Theorems · Definition · field theory
Polynomial.trailingDegree
{R : Type u} → [inst : Semiring R] → Polynomial R → ℕ∞trailingDegree p is the multiplicity of x in the polynomial p, i.e. the smallest
X-exponent in p.
trailingDegree p = some n when p ≠ 0 and n is the smallest power of X that appears
in p, otherwise
trailingDegree 0 = ⊤.
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- ENatstatement · cited by 4,985
- Polynomial.supportproof · cited by 237
- Finset.minproof · cited by 36
Cited by40
Results whose statement or proof uses this declaration.
- Polynomial.natTrailingDegreeproof · cited by 87
- Polynomial.trailingDegree_eq_natTrailingDegreestatement · cited by 8
- Polynomial.trailingDegree_monomialstatement · cited by 6
- Polynomial.coeff_eq_zero_of_lt_natTrailingDegreeproof · cited by 5
- Polynomial.trailingDegree_le_of_ne_zerostatement · cited by 5
- Polynomial.le_trailingDegree_monomialstatement and proof · cited by 3
- Polynomial.le_trailingDegree_mulstatement · cited by 2
- Polynomial.natTrailingDegree_le_trailingDegreestatement and proof · cited by 2
- Polynomial.natTrailingDegree_mul'proof · cited by 2
- Polynomial.coeff_eq_zero_of_lt_trailingDegreestatement and proof · cited by 2
- Polynomial.trailingDegree_zerostatement · cited by 2
- Polynomial.natTrailingDegree_eq_of_trailingDegree_eq_somestatement and proof · cited by 2