Theorems · Theorem · field theory
Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegree
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R},
p.Monic → (p = Polynomial.X ^ p.natDegree ↔ p.natDegree ≤ p.natTrailingDegree)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 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.
Cites20
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
- Nontrivialproof · cited by 2,416
- le_reflproof · cited by 2,061
- Polynomial.Xstatement and proof · cited by 1,639
- LT.lt.ne'proof · cited by 1,417
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- LT.lt.neproof · cited by 872
- LT.lt.trans_leproof · cited by 678
- Polynomial.Monicstatement and proof · cited by 461
- lt_trichotomyproof · cited by 178
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegreeproof · cited by 1
- spectralValue_eq_zero_iffproof · cited by 1