Loogle!

Result

Found 22 declarations mentioning PowerSeries.map.

• PowerSeries.map 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] {S : Type u_2} [Semiring S] (f : R →+* S) : PowerSeries R →+* PowerSeries S
• PowerSeries.map_id 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] : ⇑(PowerSeries.map (RingHom.id R)) = id
• PowerSeries.map_X 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] {S : Type u_2} [Semiring S] (f : R →+* S) : (PowerSeries.map f) PowerSeries.X = PowerSeries.X
• PowerSeries.map_injective 📋 Mathlib.RingTheory.PowerSeries.Basic
  {S : Type u_2} {T : Type u_3} [Semiring S] [Semiring T] (f : S →+* T) (hf : Function.Injective ⇑f) : Function.Injective ⇑(PowerSeries.map f)
• PowerSeries.map_surjective 📋 Mathlib.RingTheory.PowerSeries.Basic
  {S : Type u_2} {T : Type u_3} [Semiring S] [Semiring T] (f : S →+* T) (hf : Function.Surjective ⇑f) : Function.Surjective ⇑(PowerSeries.map f)
• PowerSeries.map_comp 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] {S : Type u_2} {T : Type u_3} [Semiring S] [Semiring T] (f : R →+* S) (g : S →+* T) : PowerSeries.map (g.comp f) = (PowerSeries.map g).comp (PowerSeries.map f)
• Polynomial.polynomial_map_coe 📋 Mathlib.RingTheory.PowerSeries.Basic
  {U : Type u_2} {V : Type u_3} [CommSemiring U] [CommSemiring V] {φ : U →+* V} {f : Polynomial U} : ↑(Polynomial.map φ f) = (PowerSeries.map φ) ↑f
• PowerSeries.map_eq_zero 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_2} {S : Type u_3} [DivisionSemiring R] [Semiring S] [Nontrivial S] (φ : PowerSeries R) (f : R →+* S) : (PowerSeries.map f) φ = 0 ↔ φ = 0
• PowerSeries.algebraMap_apply'' 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} (A : Type u_2) [CommSemiring R] [CommSemiring A] [Algebra R A] (f : PowerSeries R) : (algebraMap (PowerSeries R) (PowerSeries A)) f = (PowerSeries.map (algebraMap R A)) f
• PowerSeries.map_C 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] {S : Type u_2} [Semiring S] (f : R →+* S) (r : R) : (PowerSeries.map f) ((PowerSeries.C R) r) = (PowerSeries.C S) (f r)
• Polynomial.coeToPowerSeries.algHom_apply 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [CommSemiring R] (φ : Polynomial R) (A : Type u_2) [Semiring A] [Algebra R A] : (Polynomial.coeToPowerSeries.algHom A) φ = (PowerSeries.map (algebraMap R A)) ↑φ
• PowerSeries.algebraMap_apply' 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} (A : Type u_2) [CommSemiring R] [CommSemiring A] [Algebra R A] (p : Polynomial R) : (algebraMap (Polynomial R) (PowerSeries A)) p = (PowerSeries.map (algebraMap R A)) ↑p
• PowerSeries.mapAlgHom_apply 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} {A : Type u_2} {B : Type u_3} [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B] (φ : A →ₐ[R] B) (f : PowerSeries A) : (PowerSeries.mapAlgHom φ) f = (PowerSeries.map ↑φ) f
• PowerSeries.coeff_map 📋 Mathlib.RingTheory.PowerSeries.Basic
  {R : Type u_1} [Semiring R] {S : Type u_2} [Semiring S] (f : R →+* S) (n : ℕ) (φ : PowerSeries R) : (PowerSeries.coeff S n) ((PowerSeries.map f) φ) = f ((PowerSeries.coeff R n) φ)
• PowerSeries.map.isLocalHom 📋 Mathlib.RingTheory.PowerSeries.Inverse
  {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] (f : R →+* S) [IsLocalHom f] : IsLocalHom (PowerSeries.map f)
• PowerSeries.map_cos 📋 Mathlib.RingTheory.PowerSeries.WellKnown
  {A : Type u_1} {A' : Type u_2} [Ring A] [Ring A'] [Algebra ℚ A] [Algebra ℚ A'] (f : A →+* A') : (PowerSeries.map f) (PowerSeries.cos A) = PowerSeries.cos A'
• PowerSeries.map_exp 📋 Mathlib.RingTheory.PowerSeries.WellKnown
  {A : Type u_1} {A' : Type u_2} [Ring A] [Ring A'] [Algebra ℚ A] [Algebra ℚ A'] (f : A →+* A') : (PowerSeries.map f) (PowerSeries.exp A) = PowerSeries.exp A'
• PowerSeries.map_sin 📋 Mathlib.RingTheory.PowerSeries.WellKnown
  {A : Type u_1} {A' : Type u_2} [Ring A] [Ring A'] [Algebra ℚ A] [Algebra ℚ A'] (f : A →+* A') : (PowerSeries.map f) (PowerSeries.sin A) = PowerSeries.sin A'
• PowerSeries.map_invUnitsSub 📋 Mathlib.RingTheory.PowerSeries.WellKnown
  {R : Type u_1} {S : Type u_2} [Ring R] [Ring S] (f : R →+* S) (u : Rˣ) : (PowerSeries.map f) (PowerSeries.invUnitsSub u) = PowerSeries.invUnitsSub ((Units.map ↑f) u)
• PowerSeries.trunc_map 📋 Mathlib.RingTheory.PowerSeries.Trunc
  {R : Type u_1} {S : Type u_2} [Semiring R] [Semiring S] (f : R →+* S) (p : PowerSeries R) (n : ℕ) : PowerSeries.trunc n ((PowerSeries.map f) p) = Polynomial.map f (PowerSeries.trunc n p)
• IsDistinguishedAt.degree_eq_order_map 📋 Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished
  {R : Type u_1} [CommRing R] {I : Ideal R} (f h : PowerSeries R) {g : Polynomial R} (distinguish : g.IsDistinguishedAt I) (nmem : (PowerSeries.constantCoeff R) h ∉ I) (eq : f = ↑g * h) : g.degree = ((PowerSeries.map (Ideal.Quotient.mk I)) f).order
• Polynomial.IsDistinguishedAt.degree_eq_order_map 📋 Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished
  {R : Type u_1} [CommRing R] {I : Ideal R} (f h : PowerSeries R) {g : Polynomial R} (distinguish : g.IsDistinguishedAt I) (nmem : (PowerSeries.constantCoeff R) h ∉ I) (eq : f = ↑g * h) : g.degree = ((PowerSeries.map (Ideal.Quotient.mk I)) f).order

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