Theorems · Theorem · field theory
Polynomial.coeff_mul_mirror
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R),
(p * p.mirror).coeff (p.natDegree + p.natTrailingDegree) = p.sum fun x x_1 => x_1 ^ 2- Defined in
- Mathlib.Algebra.Polynomial.Mirror
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- LE.le.transproof · cited by 3,151
- Finset.sum_congrproof · cited by 2,323
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- zero_powproof · cited by 361
- sqproof · cited by 280
- two_ne_zeroproof · cited by 251
- Polynomial.supportproof · cited by 237
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isUnitTrinomial_iff'proof · cited by 1