Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be solved in terms of numbers, even representing solution sets for inequalities is only made possible by
Mathematica's symbolic capabilities.
Boole — convert from inequalities to 0, 1 values
Piecewise — general piecewise function
FindInstance — search for particular solutions to inequalities
Reduce — reduce systems of inequalities to explicit nested form
Integrate,
NIntegrate — integrate over regions defined by inequalities
RegionPlot,
RegionPlot3D — plot regions defined by inequalities
FindMinimum,
NMinimize,
Minimize,
... — optimization over regions
»
RegionFunction — option for constraining 2D or 3D plots to a region
PolyhedronData — find inequalities corresponding to named polyhedra
LogicalExpand — expand out composite inequalities
PiecewiseExpand — expand out piecewise functions
