Theorems · Theorem · field theory
Polynomial.Monic.comp_X_add_C
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R},
p.Monic → ∀ (r : R), (p.comp (Polynomial.X + Polynomial.C r)).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 118 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.
Cites14
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 · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Nontrivialproof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- one_ne_zeroproof · cited by 885
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.compstatement and proof · cited by 193
- Polynomial.monic_X_add_Cproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- minpoly.add_algebraMapproof · cited by 4
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1
- Polynomial.Monic.comp_X_sub_Cproof · cited by 1