Theorems · Theorem · field theory
Polynomial.degree_neg
∀ {R : Type u} [inst : Ring R] (p : Polynomial R), (-p).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Polynomial.supportproof · cited by 237
- Finset.maxproof · cited by 50
- Polynomial.support_negproof · cited by 2
Cited by21
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_negproof · cited by 26
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- Polynomial.degree_sub_eq_left_of_degree_ltproof · cited by 10
- Polynomial.degree_sub_lt_leftproof · cited by 9
- Matrix.charpoly_monicproof · cited by 9
- Polynomial.degree_sub_leproof · cited by 8
- Polynomial.Monic.sub_of_leftproof · cited by 5
- Polynomial.leadingCoeff_sub_of_degree_ltproof · cited by 3
- Polynomial.degree_sub_eq_right_of_degree_ltproof · cited by 3
- Polynomial.Chebyshev.degree_U_of_ne_neg_oneproof · cited by 2
- minpoly.negproof · cited by 2
- FiniteField.exists_root_sum_quadraticproof · cited by 1