Theorems · Theorem · field theory
Polynomial.coeff_comp_degree_mul_degree
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R},
q.natDegree ≠ 0 → (p.comp q).coeff (p.natDegree * q.natDegree) = p.leadingCoeff * q.leadingCoeff ^ p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 115 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.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Polynomial.coeffstatement and proof · cited by 1,045
- LE.le.trans_ltproof · cited by 795
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.Monic.compproof · cited by 4
- Polynomial.natDegree_comp_eq_of_mul_ne_zeroproof · cited by 4
- Polynomial.leadingCoeff_compproof · cited by 4
- Polynomial.comp_neg_X_leadingCoeff_eqproof · cited by 4
- IsAlgebraic.of_smul_isIntegralproof · cited by 2
- Polynomial.IsMonicOfDegree.compproof · cited by 1
- IsAlgebraic.of_aevalproof · cited by 1