Loogle!

Result

Found 17 declarations mentioning MvPowerSeries.map.

• MvPowerSeries.map 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  (σ : Type u_1) {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) : MvPowerSeries σ R →+* MvPowerSeries σ S
• MvPowerSeries.map_id 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} [Semiring R] : MvPowerSeries.map σ (RingHom.id R) = RingHom.id (MvPowerSeries σ R)
• MvPowerSeries.map_X 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) (s : σ) : (MvPowerSeries.map σ f) (MvPowerSeries.X s) = MvPowerSeries.X s
• MvPowerSeries.map_comp 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} {T : Type u_4} [Semiring R] [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) : MvPowerSeries.map σ (g.comp f) = (MvPowerSeries.map σ g).comp (MvPowerSeries.map σ f)
• MvPowerSeries.map_eq_zero 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [DivisionSemiring R] [Semiring S] [Nontrivial S] (φ : MvPowerSeries σ R) (f : R →+* S) : (MvPowerSeries.map σ f) φ = 0 ↔ φ = 0
• MvPowerSeries.map_C 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) (a : R) : (MvPowerSeries.map σ f) ((MvPowerSeries.C σ R) a) = (MvPowerSeries.C σ S) (f a)
• MvPowerSeries.algebraMap_apply'' 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} (A : Type u_3) [CommSemiring R] [CommSemiring A] [Algebra R A] (f : MvPowerSeries σ R) : (algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A)) f = (MvPowerSeries.map σ (algebraMap R A)) f
• MvPowerSeries.constantCoeff_map 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) (φ : MvPowerSeries σ R) : (MvPowerSeries.constantCoeff σ S) ((MvPowerSeries.map σ f) φ) = f ((MvPowerSeries.constantCoeff σ R) φ)
• MvPowerSeries.algebraMap_apply' 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} (A : Type u_3) [CommSemiring R] [CommSemiring A] [Algebra R A] (p : MvPolynomial σ R) : (algebraMap (MvPolynomial σ R) (MvPowerSeries σ A)) p = (MvPowerSeries.map σ (algebraMap R A)) ↑p
• MvPolynomial.coeToMvPowerSeries.algHom_apply 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} [CommSemiring R] (φ : MvPolynomial σ R) (A : Type u_3) [CommSemiring A] [Algebra R A] : (MvPolynomial.coeToMvPowerSeries.algHom A) φ = (MvPowerSeries.map σ (algebraMap R A)) ↑φ
• MvPowerSeries.mapAlgHom_apply 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {A : Type u_3} [CommSemiring R] [Semiring A] [Algebra R A] {B : Type u_4} [Semiring B] [Algebra R B] (φ : A →ₐ[R] B) (f : MvPowerSeries σ A) : (MvPowerSeries.mapAlgHom φ) f = (MvPowerSeries.map σ ↑φ) f
• MvPowerSeries.map_monomial 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) (n : σ →₀ ℕ) (a : R) : (MvPowerSeries.map σ f) ((MvPowerSeries.monomial R n) a) = (MvPowerSeries.monomial S n) (f a)
• MvPowerSeries.coeff_map 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [Semiring R] [Semiring S] (f : R →+* S) (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) : (MvPowerSeries.coeff S n) ((MvPowerSeries.map σ f) φ) = f ((MvPowerSeries.coeff R n) φ)
• MvPowerSeries.map.isLocalHom 📋 Mathlib.RingTheory.MvPowerSeries.Inverse
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalHom f] : IsLocalHom (MvPowerSeries.map σ f)
• MvPowerSeries.trunc'_map 📋 Mathlib.RingTheory.MvPowerSeries.Trunc
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [DecidableEq σ] [CommSemiring R] [CommSemiring S] (n : σ →₀ ℕ) (f : R →+* S) (p : MvPowerSeries σ R) : (MvPowerSeries.trunc' S n) ((MvPowerSeries.map σ f) p) = (MvPolynomial.map f) ((MvPowerSeries.trunc' R n) p)
• MvPowerSeries.trunc_map 📋 Mathlib.RingTheory.MvPowerSeries.Trunc
  {σ : Type u_1} {R : Type u_2} {S : Type u_3} [DecidableEq σ] [CommSemiring R] [CommSemiring S] (n : σ →₀ ℕ) (f : R →+* S) (p : MvPowerSeries σ R) : (MvPowerSeries.trunc S n) ((MvPowerSeries.map σ f) p) = (MvPolynomial.map f) ((MvPowerSeries.trunc R n) p)
• MvPowerSeries.map_algebraMap_eq_subst_X 📋 Mathlib.RingTheory.MvPowerSeries.Substitution
  {σ : Type u_1} {R : Type u_3} [CommRing R] {S : Type u_5} [CommRing S] [Algebra R S] (f : MvPowerSeries σ R) : (MvPowerSeries.map σ (algebraMap R S)) f = MvPowerSeries.subst MvPowerSeries.X f

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