Theorems · Definition · field theory
RatFunc.intDegree
{K : Type u} → [inst : Field K] → RatFunc K → ℤintDegree x is the degree of the rational function x, defined as the difference between
the natDegree of its numerator and the natDegree of its denominator. In particular,
intDegree 0 = 0.
- Defined in
- Mathlib.FieldTheory.RatFunc.Degree
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 127 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomial.natDegreeproof · cited by 1,105
- RatFuncstatement and proof · cited by 301
- RatFunc.denomproof · cited by 59
- RatFunc.numproof · cited by 49
Cited by19
Results whose statement or proof uses this declaration.
- RatFunc.inftyValuationDefproof · cited by 17
- RatFunc.intDegree_mulstatement · cited by 3
- RatFunc.intDegree_onestatement · cited by 2
- RatFunc.intDegree_polynomialstatement · cited by 2
- RatFunc.intDegree_zerostatement · cited by 2
- RatFunc.inftyValuation_of_nonzerostatement and proof · cited by 2
- RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_Xstatement and proof · cited by 1
- RatFunc.valuation_isEquiv_inftyValuation_of_one_lt_valuation_Xproof · cited by 1
- RatFunc.InftyValuation.map_add_le_max'proof · cited by 1
- RatFunc.InftyValuation.map_mul'proof · cited by 1
- RatFunc.intDegree_Cstatement · cited by 1
- RatFunc.intDegree_Xstatement · cited by 1