Theorems · Theorem · field theory
Polynomial.coeff_mul_degree_add_degree
∀ {R : Type u} [inst : Semiring R] (p q : Polynomial R),
(p * q).coeff (p.natDegree + q.natDegree) = p.leadingCoeff * q.leadingCoeff- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 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.
Cites17
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
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.leadingCoeffstatement · cited by 498
- lt_of_le_of_ltproof · cited by 432
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- ne_of_ltproof · cited by 203
- Finset.sum_eq_singleproof · cited by 98
- WithBot.coe_lt_coeproof · cited by 55
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.degree_mul'proof · cited by 13
- Polynomial.leadingCoeff_mul'proof · cited by 11
- Polynomial.resultant_mul_rightproof · cited by 3
- Polynomial.coeff_pow_mul_natDegreeproof · cited by 1
- Polynomial.natDegree_add_coeff_mulproof · cited by 0