Theorems · Definition · field theory
RatFunc.coePolynomial
{K : Type u} → [inst : CommRing K] → [IsDomain K] → Polynomial K → RatFunc KThe coercion from polynomials to rational functions, implemented as the algebra map from a domain to its field of fractions
- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- RatFuncstatement and proof · cited by 301
Cited by19
Results whose statement or proof uses this declaration.
- RatFunc.uniformizingPolynomialproof · cited by 7
- RatFunc.setOfPred_polynomial_valuation_lt_one_and_ne_zero_nonemptystatement and proof · cited by 4
- RatFunc.uniformizingPolynomial_ne_zeroproof · cited by 2
- Polynomial.valuation_le_one_of_valuation_X_le_onestatement and proof · cited by 2
- RatFunc.valuation_eq_valuation_uniformizingPolynomial_pow_of_valuation_X_le_onestatement and proof · cited by 2
- RatFunc.coePolynomial.congr_simpstatement and proof · cited by 2
- RatFunc.uniformizingPolynomial_isUniformizerstatement and proof · cited by 1
- Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_Xstatement and proof · cited by 1
- RatFunc.coePolynomial_eq_algebraMapstatement · cited by 1
- RatFunc.coe_coestatement · cited by 1
- RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_Xproof · cited by 1
- RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_oneproof · cited by 1