Theorems · Definition · ring theory

AddMonoidAlgebra.leadingCoeff

{R : Type u_1} →
  {A : Type u_3} →
    {B : Type u_5} →
      [inst : Semiring R] → [inst_1 : LinearOrder B] → [OrderBot B] → (A → B) → [Nonempty A] → AddMonoidAlgebra R A → R

If D is an injection into a linear order B, the leading coefficient of f : R[A] is the nonzero coefficient of highest degree according to D, or 0 if f = 0. In general, it is defined to be the coefficient at an inverse image of supDegree f (if such exists).

Defined in

Mathlib.Algebra.MonoidAlgebra.Degree

Cited by

23 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringLinearOrderOrderBotNonempty