Theorems · Theorem · field theory
Polynomial.signVariations_neg
∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsOrderedRing R] (P : Polynomial R),
(-P).signVariations = P.signVariationsThe number of sign changes does not change if we negate.
- Defined in
- Mathlib.Algebra.Polynomial.RuleOfSigns
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingLinearOrderIsOrderedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- IsOrderedRingstatement and proof · cited by 777
- SignTypeproof · cited by 318
- SignType.signproof · cited by 128
- List.destutterproof · cited by 25
- Polynomial.coeffListproof · cited by 22
- Polynomial.signVariationsstatement and proof · cited by 13
- List.destutter.congr_simpproof · cited by 6
- List.comp_mapproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.succ_signVariations_le_X_sub_C_mulproof · cited by 1
- Polynomial.signVariations_C_mulproof · cited by 0