Theorems · Theorem · field theory
RatFunc.eq_C_iff
∀ {K : Type u} [inst : Field K] (f : RatFunc K), (∃ c, f = RatFunc.C c) ↔ f.num.natDegree = 0 ∧ f.denom.natDegree = 0- Defined in
- Mathlib.FieldTheory.RatFunc.AsPolynomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- RatFuncstatement and proof · cited by 301
- map_div₀proof · cited by 98
- RatFunc.denomstatement and proof · cited by 59
- Polynomial.natDegree_Cproof · cited by 59
- RatFunc.numstatement and proof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- RatFunc.irreducible_minpolyXproof · cited by 1
- RatFunc.Luroth.eq_adjoin_generatorproof · cited by 0