Mathematica's handling of polynomial systems is a
tour de force of algebraic computation. Building on mathematical results spanning more than a century,
Mathematica for the first time implements complete efficient reduction of polynomial equation and inequality systems—making possible industrial-strength generalized algebraic geometry for many new applications.
Solve — find generic solutions for variables
Reduce — reduce systems of equations and inequalities to canonical form
Eliminate — eliminate variables between equations
SolveAlways — solve for parameter values that make equations always hold
Resolve — eliminate general quantifiers
Reduce — eliminate quantifiers and reduce the results
NSolve — solve systems of polynomial equations
ContourPlot — curve or curves defined by equation in
x and
y
ContourPlot3D — surface defined by equation in
x,
y and
z
RegionPlot,
RegionPlot3D — regions defined by inequalities
