Theorems · Theorem · field theory
Polynomial.C_mul_X_pow_eq_monomial
∀ {R : Type u} {a : R} [inst : Semiring R] {n : ℕ}, Polynomial.C a * Polynomial.X ^ n = (Polynomial.monomial n) a- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 53 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.
Cites9
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 · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.monomialstatement · cited by 256
Cited by53
Results whose statement or proof uses this declaration.
- Polynomial.induction_on'proof · cited by 50
- Polynomial.map_monomialproof · cited by 18
- Polynomial.natDegree_monomialproof · cited by 11
- Polynomial.coeff_expandproof · cited by 11
- Polynomial.coeff_C_mul_X_powproof · cited by 10
- Polynomial.derivative_monomialproof · cited by 8
- Polynomial.comp_Xproof · cited by 8
- Polynomial.degree_C_mul_X_pow_leproof · cited by 8
- Polynomial.degree_C_mul_X_powproof · cited by 7
- Polynomial.sum_C_mul_X_pow_eqproof · cited by 6
- Polynomial.support_C_mul_X_pow_subsetproof · cited by 5
- Polynomial.eraseLead_add_C_mul_X_powproof · cited by 5