Loogle!

Result

Found 9 declarations mentioning RatFunc.map.

• RatFunc.map 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [MonoidHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) : RatFunc R →* RatFunc S
• RatFunc.map_injective 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [MonoidHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) (hf : Function.Injective ⇑φ) : Function.Injective ⇑(RatFunc.map φ hφ)
• RatFunc.coe_mapRingHom_eq_coe_map 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [RingHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) : ⇑(RatFunc.mapRingHom φ hφ) = ⇑(RatFunc.map φ hφ)
• RatFunc.map_apply 📋 Mathlib.FieldTheory.RatFunc.Basic
  {K : Type u} [Field K] {R : Type u_1} {F : Type u_2} [CommRing R] [IsDomain R] [FunLike F (Polynomial K) (Polynomial R)] [MonoidHomClass F (Polynomial K) (Polynomial R)] (φ : F) (hφ : nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial R))) (f : RatFunc K) : (RatFunc.map φ hφ) f = (algebraMap (Polynomial R) (RatFunc R)) (φ f.num) / (algebraMap (Polynomial R) (RatFunc R)) (φ f.denom)
• RatFunc.map_apply_div_ne_zero 📋 Mathlib.FieldTheory.RatFunc.Basic
  {K : Type u} [CommRing K] [IsDomain K] {R : Type u_1} {F : Type u_2} [CommRing R] [IsDomain R] [FunLike F (Polynomial K) (Polynomial R)] [MonoidHomClass F (Polynomial K) (Polynomial R)] (φ : F) (hφ : nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial R))) (p q : Polynomial K) (hq : q ≠ 0) : (RatFunc.map φ hφ) ((algebraMap (Polynomial K) (RatFunc K)) p / (algebraMap (Polynomial K) (RatFunc K)) q) = (algebraMap (Polynomial R) (RatFunc R)) (φ p) / (algebraMap (Polynomial R) (RatFunc R)) (φ q)
• RatFunc.map_apply_div 📋 Mathlib.FieldTheory.RatFunc.Basic
  {K : Type u} [CommRing K] [IsDomain K] {R : Type u_1} {F : Type u_2} [CommRing R] [IsDomain R] [FunLike F (Polynomial K) (Polynomial R)] [MonoidWithZeroHomClass F (Polynomial K) (Polynomial R)] (φ : F) (hφ : nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial R))) (p q : Polynomial K) : (RatFunc.map φ hφ) ((algebraMap (Polynomial K) (RatFunc K)) p / (algebraMap (Polynomial K) (RatFunc K)) q) = (algebraMap (Polynomial R) (RatFunc R)) (φ p) / (algebraMap (Polynomial R) (RatFunc R)) (φ q)
• RatFunc.coe_mapAlgHom_eq_coe_map 📋 Mathlib.FieldTheory.RatFunc.Basic
  {K : Type u} [CommRing K] [IsDomain K] {R : Type u_2} {S : Type u_3} [CommRing R] [IsDomain R] [CommSemiring S] [Algebra S (Polynomial K)] [Algebra S (Polynomial R)] (φ : Polynomial K →ₐ[S] Polynomial R) (hφ : nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial R))) : ⇑(RatFunc.mapAlgHom φ hφ) = ⇑(RatFunc.map φ hφ)
• RatFunc.map_apply_ofFractionRing_mk 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [MonoidHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) (n : Polynomial R) (d : ↥(nonZeroDivisors (Polynomial R))) : (RatFunc.map φ hφ) { toFractionRing := Localization.mk n d } = { toFractionRing := Localization.mk (φ n) ⟨φ ↑d, ⋯⟩ }
• RatFunc.map.eq_1 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [MonoidHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) : RatFunc.map φ hφ = { toFun := fun f => f.liftOn (fun n d => if h : φ d ∈ nonZeroDivisors (Polynomial S) then { toFractionRing := Localization.mk (φ n) ⟨φ d, h⟩ } else 0) ⋯, map_one' := ⋯, map_mul' := ⋯ }

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