Theorems · Theorem · field theory
Polynomial.rootSet_C
∀ {S : Type v} {T : Type w} [inst : CommRing T] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra T S]
(a : T), (Polynomial.C a).rootSet S = ∅- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Polynomialstatement · cited by 5,681
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.toFinsetproof · cited by 230
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.rootSet_zeroproof · cited by 4
- Polynomial.isSplittingField_Cproof · cited by 0
- Polynomial.rootSet_oneproof · cited by 0