Theorems · Theorem · field theory
Polynomial.map_sub
∀ {R : Type u} [inst : Ring R] {p q : Polynomial R} {S : Type u_1} [inst_1 : Ring S] (f : R →+* S),
Polynomial.map f (p - q) = Polynomial.map f p - Polynomial.map f q- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.mapRingHomproof · cited by 98
- RingHom.map_subproof · cited by 15
Cited by49
Results whose statement or proof uses this declaration.
- descPochhammer_succ_rightproof · cited by 14
- Polynomial.prod_cyclotomic_eq_X_pow_sub_oneproof · cited by 11
- Polynomial.cyclotomic_oneproof · cited by 7
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- WeierstrassCurve.Affine.map_polynomialproof · cited by 4
- WeierstrassCurve.map_preΨ₄proof · cited by 4
- descPochhammer_mapproof · cited by 3
- Polynomial.int_coeff_of_cyclotomic'proof · cited by 3
- Polynomial.count_map_rootsproof · cited by 2
- WeierstrassCurve.Affine.map_polynomialXproof · cited by 2
- X_pow_sub_C_eq_prodproof · cited by 2
- minpoly_add_algebraMap_splitsproof · cited by 2