Theorems · Theorem · field theory
Polynomial.degree_zero
∀ {R : Type u} [inst : Semiring R], Polynomial.degree 0 = ⊥- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 83 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.
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 · cited by 5,681
- Bot.botstatement · cited by 4,720
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.degree_of_subsingletonproof · cited by 8
- Lagrange.degree_interpolate_ltproof · cited by 4
- Polynomial.degree_monomial_leproof · cited by 4
- minpoly.mem_range_of_degree_eq_oneproof · cited by 3
- Polynomial.degree_le_degreeproof · cited by 3
- PowerSeries.isWeierstrassDivisionAt_zeroproof · cited by 2
- Polynomial.eq_cyclotomic_iffproof · cited by 2
- Polynomial.div_tendsto_atTop_zero_iff_degree_ltproof · cited by 2
- Polynomial.exists_approx_polynomial_auxproof · cited by 1
- Polynomial.degree_map_ltproof · cited by 1
- Polynomial.exists_degree_le_of_mem_spanproof · cited by 1
- Polynomial.eq_of_degree_le_of_eval_index_eqproof · cited by 1