Theorems · Theorem · commutative algebra
Polynomial.scaleRoots_zero
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R), p.scaleRoots 0 = p.leadingCoeff • Polynomial.X ^ p.natDegree- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 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.
Cites18
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
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Eq.geproof · cited by 375
- lt_of_le_of_neproof · cited by 230
- mul_iteproof · cited by 159
- Polynomial.extproof · cited by 118
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1