Theorems · Theorem · field theory
Polynomial.signVariations_eraseLead_le
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] (P : Polynomial R),
P.eraseLead.signVariations ≤ P.signVariationsWe can only lose, not gain, sign changes if we drop the leading coefficient.
- Defined in
- Mathlib.Algebra.Polynomial.RuleOfSigns
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearOrderstatement and proof · cited by 8,572
- Polynomialstatement and proof · cited by 5,681
- Polynomial.eraseLeadstatement and proof · cited by 65
- Polynomial.signVariationsstatement and proof · cited by 13
- Polynomial.eraseLead_zeroproof · cited by 7
- Polynomial.signVariations_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.succ_signVariations_le_X_sub_C_mulproof · cited by 1