Theorems · Theorem · commutative algebra
MvPolynomial.prod_X_pow
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (x : σ → ℕ) (t : Finset σ),
∏ y ∈ t, MvPolynomial.X y ^ x y = (MvPolynomial.monomial (Finsupp.indicator t fun i x_1 => x i)) 1- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 1 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.
Cites28
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
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- Finset.prodstatement and proof · cited by 2,356
- MvPolynomialstatement and proof · cited by 2,140
- pow_zeroproof · cited by 1,094
- Finset.filterproof · cited by 949
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_prod_X_powproof · cited by 0