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In abstract algebra, a derivation on an
associative algebra A over a field k is a linear map D:A→A that satisfies Leibniz' law:
- D(ab) = (Da)b + a(Db).
Examples of derivations are partial derivatives, Lie derivatives, the Pincherle derivative, and the commutator with
respect to an element of the algebra. All these examples are tightly related, with the concept of derivation as the major
unifying theme.
See also: Kähler differential
Derivation may also be used as a synonym for proof,
particularly for formulae.
In music using the twelve tone technique see derived row, where a
tone row whose entirety of twelve tones is constructed from a segment or portion of
the whole, the generator.
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