Theorems · Theorem · commutative algebra
MonomialOrder.coeff_prod_sum_degree
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {ι : Type u_3} (P : ι → MvPolynomial σ R)
(s : Finset ι), MvPolynomial.coeff (∑ i ∈ s, m.degree (P i)) (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidproof · cited by 2,264
- MvPolynomialstatement and proof · cited by 2,140
- le_of_eqproof · cited by 366
- MvPolynomial.coeffstatement and proof · cited by 315
- MonomialOrderstatement and proof · cited by 199
- Finset.sum_insertproof · cited by 196
Cited by5
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_prod_of_regularproof · cited by 1
- MonomialOrder.leadingCoeff_prod_of_regularproof · cited by 1
- MonomialOrder.degree_prod_of_mem_nonZeroDivisorsproof · cited by 1
- MonomialOrder.leadingCoeff_prod_of_mem_nonZeroDivisorsproof · cited by 0
- MonomialOrder.degree_prodproof · cited by 0