Theorems · Theorem · commutative algebra
MvPolynomial.coeffs_mul_X
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (p : MvPolynomial σ R) (n : σ),
(p * MvPolynomial.X n).coeffs = p.coeffs- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.singleproof · cited by 943
- Finset.extproof · cited by 565
- MvPolynomial.Xstatement and proof · cited by 552
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.coeffsstatement · cited by 24
- addRightEmbedding_applyproof · cited by 13
- MvPolynomial.support_mul_Xproof · cited by 3
- MvPolynomial.coeff_mul_Xproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.mem_range_map_iff_coeffs_subsetproof · cited by 5
- MvPolynomial.coeffs_mapproof · cited by 1