Differential Field
A differential field is a field K, together with a derivation. The theory of differential fields, DF, is given by the usual field axioms along with two extra axioms involving the derivation. As above, the derivation must obey the product rule, or Leibniz rule over the elements of the field, to be worthy of being called a derivation. That is, for any two elements u, v of the field, one has
since multiplication on the field is commutative. The derivation must also be distributive over addition in the field:
If K is a differential field then the field of constants
Read more about this topic: Differential Algebra
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