Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_eq_zero_iff_eq_C
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p : MvPolynomial σ R},
p.totalDegree = 0 ↔ p = MvPolynomial.C (MvPolynomial.coeff 0 p)- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 85 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.
Cites17
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.supportproof · cited by 828
- MvPolynomial.Cstatement and proof · cited by 400
- MvPolynomial.coeffstatement and proof · cited by 315
- Finsupp.mem_support_iffproof · cited by 89
- MvPolynomial.totalDegreestatement and proof · cited by 76
- MvPolynomial.extproof · cited by 61
Cited by9
Results whose statement or proof uses this declaration.
- MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_leproof · cited by 1
- MvPolynomial.dvd_C_iff_existsproof · cited by 1
- MvPolynomial.homogeneousSubmodule_zeroproof · cited by 1
- MvPolynomial.irreducible_of_forall_totalDegree_leproof · cited by 1
- MvPolynomial.irreducible_of_totalDegree_eq_oneproof · cited by 1
- MvPolynomial.vars_eq_empty_iff_eq_Cproof · cited by 0
- MvPolynomial.IsHomogeneous.pderivproof · cited by 0
- MvPolynomial.isUnit_iff_eq_C_of_isReducedproof · cited by 0
- MvPolynomial.degreesLE_zeroproof · cited by 0