Loogle!

Result

Found 11 declarations mentioning WeierstrassCurve.VariableChange.map.

• WeierstrassCurve.VariableChange.map_id 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] (C : WeierstrassCurve.VariableChange R) : WeierstrassCurve.VariableChange.map (RingHom.id R) C = C
• WeierstrassCurve.VariableChange.map 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : WeierstrassCurve.VariableChange A
• WeierstrassCurve.VariableChange.map_injective 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] {φ : R →+* A} (hφ : Function.Injective ⇑φ) : Function.Injective (WeierstrassCurve.VariableChange.map φ)
• WeierstrassCurve.VariableChange.map_r 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : (WeierstrassCurve.VariableChange.map φ C).r = φ C.r
• WeierstrassCurve.VariableChange.map_s 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : (WeierstrassCurve.VariableChange.map φ C).s = φ C.s
• WeierstrassCurve.VariableChange.map_t 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : (WeierstrassCurve.VariableChange.map φ C).t = φ C.t
• WeierstrassCurve.map_variableChange 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] (W : WeierstrassCurve R) {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : WeierstrassCurve.VariableChange.map φ C • W.map φ = (C • W).map φ
• WeierstrassCurve.VariableChange.map_map 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] (C : WeierstrassCurve.VariableChange R) {A : Type v} [CommRing A] (φ : R →+* A) {B : Type w} [CommRing B] (ψ : A →+* B) : WeierstrassCurve.VariableChange.map ψ (WeierstrassCurve.VariableChange.map φ C) = WeierstrassCurve.VariableChange.map (ψ.comp φ) C
• WeierstrassCurve.VariableChange.map_u 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : (WeierstrassCurve.VariableChange.map φ C).u = (Units.map ↑φ) C.u
• WeierstrassCurve.VariableChange.map_baseChange 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] (C : WeierstrassCurve.VariableChange R) {S : Type s} [CommRing S] [Algebra R S] {A : Type v} [CommRing A] [Algebra R A] [Algebra S A] [IsScalarTower R S A] {B : Type w} [CommRing B] [Algebra R B] [Algebra S B] [IsScalarTower R S B] (ψ : A →ₐ[S] B) : WeierstrassCurve.VariableChange.map (↑ψ) (WeierstrassCurve.VariableChange.baseChange A C) = WeierstrassCurve.VariableChange.baseChange B C
• WeierstrassCurve.VariableChange.map.eq_1 📋 Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange
  {R : Type u} [CommRing R] {A : Type v} [CommRing A] (φ : R →+* A) (C : WeierstrassCurve.VariableChange R) : WeierstrassCurve.VariableChange.map φ C = { u := (Units.map ↑φ) C.u, r := φ C.r, s := φ C.s, t := φ C.t }

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