Simplifying an expression often means different things at different times. Axiom offers a large number of "simplification" functions. The most common one, which performs the usual trigonometric simplifications is simplify. If the result of simplify is not satisfactory, specific transformations are available. For example, to rewrite g in terms of secants and cosecants instead of sines and cosines, issues: To apply the logarithm simplification rules to h, issue: Since the square root of x^2 is the absolute value of x and not x itself, algebraic radicals are not automatically simplified, but you can specifically request it by calling rootSimp: There are other transformations which are sometimes useful. Use the functions complexElementary and trigs to go back and forth between the complex exponential and trigonometric forms of an elementary function. Similarly, the functions realElementary and htrigs convert hyperbolic functions in and out of their exponential form. Axiom has other transformations, most of which are in the packages ElementaryFunctionStructurePackage, TrigonometricManipulations, AlgebraicManipulations, and TranscendentalManipulations. If you need to apply a simplification rule not built into the system you can use Axiom's pattern matcher.