Theorems · Definition · field theory
Polynomial.reverse
{R : Type u_1} → [inst : Semiring R] → Polynomial R → Polynomial RThe reverse of a polynomial f is the polynomial obtained by "reading f backwards".
Even though this is not the actual definition, reverse f = f (1/X) * X ^ f.natDegree.
- Defined in
- Mathlib.Algebra.Polynomial.Reverse
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.reflectproof · cited by 31
Cited by39
Results whose statement or proof uses this declaration.
- Polynomial.mirrorproof · cited by 32
- Polynomial.coeff_reversestatement · cited by 7
- Polynomial.reverse_leadingCoeffstatement and proof · cited by 5
- Polynomial.mirror_natDegreeproof · cited by 4
- Polynomial.coeff_zero_reversestatement · cited by 4
- Polynomial.coeff_mirrorproof · cited by 4
- Polynomial.trinomial_mirrorproof · cited by 4
- Polynomial.eval₂_reverse_eq_zero_iffstatement · cited by 3
- Polynomial.Monic.nextCoeff_mulproof · cited by 3
- Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_topproof · cited by 3
- Polynomial.reverse_eq_zerostatement · cited by 3
- Polynomial.reverse_mul_Xstatement and proof · cited by 3