Theorems · Theorem · field theory
Polynomial.coeff_mul_X_pow
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R) (n d : ℕ), (p * Polynomial.X ^ n).coeff (d + n) = p.coeff d- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 106 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.
Cites10
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
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.coeffstatement and proof · cited by 1,045
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- Finset.sum_eq_singleproof · cited by 98
- Polynomial.coeff_X_powproof · cited by 50
- Polynomial.coeff_mulproof · cited by 29
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mul_Xproof · cited by 22
- Polynomial.coeff_mul_X_pow'proof · cited by 5
- Polynomial.coeff_X_pow_mulproof · cited by 3
- Polynomial.coeff_mul_monomialproof · cited by 2
- Polynomial.natDegree_cancelLeads_lt_of_natDegree_le_natDegree_of_commproof · cited by 1
- Polynomial.mul_X_pow_eq_zeroproof · cited by 1
- Polynomial.natTrailingDegree_mul_X_powproof · cited by 1
- Ideal.mem_leadingCoeffNthproof · cited by 1
- Polynomial.coeff_monomial_mulproof · cited by 1