Loogle!

Result

Found 12 declarations mentioning Matrix.SpecialLinearGroup.map.

• Matrix.SpecialLinearGroup.map 📋 Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
  {n : Type u} [DecidableEq n] [Fintype n] {R : Type v} [CommRing R] {S : Type u_1} [CommRing S] (f : R →+* S) : Matrix.SpecialLinearGroup n R →* Matrix.SpecialLinearGroup n S
• Matrix.SpecialLinearGroup.coe_matrix_coe 📋 Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
  {n : Type u} [DecidableEq n] [Fintype n] {R : Type v} [CommRing R] (g : Matrix.SpecialLinearGroup n ℤ) : ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom R)) g) = (↑g).map ⇑(Int.castRingHom R)
• Matrix.SpecialLinearGroup.coe_int_neg 📋 Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
  {n : Type u} [DecidableEq n] [Fintype n] {R : Type v} [CommRing R] [Fact (Even (Fintype.card n))] (g : Matrix.SpecialLinearGroup n ℤ) : (Matrix.SpecialLinearGroup.map (Int.castRingHom R)) (-g) = -(Matrix.SpecialLinearGroup.map (Int.castRingHom R)) g
• Matrix.SpecialLinearGroup.map_apply_coe 📋 Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
  {n : Type u} [DecidableEq n] [Fintype n] {R : Type v} [CommRing R] {S : Type u_1} [CommRing S] (f : R →+* S) (g : Matrix.SpecialLinearGroup n R) : ↑((Matrix.SpecialLinearGroup.map f) g) = f.mapMatrix ↑g
• ModularGroup.coe.eq_1 📋 Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
  (g : Matrix.SpecialLinearGroup (Fin 2) ℤ) : ↑g = Matrix.SpecialLinearGroup.toGLPos ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) g)
• ModularGroup.tendsto_lcRow0 📋 Mathlib.NumberTheory.Modular
  {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) : Filter.Tendsto (fun g => (ModularGroup.lcRow0 cd) ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) ↑g)) Filter.cofinite (Filter.cocompact ℝ)
• ModularGroup.smul_eq_lcRow0_add 📋 Mathlib.NumberTheory.Modular
  {g : Matrix.SpecialLinearGroup (Fin 2) ℤ} (z : UpperHalfPlane) {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg : ↑g 1 = p) : ↑(g • z) = ↑((ModularGroup.lcRow0 p) ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) g)) / (↑(p 0) ^ 2 + ↑(p 1) ^ 2) + (↑(p 1) * ↑z - ↑(p 0)) / ((↑(p 0) ^ 2 + ↑(p 1) ^ 2) * (↑(p 0) * ↑z + ↑(p 1)))
• SL_reduction_mod_hom_val 📋 Mathlib.NumberTheory.ModularForms.CongruenceSubgroups
  (N : ℕ) (γ : Matrix.SpecialLinearGroup (Fin 2) ℤ) (i j : Fin 2) : ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ) i j = ↑(↑γ i j)
• CongruenceSubgroup.Gamma_mem' 📋 Mathlib.NumberTheory.ModularForms.CongruenceSubgroups
  {N : ℕ} {γ : Matrix.SpecialLinearGroup (Fin 2) ℤ} : γ ∈ CongruenceSubgroup.Gamma N ↔ (Matrix.SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ = 1
• EisensteinSeries.gammaSetEquiv 📋 Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
  {N : ℕ} (a : Fin 2 → ZMod N) (γ : Matrix.SpecialLinearGroup (Fin 2) ℤ) : ↑(EisensteinSeries.gammaSet N a) ≃ ↑(EisensteinSeries.gammaSet N (Matrix.vecMul a ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ)))
• EisensteinSeries.eisensteinSeries_slash_apply 📋 Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
  {N : ℕ} (a : Fin 2 → ZMod N) (k : ℤ) (γ : Matrix.SpecialLinearGroup (Fin 2) ℤ) : SlashAction.map ℂ k γ (eisensteinSeries a k) = eisensteinSeries (Matrix.vecMul a ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ)) k
• EisensteinSeries.vecMul_SL2_mem_gammaSet 📋 Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
  {N : ℕ} {a : Fin 2 → ZMod N} {v : Fin 2 → ℤ} (hv : v ∈ EisensteinSeries.gammaSet N a) (γ : Matrix.SpecialLinearGroup (Fin 2) ℤ) : Matrix.vecMul v ↑γ ∈ EisensteinSeries.gammaSet N (Matrix.vecMul a ↑((Matrix.SpecialLinearGroup.map (Int.castRingHom (ZMod N))) γ))

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 19971e9 serving mathlib revision bce1d65