Theorems · Theorem · field theory
Polynomial.map_zero
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S), Polynomial.map f 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 102 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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- RingHom.compproof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.eval₂_zeroproof · cited by 14
Cited by34
Results whose statement or proof uses this declaration.
- Polynomial.mapRingHomproof · cited by 98
- Polynomial.map_dvd_map'proof · cited by 14
- Polynomial.map_dvd_mapproof · cited by 5
- IsAlgebraic.of_ringHom_of_comp_eqproof · cited by 4
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.gcd_mapproof · cited by 2
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2
- IntermediateField.AdjoinSimple.norm_gen_eq_prod_rootsproof · cited by 2
- Polynomial.natDegree_map_ltproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1
- splits_X_pow_sub_one_of_X_pow_sub_Cproof · cited by 1
- Polynomial.eq_rootMultiplicity_mapproof · cited by 1