Theorems · Theorem · field theory
Polynomial.comp_C_mul_X_coeff
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {r : R} {n : ℕ},
(p.comp (Polynomial.C r * Polynomial.X)).coeff n = p.coeff n * r ^ n- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 2 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cstatement and proof · cited by 1,598
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.bernoulli_comp_neg_Xproof · cited by 2
- Polynomial.comp_C_mul_X_eq_zero_iffproof · cited by 2