Theorems · Theorem · commutative algebra
MvPolynomial.as_sum
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (p : MvPolynomial σ R),
p = ∑ v ∈ p.support, (MvPolynomial.monomial v) (MvPolynomial.coeff v p)- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 83 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffstatement · cited by 315
- MvPolynomial.monomialstatement · cited by 253
- MvPolynomial.supportstatement · cited by 220
- MvPolynomial.support_sum_monomial_coeffproof · cited by 6
Cited by14
Results whose statement or proof uses this declaration.
- MvPolynomial.eval₂Hom_congr'proof · cited by 9
- MvPolynomial.esymmAlgHom_fin_injectiveproof · cited by 2
- MvPolynomial.support_expand_subsetproof · cited by 2
- MvPolynomial.eval₂_C_mk_eq_zeroproof · cited by 2
- MvPolynomial.mem_map_C_iffproof · cited by 2
- MvPolynomial.vars_bind₁proof · cited by 1
- MvPolynomial.eval₂Hom_eq_constantCoeff_of_varsproof · cited by 1
- MvPolynomial.eval₂Hom_eq_zeroproof · cited by 1
- Polynomial.homogenize_eq_of_isHomogeneousproof · cited by 1
- MvPolynomial.coeffsIn_eq_span_monomialproof · cited by 1
- MvPolynomial.aeval_ite_mem_eq_selfproof · cited by 1
- MvPolynomial.map_mvPolynomial_eq_eval₂proof · cited by 0