Loogle!

Result

Found 12 declarations mentioning Polynomial and Subsingleton.

• Polynomial.unique 📋 Mathlib.Algebra.Polynomial.Basic
  {R : Type u} [Semiring R] [Subsingleton R] : Unique (Polynomial R)
• Polynomial.subsingleton_iff_subsingleton 📋 Mathlib.Algebra.Polynomial.Basic
  {R : Type u} [Semiring R] : Subsingleton (Polynomial R) ↔ Subsingleton R
• Polynomial.monic_of_subsingleton 📋 Mathlib.Algebra.Polynomial.Degree.Operations
  {R : Type u} [Semiring R] [Subsingleton R] (p : Polynomial R) : p.Monic
• Polynomial.natDegree_of_subsingleton 📋 Mathlib.Algebra.Polynomial.Degree.Operations
  {R : Type u} [Semiring R] {p : Polynomial R} [Subsingleton R] : p.natDegree = 0
• Polynomial.degree_of_subsingleton 📋 Mathlib.Algebra.Polynomial.Degree.Operations
  {R : Type u} [Semiring R] {p : Polynomial R} [Subsingleton R] : p.degree = ⊥
• Polynomial.monic_zero_iff_subsingleton 📋 Mathlib.Algebra.Polynomial.Monic
  {R : Type u} [Semiring R] : Polynomial.Monic 0 ↔ Subsingleton R
• minpoly.subsingleton 📋 Mathlib.FieldTheory.Minpoly.Basic
  (A : Type u_1) {B : Type u_2} [CommRing A] [Ring B] [Algebra A B] (x : B) [Subsingleton B] : minpoly A x = 1
• Polynomial.separable_of_subsingleton 📋 Mathlib.FieldTheory.Separable
  {R : Type u} [CommSemiring R] [Subsingleton R] (f : Polynomial R) : f.Separable
• AdjoinRoot.algHom_subsingleton 📋 Mathlib.RingTheory.AdjoinRoot
  {R : Type u} [CommRing R] {S : Type u_1} [CommRing S] [Algebra R S] {r : R} : Subsingleton (AdjoinRoot (Polynomial.C r * Polynomial.X - 1) →ₐ[R] S)
• WeierstrassCurve.Affine.CoordinateRing.basis.eq_1 📋 Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
  {R : Type r} [CommRing R] (W' : WeierstrassCurve.Affine R) : WeierstrassCurve.Affine.CoordinateRing.basis W' = ⋯.by_cases (fun x => default) fun x => (AdjoinRoot.powerBasis' ⋯).basis.reindex (finCongr ⋯)
• IsTranscendenceBasis.polynomial 📋 Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis
  (ι : Type u) (R : Type u_1) [CommRing R] [Nonempty ι] [Subsingleton ι] : IsTranscendenceBasis R fun x => Polynomial.X
• IsAdjoinRoot.subsingleton 📋 Mathlib.RingTheory.IsAdjoinRoot
  {R : Type u} {S : Type v} [CommRing R] [Ring S] {f : Polynomial R} [Algebra R S] (h : IsAdjoinRoot S f) [Subsingleton R] : Subsingleton S

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 f167e8d