Theorems · Theorem · commutative algebra
MvPolynomial.coeff_X
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : DecidableEq σ] (i : σ) (m : σ →₀ ℕ),
MvPolynomial.coeff m (MvPolynomial.X i) = if (fun₀ | i => 1) = m then 1 else 0- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 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
- MvPolynomialproof · cited by 2,140
- Finsupp.singlestatement · cited by 943
- pow_oneproof · cited by 894
- MvPolynomial.Xstatement and proof · cited by 552
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.coeff_X_powproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_X_sameproof · cited by 1
- TensorProduct.toIntegralClosure_mvPolynomial_bijectiveproof · cited by 1
- MvPolynomial.coeff_sumSMulXproof · cited by 1
- MvPolynomial.coeff_X'proof · cited by 0