Theorems · Theorem · field theory
Polynomial.nextCoeff_C_mul
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {a : R} [NoZeroDivisors R],
(Polynomial.C a * p).nextCoeff = a * p.nextCoeff- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- NoZeroDivisorsstatement and proof · cited by 545
- mul_iteproof · cited by 159
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Splits.nextCoeff_eq_neg_sum_roots_mul_leadingCoeffproof · cited by 1