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The art of manipulating an algebraic expression into the desired form.

It is often difficult in Mathematica to convert an algebraic expression into a specific form. Algebraic manipulation involves structural and algebraic operations of polynomials, rationals, complex numbers, trigonometric, logical or any other mathematical expression, according to the rules of algebra. There are a number of high-level functions that can perform complex structural changes like Simplify, FullSimplify and Reduce. Additionally, there are many others that can perform more controlled structural changes such as Collect, Together, Cancel, Expand, etc.

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For (non-algebraic) structural manipulation, use , for controlled evaluation use , for algebraic simplification, use .