Theorems · Theorem · commutative algebra
MvPolynomial.coeff_mul
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : DecidableEq σ] (p q : MvPolynomial σ R) (n : σ →₀ ℕ),
MvPolynomial.coeff n (p * q) =
∑ x ∈ Finset.HasAntidiagonal.antidiagonal n, MvPolynomial.coeff x.1 p * MvPolynomial.coeff x.2 q- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffstatement · cited by 315
- Finset.HasAntidiagonal.antidiagonalstatement and proof · cited by 218
- Finset.HasAntidiagonal.mem_antidiagonalproof · cited by 51
- AddMonoidAlgebra.coeff_mul_antidiagproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mul_leproof · cited by 10
- MvPowerSeries.coeff_truncFinset_mul_truncFinset_eq_coeff_mul₂proof · cited by 3
- MonomialOrder.coeff_mul_of_add_of_degree_leproof · cited by 3
- MvPolynomial.mem_map_C_iffproof · cited by 2
- MvPolynomial.weightedHomogeneousSubmodule_mulproof · cited by 2
- MvPowerSeries.coeff_truncTotal_powproof · cited by 2
- MvPolynomial.X_dvd_mul_iffproof · cited by 1
- MvPolynomial.coe_mulproof · cited by 1
- MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzeroproof · cited by 0
- MvPolynomial.coeffsIn_mulproof · cited by 0