Theorems · Theorem · commutative algebra
Polynomial.integralNormalization_mul_C_leadingCoeff
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R),
p.integralNormalization * Polynomial.C p.leadingCoeff = p.scaleRoots p.leadingCoeff- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 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.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- pow_zeroproof · cited by 1,094
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_smul_integralNormalizationproof · cited by 0
- Polynomial.resultant_integralNormalizationproof · cited by 0