This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Polynomial Systems
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.
Solving & Reducing
Solve find generic solutions for variables
Reduce reduce systems of equations and inequalities to canonical form
Complexes, Reals, Integers domains for variables
Eliminating Variables
Eliminate eliminate variables between equations
SolveAlways solve for parameter values that make equations always hold
Quantifier Elimination
ForAll ( ▪ Exists ()
Resolve eliminate general quantifiers
Reduce eliminate quantifiers and reduce the results
Structure of Solution Sets
Numerical Solutions
NSolve solve systems of polynomial equations
Minimize  ▪ Maximize  ▪ NMinimize  ▪ NMaximize
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
Equation Structure