Theorems · Theorem · field theory
Polynomial.monomial_comp
∀ {R : Type u} {a : R} [inst : Semiring R] {p : Polynomial R} (n : ℕ),
((Polynomial.monomial n) a).comp p = Polynomial.C a * p ^ n- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 102 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.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.monomialstatement · cited by 256
- Polynomial.compstatement · cited by 193
- Polynomial.eval₂_monomialproof · cited by 19
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.eval_compproof · cited by 29
- Polynomial.mul_X_compproof · cited by 5
- Polynomial.smeval_compproof · cited by 5
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.derivative_compproof · cited by 2
- Polynomial.eval₂_comp'proof · cited by 2
- Polynomial.taylor_monomialproof · cited by 1
- Polynomial.C_mul_compproof · cited by 1