Theorems · Definition · field theory
Polynomial.supNorm
{A : Type u_1} → [inst : SeminormedRing A] → Polynomial A → ℝThe sup norm of a polynomial on a semi-normed ring, defined as the maximum of its coefficients.
Often called the _(naive) height_ of the polynomial.
This is defined in terms of Polynomial.gaussNorm.
- Defined in
- Mathlib.Analysis.Polynomial.Norm
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 107 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.
Cites5
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
- SeminormedRingstatement and proof · cited by 446
- Polynomial.gaussNormproof · cited by 20
- SeminormedRing.toRingSeminormproof · cited by 10
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.exists_eq_supNormstatement · cited by 2
- Polynomial.le_supNormstatement · cited by 2
- Polynomial.supNorm_monomialstatement and proof · cited by 1
- Polynomial.supNorm_nonnegstatement · cited by 1
- Polynomial.supNorm_zerostatement · cited by 1
- Polynomial.isGreatest_supNormstatement and proof · cited by 1
- Polynomial.supNorm_Cstatement · cited by 0
- Polynomial.supNorm_Xstatement and proof · cited by 0
- Polynomial.supNorm_def'statement and proof · cited by 0
- Polynomial.supNorm_eq_iSupstatement · cited by 0
- Polynomial.supNorm_eq_zero_iffstatement · cited by 0
- Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasurestatement and proof · cited by 0