The mathematical definition of an elementary function , or a function in elementary form, is considered in the context of differential algebra . A differential algebra is an algebra with the extra operation of derivation (algebraic version of differentiation). Using the derivation operation new equations can be written and their solutions used in extensions of the algebra. By starting with the field of rational functions , two special types of transcendental extensions (the logarithm and the exponential) can be added to the field building a tower containing elementary functions.
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