TDP-4-oxo-6-deoxy-alpha-D-glucose-3,4-oxoisomerase (dTDP-3-dehydro-6-deoxy-alpha-D-galactopyranose-forming)
In mathematics, the Hasse derivative is a derivation, a generalisation of the derivative which allows the formulation of Taylor's theorem in coordinate rings of algebraic varieties.
Definition
Let k[X] be a polynomial ring over a field k. The r-th Hasse derivative of Xn is
if n ≥ r and zero otherwise.[1] In characteristic zero we have
Properties
The Hasse derivative is a derivation on k[X] and extends to a derivation on the function field k(X),[1] satisfying the product rule and the chain rule.[2]
A form of Taylor's theorem holds for a function f defined in terms of a local parameter t on an algebraic variety:[3]
References
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