Theorems · Theorem · field theory
Polynomial.natDegree_X_pow
∀ {R : Type u} [inst : Semiring R] [Nontrivial R] (n : ℕ), (Polynomial.X ^ n).natDegree = n- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 104 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
- Polynomialstatement · cited by 5,681
- 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_X_powproof · cited by 15
Cited by12
Results whose statement or proof uses this declaration.
- FiniteField.X_pow_card_sub_X_natDegree_eqproof · cited by 4
- IsIntegral.coeffproof · cited by 4
- Polynomial.mirror_natDegreeproof · cited by 4
- Polynomial.natDegree_mul_X_powproof · cited by 3
- Polynomial.natDegree_X_pow_add_Cproof · cited by 3
- spectralValue_X_powproof · cited by 2
- Polynomial.natDegree_X_pow_leproof · cited by 2
- IsPurelyInseparable.finrank_eq_powproof · cited by 2
- Polynomial.det_taylorLinearEquiv_toLinearMapproof · cited by 1
- solvableByRad_le_algClosureproof · cited by 1
- Matrix.isNilpotent_charpoly_sub_pow_of_isNilpotentproof · cited by 1
- LindemannWeierstrass.exp_polynomial_approxproof · cited by 0