Theorems · Theorem · commutative algebra
MvPolynomial.coeff_sum_X_pow_of_fintype
∀ {R : Type u_1} {σ : Type u_2} [inst : CommSemiring R] [inst_1 : Fintype σ] (d : σ →₀ ℕ) (n : ℕ),
MvPolynomial.coeff d ((∑ i, MvPolynomial.X i) ^ n) = ↑(if (d.sum fun x m => m) = n then d.multinomial else 0)- Defined in
- Mathlib.Algebra.MvPolynomial.Coeff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintype
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.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement · cited by 2,140
- Nat.cast_zeroproof · cited by 1,870
- one_smulproof · cited by 1,374
- MvPolynomial.Xstatement and proof · cited by 552
- one_powproof · cited by 521
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_add_powproof · cited by 1