Theorems · Theorem · field theory
Polynomial.Monic.comp
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p.Monic → q.Monic → q.natDegree ≠ 0 → (p.comp q).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 117 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.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Nontrivialproof · cited by 2,416
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- one_powproof · cited by 521
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.compstatement and proof · cited by 193
- Polynomial.Monic.leadingCoeffproof · cited by 101
- Polynomial.Monic.defproof · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.Monic.comp_X_add_Cproof · cited by 3
- IsIntegral.of_aeval_monicproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- cyclotomic_prime_pow_comp_X_add_one_isEisensteinAtproof · cited by 1