Theorems · Theorem · field theory
Polynomial.natDegree_mul_mirror
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R) [NoZeroDivisors R], (p * p.mirror).natDegree = 2 * p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Mirror
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.natDegreestatement and proof · cited by 1,105
- NoZeroDivisorsstatement and proof · cited by 545
- two_mulproof · cited by 232
- Polynomial.mirrorstatement and proof · cited by 32
- Polynomial.natDegree_zeroproof · cited by 24
- Polynomial.natDegree_mulproof · cited by 23
- Polynomial.mirror_natDegreeproof · cited by 4
- Polynomial.mirror_eq_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.IsUnitTrinomial.irreducible_of_coprimeproof · cited by 2
- Polynomial.isUnitTrinomial_iff'proof · cited by 1