Theorems · Theorem · field theory
RatFunc.algebraMap_monomial
∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] (n : ℕ) (a : K),
(algebraMap (Polynomial K) (RatFunc K)) ((Polynomial.monomial n) a) = RatFunc.C a * RatFunc.X ^ n- Defined in
- Mathlib.FieldTheory.RatFunc.AsPolynomial
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- map_powproof · cited by 503
Cited by4
Results whose statement or proof uses this declaration.
- RatFunc.aeval_X_left_eq_algebraMapproof · cited by 2
- Polynomial.valuation_le_one_of_valuation_X_le_oneproof · cited by 2
- Polynomial.valuation_monomial_eq_valuation_X_powproof · cited by 0
- Polynomial.valuation_inv_monomial_eq_valuation_X_zpowproof · cited by 0