Theorems · Definition · commutative algebra
spectralValueTerms
{R : Type u_1} → [inst : SeminormedRing R] → Polynomial R → ℕ → ℝThe function ℕ → ℝ sending n to ‖ p.coeff n ‖^(1/(p.natDegree - n : ℝ)), if
n < p.natDegree, or to 0 otherwise.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRing
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.
- Realstatement · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- Norm.normproof · cited by 5,413
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- SeminormedRingstatement and proof · cited by 446
Cited by9
Results whose statement or proof uses this declaration.
- spectralValueproof · cited by 13
- spectralValueTerms_bddAbovestatement · cited by 3
- spectralValueTerms_nonnegstatement · cited by 3
- spectralValueTerms_of_lt_natDegreestatement · cited by 3
- norm_root_le_spectralValueproof · cited by 3
- spectralValueTerms_finite_rangestatement and proof · cited by 2
- spectralValue_eq_zero_iffproof · cited by 1
- spectralValueTerms_of_natDegree_lestatement · cited by 0
- spectralValue_le_one_iffproof · cited by 0