Theorems · Theorem · commutative algebra
Polynomial.coe_mul
∀ {R : Type u_1} [inst : Semiring R] (φ ψ : Polynomial R), ↑(φ * ψ) = ↑φ * ↑ψ- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Polynomial.coeffproof · cited by 1,045
- PowerSeriesstatement · cited by 797
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- Polynomial.toPowerSeriesstatement and proof · cited by 96
- PowerSeries.extproof · cited by 69
- Polynomial.coeff_mulproof · cited by 29
- PowerSeries.coeff_mulproof · cited by 29
- Polynomial.coeff_coeproof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.coeToPowerSeries.ringHomproof · cited by 5
- PowerSeries.IsWeierstrassDivisionAt.smulproof · cited by 2
- PowerSeries.IsWeierstrassFactorizationAt.mulproof · cited by 2
- Polynomial.hilbertPoly_mul_one_sub_succproof · cited by 1