Theorems · Definition · commutative algebra

HahnSeries.SummableFamily.binomialFamily

{Γ : Type u_1} →
  {R : Type u_2} →
    {A : Type u_3} →
      [inst : LinearOrder Γ] →
        [inst_1 : AddCommMonoid Γ] →
          [IsOrderedCancelAddMonoid Γ] →
            [inst_3 : CommRing R] →
              [BinomialRing R] →
                [inst_5 : CommRing A] → [Algebra R A] → HahnSeries Γ A → R → HahnSeries.SummableFamily Γ A ℕ

A summable family of Hahn series, whose nth term is Ring.choose r n • (x - 1) ^ n when x is close to 1 (more precisely, when 0 < (x - 1).orderTop), and 0 ^ n otherwise. These terms give a formal expansion of x ^ r as (1 + (x - 1)) ^ r.

Defined in

Mathlib.RingTheory.HahnSeries.Binomial

Cited by

8 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderAddCommMonoidIsOrderedCancelAddMonoidCommRingBinomialRingCommRingAlgebra