Theorems · Theorem · field theory
Polynomial.degree_X
∀ {R : Type u} [inst : Semiring R] [Nontrivial R], Polynomial.X.degree = 1- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement · cited by 1,639
- WithBotstatement · cited by 1,498
- one_ne_zeroproof · cited by 885
- Polynomial.degreestatement · cited by 643
- Polynomial.degree_monomialproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_Xproof · cited by 43
- Polynomial.Chebyshev.degree_Tproof · cited by 7
- Polynomial.degree_mul_Xproof · cited by 4
- FiniteField.X_pow_card_sub_X_natDegree_eqproof · cited by 4
- Polynomial.degree_lt_degree_mul_Xproof · cited by 3
- Polynomial.degree_X_add_Cproof · cited by 2
- Polynomial.degree_divX_ltproof · cited by 1
- WittVector.RecursionMain.succNthDefiningPoly_degreeproof · cited by 1
- Lagrange.nodal_subgroup_eq_X_pow_card_sub_oneproof · cited by 0