Theorems · Theorem · field theory
Polynomial.monic_prod_of_monic
∀ {R : Type u} {ι : Type y} [inst : CommSemiring R] (s : Finset ι) (f : ι → Polynomial R),
(∀ i ∈ s, (f i).Monic) → (∏ i ∈ s, f i).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 111 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.
Cites7
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
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Finset.prodstatement · cited by 2,356
- Polynomial.Monicstatement and proof · cited by 461
- Finset.valproof · cited by 438
- Polynomial.monic_multiset_prod_of_monicproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.charpoly_monicproof · cited by 9
- Polynomial.cyclotomic'.monicproof · cited by 3
- Polynomial.int_coeff_of_cyclotomic'proof · cited by 3
- Polynomial.cyclotomic_eq_X_pow_sub_one_divproof · cited by 2
- Polynomial.eq_cyclotomic_iffproof · cited by 2
- MulSemiringAction.monic_charpolyproof · cited by 2
- Lagrange.nodal_monicproof · cited by 1
- Polynomial.monic_prod_X_sub_Cproof · cited by 1
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- Polynomial.cyclotomic'_eq_X_pow_sub_one_divproof · cited by 1
- prodXSubSMul.monicproof · cited by 1
- Polynomial.monic_finprod_of_monicproof · cited by 1