Theorems · Theorem · commutative algebra
MvPolynomial.support_sum_monomial_coeff
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (p : MvPolynomial σ R),
∑ v ∈ p.support, (MvPolynomial.monomial v) (MvPolynomial.coeff v p) = p- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 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.
Cites14
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
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- AddMonoidAlgebra.coeffproof · cited by 365
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.monomialstatement and proof · cited by 253
- MvPolynomial.supportstatement and proof · cited by 220
- AddMonoidAlgebra.extproof · cited by 90
Cited by6
Results whose statement or proof uses this declaration.
- MvPolynomial.as_sumproof · cited by 14
- Algebra.Generators.map_toComp_kerproof · cited by 3
- Algebra.Generators.ofComp_kerCompPreimageproof · cited by 2
- MvPolynomial.IsHomogeneous.rename_isHomogeneousproof · cited by 2
- MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_leproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1