Theorems · Theorem · ring theory
SkewPolynomial.mul_def
∀ {R : Type u_1} [inst : Semiring R] {f g : SkewPolynomial R} [inst_1 : MulSemiringAction (Multiplicative ℕ) R],
f * g = f.sum fun a₁ b₁ => g.sum fun a₂ b₂ => (SkewPolynomial.monomial (a₁ + a₂)) (b₁ * (⇑SkewPolynomial.φ)^[a₁] b₂)- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulSemiringAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Multiplicativestatement and proof · cited by 875
- Nat.iteratestatement · cited by 740
- Finsupp.sumproof · cited by 481
- MulSemiringActionstatement and proof · cited by 423
- Multiplicative.ofAddproof · cited by 237
- SkewPolynomialstatement and proof · cited by 124
- SkewMonoidAlgebra.coeffproof · cited by 110
Cited by1
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_mulproof · cited by 2