Theorems · Theorem · field theory
Polynomial.map_id
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, Polynomial.map (RingHom.id R) p = p- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement · cited by 806
- Polynomial.coeff_mapproof · cited by 114
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.map_cyclotomic_intproof · cited by 21
- AdjoinRoot.aeval_eqproof · cited by 10
- FiniteField.expand_cardproof · cited by 2
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- Polynomial.mapRingHom_idproof · cited by 1
- Polynomial.pow_eq_one_of_mahlerMeasure_eq_oneproof · cited by 1
- polynomial_expand_eqproof · cited by 1
- Polynomial.eval_sumIDeriv_of_posproof · cited by 1
- Polynomial.map_iterateFrobenius_expandproof · cited by 1
- Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splitsproof · cited by 0
- gal_X_pow_sub_C_isSolvableproof · cited by 0
- Polynomial.mem_roots_iff_aeval_eq_zeroproof · cited by 0