Theorems · Theorem · field theory
Polynomial.leadingCoeff_mul
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] (p q : Polynomial R),
(p * q).leadingCoeff = p.leadingCoeff * q.leadingCoeff- Cited by
- 32 results in Mathlib
- Foundations
- Depth 92 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.
Cites9
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NoZeroDivisorsstatement and proof · cited by 545
- Polynomial.leadingCoeffstatement and proof · cited by 498
- mul_ne_zeroproof · cited by 178
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.leadingCoeff_mul'proof · cited by 11
Cited by33
Results whose statement or proof uses this declaration.
- Polynomial.monic_mul_leadingCoeff_invproof · cited by 19
- minpoly.eq_of_irreducibleproof · cited by 8
- Polynomial.leadingCoeffHomproof · cited by 6
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.irreducible_of_monicproof · cited by 3
- monic_ascPochhammerproof · cited by 2
- Polynomial.isIntegral_of_mahlerMeasure_eq_oneproof · cited by 2
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2
- LocalSubring.exists_valuationRing_of_isMaxproof · cited by 2
- Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeffproof · cited by 1
- monic_descPochhammerproof · cited by 1
- Polynomial.eq_of_dvd_of_natDegree_le_of_leadingCoeffproof · cited by 1