Theorems · Theorem · field theory
Polynomial.coeff_smul
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : SMulZeroClass S R] (r : S) (p : Polynomial R) (n : ℕ),
(r • p).coeff n = r • p.coeff n- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringSMulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Polynomial.coeffstatement and proof · cited by 1,045
- SMulZeroClassstatement and proof · cited by 213
Cited by31
Results whose statement or proof uses this declaration.
- Polynomial.C_mul'proof · cited by 12
- Polynomial.smul_eq_C_mulproof · cited by 9
- Polynomial.degree_smul_leproof · cited by 5
- Polynomial.eval₂_smulproof · cited by 5
- Polynomial.mem_nonzeroDivisors_of_coeff_memproof · cited by 4
- Polynomial.leadingCoeff_smul_of_smul_regularproof · cited by 3
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- Polynomial.natDegree_smulproof · cited by 2
- Polynomial.degree_smul_of_isRightRegular_leadingCoeffproof · cited by 2
- Polynomial.coeff_preHilbertPoly_selfproof · cited by 2
- Polynomial.degree_smul_of_smul_regularproof · cited by 2
- Polynomial.bernoulli_comp_neg_Xproof · cited by 2