Theorems · Theorem · field theory
Polynomial.degree_mul
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {p q : Polynomial R}, (p * q).degree = p.degree + q.degree- Cited by
- 25 results in Mathlib
- Foundations
- Depth 90 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.
Cites12
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
- Bot.botproof · cited by 4,720
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- mul_ne_zeroproof · cited by 178
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- WithBot.add_botproof · cited by 20
- Polynomial.degree_mul'proof · cited by 13
Cited by26
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_mulproof · cited by 23
- Polynomial.degree_eq_one_of_irreducible_of_rootproof · cited by 7
- Polynomial.associated_content_mulproof · cited by 6
- Polynomial.degree_C_mulproof · cited by 6
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
- Polynomial.degreeMonoidHomproof · cited by 4
- Polynomial.coeff_isUnit_isNilpotent_of_isUnitproof · cited by 2
- Module.End.hasEigenvalue_of_isRootproof · cited by 2
- Polynomial.degree_mul_Cproof · cited by 2
- Polynomial.degree_eq_degree_of_associatedproof · cited by 2
- minpoly.negproof · cited by 2
- Polynomial.degree_le_mul_leftproof · cited by 2