Theorems · Theorem · field theory
Polynomial.expand_X
∀ {R : Type u} [inst : CommSemiring R] (p : ℕ), (Polynomial.expand R p) Polynomial.X = Polynomial.X ^ p- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.expandstatement · cited by 90
- Polynomial.eval₂_Xproof · cited by 34
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.expand_oneproof · cited by 10
- Polynomial.expand_aevalproof · cited by 4
- Polynomial.natSepDegree_X_pow_char_pow_sub_Cproof · cited by 3
- minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_Cproof · cited by 3
- Polynomial.expand_expandproof · cited by 3
- Polynomial.roots_X_pow_char_pow_sub_Cproof · cited by 2
- Polynomial.rootMultiplicity_expand_powproof · cited by 2
- Polynomial.expand_evalproof · cited by 2
- matPolyEquiv_eq_X_pow_sub_Cproof · cited by 1
- Irreducible.natSepDegree_eq_one_iff_of_monicproof · cited by 1
- Polynomial.expand_monomialproof · cited by 1
- Polynomial.cyclotomic_sixproof · cited by 0