Theorems · Theorem · field theory
Polynomial.map_eq_zero_iff
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] {f : R →+* S},
Function.Injective ⇑f → (Polynomial.map f p = 0 ↔ p = 0)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.mapRingHomproof · cited by 98
- map_eq_zero_iffproof · cited by 62
- Polynomial.map_injectiveproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.map_ne_zero_iffproof · cited by 12
- Polynomial.map_eq_zeroproof · cited by 4
- Polynomial.aeval_sumIDeriv_of_posproof · cited by 1
- Polynomial.mapMahlerMeasure_pos_of_ne_zeroproof · cited by 0
- WeierstrassCurve.Affine.CoordinateRing.map_injectiveproof · cited by 0