero_of_mem_Ioo ⟨(Nat.lt_add_of_pos_right <| succ_pos n),
(Nat.mul_add _ _ _▸ Nat.mul_one _ ▸ ((add_lt_add_iff_left (p * m)).mpr h))⟩,
zero_add]
/-- The `p`-adic valuation of `n!` is equal to the `p`-adic valuation of the factorial of the
largest multiple of `p` below `n`, i.e. `(p * ⌊n / ... |
3,600 | lean_file_chunk | 5237f3bdf8555abb38ea35ae887e7c454a9f670e805451ae6b01594365939fdb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Matthew Robert Ballard
-/
module
public import Mathlib.Data.Nat.MaxPowDiv
public import Mathlib.RingTheory.Multiplicity
public import Mathlib.Data.Nat.Factors
/-!
#... |
14,655 | lean_file_chunk | c68c66ae21fb4510fc1200959e9735df017ee676adf7165339b1b432a79371ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.Analysis.PSeries
public import Mathlib.Order.Interval.Finset.Box
public i... |
2,767 | lean_file_chunk | 00952dca32fe3d9adb53992cd543c435034e4de2992950eb935dd8bedee98368 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence
public import Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
public impo... |
1,751 | lean_file_chunk | d9ab3721fa6db70136e8c1bcb4305fd8a4852902e73f6f267805a2ae5bc44a36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.NumberTheory.ModularForms.Basic
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty
public import Mathli... |
3,146 | lean_file_chunk | 4008fab2e21c5cabed558a44c7e159bce94e463dc85a045fb6ea772aed101d65 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Analysis.Normed.Group.FunctionSeries
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
public import... |
3,345 | lean_file_chunk | 4d367ee8b97d8639a4a9bb674cd4bb6e974cde64586a226be86943708f68db4a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
public imp... |
9,386 | lean_file_chunk | b59b29aec6a7a4810ae505f2fd6ddc3aa5675ee965b5c7b41823ecf9f33d6d0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.NumberTheory.ModularForms.SlashInvariantForms
public import Mathlib.Ri... |
18,657 | lean_file_chunk | 7e41fcd2bf5dcbb2d436923dbeb8e3efc469df927aad9c5780b2fe9e8c3bf21f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.SummableUniformlyOn
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent
public import Mathlib.Numbe... |
23,993 | lean_file_chunk | 5c3c085ee4f656eb1fbb75903e5227c30f6fc602cb80b3adef0dc7d78623ef32 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Calculus.SmoothSeries
public import Mathlib.Analysis.Normed.Operator.Prod
public import Mathlib.Analysis.SpecialFunctions.Gauss... |
3,473 | lean_file_chunk | c347e31b51a79ffb81203c07b80eaf962197dc0c487e32529366ea3391b0a716 | lean_source_file | pkg_mathlib_source_file_chunks | equation for L-series of even Dirichlet characters. -/
theorem jacobiTheta₂_functional_equation (z τ : ℂ) : jacobiTheta₂ z τ =
1 / (-I * τ) ^ (1 / 2 : ℂ) * cexp (-π * I * z ^ 2 / τ) * jacobiTheta₂ (z / τ) (-1 / τ) := by
rcases le_or_gt (im τ) 0 with hτ | hτ
· have : (-1 / τ).im ≤ 0 := by
rw [neg_div, neg_... |
6,398 | lean_file_chunk | 1ded47db1e31a9a40ebe3fb3e4f1ef245359192641d94cbf53d84eef92520c96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
public import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
/-! # Jacobi's th... |
807 | lean_file_chunk | 14b2609b71d13ceb7c73941ee2b027ea4bd5e7be9b63807fa3d31efe0eef453c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
public import Mathlib.Geometry.Manifold.MFDeriv.FDeriv
public import Mathlib.NumberTheory.Modul... |
11,883 | lean_file_chunk | 68d327cb6b9498bf29763154d5f41ae6f5f24b6c87f8060fdb5b193fbe74520a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
/-!
# Asymptotic bounds for Jacobi theta functions
The goal of this file is to estab... |
13,456 | lean_file_chunk | 42c11a63d50dd5bcf9266a0abc6a21d0137203e01946e337aa4883b1b3edeaff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.QEx... |
1,245 | lean_file_chunk | 0fb0ca83dae68300d3ea5d39ff4d20025f866189532035cef682801543f9a0c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, Gauss AI (Math Inc)
-/
module
public import Mathlib.NumberTheory.ModularForms.DedekindEta
/-!
# MDifferentiability of the weight 2 Eisenstein series
We show that th... |
9,553 | lean_file_chunk | daae817e6859652c6988de072ae4afece4927741e3b9565c80adc297362ba722 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable
public import Mathlib.LinearAlgebra.Matrix.FixedDetMatrices
/-!
# Slash action ... |
4,049 | lean_file_chunk | cb86503150e3b729116e0bdbd00539f5b6395835632e6edcc5c115cab175a48e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.CStarAlgebra.Classes
public import Mathlib.NumberTheory.LSeries.RiemannZeta
public import Mathlib.NumberTheory.ModularForms.Ei... |
4,570 | lean_file_chunk | 77f31aae3f306496d27802979216b4db0a85f49ccbb343c1e16bcf9600f806e2 | 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.NumberTheory.LegendreSymbol.QuadraticChar.Basic
public import Mathlib.NumberTheory.GaussSum
/-!
# Quadratic characters of finite fields
... |
11,673 | lean_file_chunk | 0c1f8ae54e3d56ab61194d2198108286e204a391089a0b229b63537fe8af1110 | 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.Data.Fintype.Parity
public import Mathlib.NumberTheory.LegendreSymbol.ZModChar
public import Mathlib.FieldTheory.Finite.Basic
/-!
# Quadr... |
11,553 | lean_file_chunk | aa2da333eaff3e9530b71273e2dbc253597460e8e0e86399c85989c145a37b02 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Jujian Zhang
-/
module
public import Mathlib.Algebra.Polynomial.DenomsClearable
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Analysis.Calculus.... |
7,634 | lean_file_chunk | 79f0731c67c1f39a33ab30475d0ae39ede51703d3fae8d9d563e18ed5a7f1731 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Jujian Zhang
-/
module
public import Mathlib.NumberTheory.Transcendental.Liouville.Basic
/-!
# Liouville constants
This file contains a construction of a family of Lio... |
13,933 | lean_file_chunk | 720d161b66bb0f7b7412acd05867868e3504c5e048ef270fc0bd6b4d9211b7d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
public import Mathlib.NumberTheory.Transcendental.Liouville.Basic
public import Mathlib.Topo... |
6,070 | lean_file_chunk | de970259efcdea73d96a8cc125d08480b6debb0e2e36669aa249f3aa53cb5377 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
public import Mathlib.NumberTheory.Transcendental.Liouville.Residual
public import Mathlib.Number... |
3,130 | lean_file_chunk | c7b3432f931a72e46f554299e6d7f0f0ecadc1957d10ca3138d909d45c38d516 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.NumberTheory.Transcendental.Liouville.Basic
public import Mathlib.Topology.Baire.Lemmas
public import Mathlib.Topology.Baire.LocallyCo... |
9,106 | lean_file_chunk | 8d11aba8ffa517c6d2c59cc3e1b643ad5be1b60934d55edd0f808c0f7745b123 | 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.SumIteratedDerivative
public import Mathlib.Analysis.Calculus.Deriv.Polynomial
public import Mathlib.Analysis.SpecialFuncti... |
10,206 | lean_file_chunk | a68ac0f7f2db17fe254d3b47bb308a430af8f20e28480902cf69f25c2abf1971 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.FieldTheory.Finite.Extension
public import Mathlib.NumberTheory.Cyclotomic.Gal
public import Mathlib.NumberTheory.DirichletCharacter.Basic... |
2,570 | lean_file_chunk | 6d61b4f8b13af557926c13cd8c24994015d7b0362704f00ff3f11a6f927e3baa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.NumberTheory.NumberField.ClassNumber
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
public import Mathlib.NumberTheor... |
23,999 | lean_file_chunk | 0e5c8a2710f83e9429afc597a65c27b370a4208800d44dc4e43731ae2f448e27 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.NumberTheory.Cyclotomic.Discriminant
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings
public import Mathlib.Number... |
23,959 | lean_file_chunk | aec20df91c2ee38420d2ffbe1bb59c9c8cbf30559295f2eeb209725f47fe3757 | lean_source_file | pkg_mathlib_source_file_chunks | refine not_exists_int_prime_dvd_sub_of_prime_pow_ne_two hζ (fun h ↦ ?_)
simp_all only [(@Nat.Prime.pow_eq_iff 2 p (k + 1) Nat.prime_two).mp (by assumption_mod_cast),
pow_one, ne_eq]
/-- In a `p`-th cyclotomic extension of `ℚ `, we have that `ζ` is not congruent to an
integer modulo `p` if `p ≠ 2`. -/
theorem n... |
1,171 | lean_file_chunk | 963bd095b86986fb087371f8f9e0efe38eac0d45ddd4989e4d16cd26695db650 | lean_source_file | pkg_mathlib_source_file_chunks | -- and therefore `K` is the `l`-th cyclotomic field
have : IsCyclotomicExtension {n.lcm (torsionOrder K)} ℚ K := by
have := hK.union_of_isPrimitiveRoot _ _ _ h
rwa [Set.union_comm, ← IsCyclotomicExtension.iff_union_of_dvd] at this
exact ⟨n.lcm (torsionOrder K), by simp, NeZero.ne _, Nat.dvd_lcm_left _ _⟩
... |
17,282 | lean_file_chunk | 7eaedcef1cf900c4e320191cb5f555fd52d53b5294bc5de1c8c06cb3ffbb2053 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
public import Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind
public import Mathlib.RingTh... |
2,663 | lean_file_chunk | f0d11b1e5b25f6466c462a7da981fec78429ffffff2a7c1851fbffa55de8d1c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
public import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
/-!
# Cyclotom... |
9,026 | lean_file_chunk | 6226367174d36722cf5bed1c128d00c10d200fa8a32dbee080ea274200a0b904 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Pietro Monticone
-/
module
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
publi... |
7,935 | lean_file_chunk | 3d75de802458fb437fc40743052a9617a9fdb5b5574a3d65c76fc80f4045af49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
public import Mathlib.NumberTheory.NumberField.ClassNumber
/-!
# Asymptotics on int... |
13,305 | lean_file_chunk | 98a1b7a6ec2faaa524b84a6d1418a95f890e61b07daf9858869ef0bfa76d4320 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.KummerDedekind
public import Mathlib.NumberTheory.NumberField.Basic
public import Mathlib.NumberTheory.RamificationInertia.Ba... |
4,971 | lean_file_chunk | d0ba4aac4d4c8f6fc5b005ec8de5a054900985211fdd1f5d418842f7b76a43be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
public import Mathlib.NumberTheory.NumberField.Units.Basic
/-!
# Basic results on integral idea... |
1,793 | lean_file_chunk | cb38a44951b51f0cd8f2adab6d14e38b7c2619c0cf44127cd35417b4c40d8c0f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
/-!
# `LiesOver` instances for completions of number fields
If `L` and `K` are... |
14,240 | lean_file_chunk | e0953e160d68ece6aecf5fc9d661137123438e0cd2500bdf709c884479e96d75 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Analysis.Normed.Field.WithAbs
public import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
public import Mathlib.NumberTheor... |
5,463 | lean_file_chunk | d71a369f161502b9de82cd2e36c451777d1220bafb8972d7b1bcc61f1c406404 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.NumberTheory.NumberField.Completion.LiesOverInstances
public import Mathlib.NumberTheory.RamificationInertia.Basic
/-!
# Ramifica... |
19,229 | lean_file_chunk | 1655451ae9bbcd64a66e2ba275be1a756f7ab8bfb7e8e3636f456116e5ab7205 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Order.Archimedean.Submonoid
public import Mathlib.LinearAlgebra.FreeModule.IdealQuotient
public import Mathlib.NumberTheor... |
301 | lean_file_chunk | 8b05339ca9b5e7887e9705910662856df74b250a18f5785fa1c204d1c9adbac3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module -- shake: keep-all
public import Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
deprecated_module (since := "2026-03-09") |
23,997 | lean_file_chunk | 81cc6ab22611e50fdcf534550a6da168875765b7bb9b8aa81ece5144c81f53f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Analysis.AbsoluteValue.Equivalence
public import Mathlib.Analysis.Normed.Field.WithAbs
public import Mathlib.NumberTheory.NumberField.Infi... |
2,598 | lean_file_chunk | bbf7975d74ba9478818a85c54da9de2ebdbe7a502545b59045ad0a41d2c4ad49 | lean_source_file | pkg_mathlib_source_file_chunks | exact ⟨n, v.pos_iff.1 <| zero_lt_one.trans (by simpa), by simp [← coe_apply]; grind⟩
variable {v} (K)
open Filter in
/--
*Weak approximation for infinite places*
The number field `K` is dense when embedded diagonally in the product
`(v : InfinitePlace K) → WithAbs v.1`, in which `WithAbs v.1` represents `K` equipped ... |
14,697 | lean_file_chunk | 5ade550ae6086210811a749d3fd85bd455545db9ba65403f69e0c7a184af81e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Xavier Roblot
-/
module
public import Mathlib.Algebra.Algebra.Hom.Rat
public import Mathlib.Analysis.Complex.Polynomial.Basic
public import Mathlib.NumberTheory.NumberFie... |
23,933 | lean_file_chunk | 3a73d8726d899b0824b40939010958d4026f7b00516b0a2801a8910a72f4f29d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Analysis.Normed.Ring.WithAbs
public import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
public import Mathlib.NumberTheory.NumberField... |
9,771 | lean_file_chunk | ba8e30dd1433b2ef56a3e8559493e7dbc43260b51fdd8b522ca892baab3e5465 | lean_source_file | pkg_mathlib_source_file_chunks | lemma IsUnramifiedAtInfinitePlaces.card_infinitePlace [NumberField k] [NumberField K]
[IsGalois k K] [IsUnramifiedAtInfinitePlaces k K] :
Fintype.card (InfinitePlace K) = Fintype.card (InfinitePlace k) * finrank k K := by
classical
rw [InfinitePlace.card_eq_card_isUnramifiedIn (k := k) (K := K), Finset.filt... |
8,931 | lean_file_chunk | b4a973fccd8dddb03024a74a9cb69ced535666cd38f316f34287b69a204302ce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Xavier Roblot
-/
module
public import Mathlib.FieldTheory.PrimeField
public import Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
/-!
# Totally real and to... |
8,949 | lean_file_chunk | 62b020fd77f8ebcded1a35095668e361ed2d5d759307ddedf9fd381d238c8866 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.GroupTheory.Torsion
public import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
public import Mathlib.RingTheory.LocalRing.RingHom.... |
16,695 | lean_file_chunk | 62cad3347efc10fc5c7f9b94e64962c6008eb565e441b2457c4a15da51508fae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Algebra.Module.ZLattice.Covolume
public import Mathlib.LinearAlgebra.Matrix.Determinant.Misc
public import Mathlib.NumberTheory.NumberFiel... |
23,637 | lean_file_chunk | 34b053279555f1c132dc537f9dd186b61d0e7026eaead8b493029f516a489023 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.LinearAlgebra.Matrix.Gershgorin
public import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
public import Mathlib.NumberT... |
8,472 | lean_file_chunk | eb191b256772475057dc03dd528b48c962d3474c4fedc8de6f4291acf0d6622e | 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.NumberTheory.NumberField.Discriminant.Basic
public import Mathlib.RingTheory.DedekindDomain.LinearDisjoint
public import Mathlib.RingTheory.Id... |
23,978 | lean_file_chunk | 629280d0d4229fb66c06d1603245fdc63b56d66e55c2a2efb7ccb7936ae868b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Algebra.Module.ZLattice.Covolume
public import Mathlib.Analysis.Real.Pi.Bounds
public import Mathlib.NumberTheory.NumberField.CanonicalEmb... |
1,909 | lean_file_chunk | 3ac366d9cf2fc95f2eaa574b13532103a3f65c9b71701703ba72a7dc10ce9ac8 | lean_source_file | pkg_mathlib_source_file_chunks | rw [val_eq_coe, NNReal.coe_mul, NNReal.coe_pow, NNReal.coe_max, NNReal.coe_one,
Real.coe_sqrt, NNReal.coe_add 1, NNReal.coe_one, NNReal.coe_pow]
gcongr
· exact le_max_right _ 1
· exact rank_le_rankOfDiscrBdd hK₂
· rw [NNReal.coe_natCast, Nat.cast_le]
exact (Nat.choose... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.