Theorems · Theorem · field theory
Polynomial.natDegree_X
∀ {R : Type u} [inst : Semiring R] [Nontrivial R], Polynomial.X.natDegree = 1- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 101 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.
Cites6
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
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.natDegree_eq_of_degree_eq_someproof · cited by 42
- Polynomial.degree_Xproof · cited by 9
Cited by43
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_X_sub_Cproof · cited by 22
- Polynomial.degree_comp_neg_Xproof · cited by 7
- Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardproof · cited by 6
- natDegree_minpolyDiv_succproof · cited by 4
- Polynomial.comp_neg_X_leadingCoeff_eqproof · cited by 4
- Polynomial.resultant_X_sub_C_leftproof · cited by 3
- Polynomial.natDegree_mul_Xproof · cited by 3
- FiniteField.orderOf_frobeniusAlgHomproof · cited by 3
- Polynomial.natDegree_preHilbertPolyproof · cited by 3
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- Polynomial.reverse_mul_Xproof · cited by 3
- IsPurelyInseparable.elemExponent_le_of_pow_memproof · cited by 3