Loogle!

Result

Found 7 declarations mentioning WeierstrassCurve.Affine.Point.map.

• WeierstrassCurve.Affine.Point.map 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {S : Type s} {F : Type u} {K : Type v} [CommRing R] [CommRing S] [Field F] [Field K] {W' : WeierstrassCurve.Affine R} [Algebra R S] [Algebra R F] [Algebra S F] [IsScalarTower R S F] [Algebra R K] [Algebra S K] [IsScalarTower R S K] (f : F →ₐ[S] K) : WeierstrassCurve.Affine.Point (WeierstrassCurve.baseChange W' F) →+ WeierstrassCurve.Affine.Point (WeierstrassCurve.baseChange W' K)
• WeierstrassCurve.Affine.Point.map_id 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {F : Type u} [CommRing R] [Field F] {W' : WeierstrassCurve.Affine R} [Algebra R F] (P : WeierstrassCurve.Affine.Point (WeierstrassCurve.baseChange W' F)) : (WeierstrassCurve.Affine.Point.map (Algebra.ofId F F)) P = P
• WeierstrassCurve.Affine.Point.map_injective 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {S : Type s} {F : Type u} {K : Type v} [CommRing R] [CommRing S] [Field F] [Field K] {W' : WeierstrassCurve.Affine R} [Algebra R S] [Algebra R F] [Algebra S F] [IsScalarTower R S F] [Algebra R K] [Algebra S K] [IsScalarTower R S K] (f : F →ₐ[S] K) : Function.Injective ⇑(WeierstrassCurve.Affine.Point.map f)
• WeierstrassCurve.Affine.Point.map_zero 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {S : Type s} {F : Type u} {K : Type v} [CommRing R] [CommRing S] [Field F] [Field K] {W' : WeierstrassCurve.Affine R} [Algebra R S] [Algebra R F] [Algebra S F] [IsScalarTower R S F] [Algebra R K] [Algebra S K] [IsScalarTower R S K] (f : F →ₐ[S] K) : (WeierstrassCurve.Affine.Point.map f) 0 = 0
• WeierstrassCurve.Affine.Point.map_baseChange 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {F : Type u} {K : Type v} {L : Type w} [CommRing R] [Field F] [Field K] [Field L] {W' : WeierstrassCurve.Affine R} [Algebra R F] [Algebra R K] [Algebra R L] [Algebra F K] [IsScalarTower R F K] [Algebra F L] [IsScalarTower R F L] (f : K →ₐ[F] L) (P : WeierstrassCurve.Affine.Point (WeierstrassCurve.baseChange W' F)) : (WeierstrassCurve.Affine.Point.map f) ((WeierstrassCurve.Affine.Point.baseChange F K) P) = (WeierstrassCurve.Affine.Point.baseChange F L) P
• WeierstrassCurve.Affine.Point.map_some 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {S : Type s} {F : Type u} {K : Type v} [CommRing R] [CommRing S] [Field F] [Field K] {W' : WeierstrassCurve.Affine R} [Algebra R S] [Algebra R F] [Algebra S F] [IsScalarTower R S F] [Algebra R K] [Algebra S K] [IsScalarTower R S K] (f : F →ₐ[S] K) {x y : F} (h : (WeierstrassCurve.baseChange W' F).toAffine.Nonsingular x y) : (WeierstrassCurve.Affine.Point.map f) (WeierstrassCurve.Affine.Point.some h) = WeierstrassCurve.Affine.Point.some ⋯
• WeierstrassCurve.Affine.Point.map_map 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} {S : Type s} {F : Type u} {K : Type v} {L : Type w} [CommRing R] [CommRing S] [Field F] [Field K] [Field L] {W' : WeierstrassCurve.Affine R} [Algebra R S] [Algebra R F] [Algebra S F] [IsScalarTower R S F] [Algebra R K] [Algebra S K] [IsScalarTower R S K] [Algebra R L] [Algebra S L] [IsScalarTower R S L] (f : F →ₐ[S] K) (g : K →ₐ[S] L) (P : WeierstrassCurve.Affine.Point (WeierstrassCurve.baseChange W' F)) : (WeierstrassCurve.Affine.Point.map g) ((WeierstrassCurve.Affine.Point.map f) P) = (WeierstrassCurve.Affine.Point.map (g.comp f)) P

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 40fea08