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Algebraic Transformations
Mathematica includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated algorithms, many developed and refined at Wolfram Research.
General Operations
Simplify apply transformations to try to simplify an expression
FullSimplify apply a full set of simplification transformations
FunctionExpand attempt to expand in terms of more elementary functions
    
PowerExpand expand powers, assuming positive real variables, etc.
ComplexExpand expand complex functions into real and imaginary parts, etc.
    
Expand expand out products and powers
Factor factor sums into products and powers
Collect collect similar terms together
Together put over a common denominator
Apart break apart into partial fractions
ExpandNumerator  ▪ ExpandAll  ▪ Cancel  ▪ ...
TrigToExp, ExpToTrig convert between exponentials and trigonometric functions
RootReduce try to merge all roots to a single root
ToRadicals try to convert roots to explicit radicals
    
PiecewiseExpand expand out piecewise functions into explicit components
LogicalExpand expand out Boolean expressions
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