This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
 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 Visualization 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 TUTORIALS Structural Operations on Polynomials Algebraic Operations on Polynomials Polynomials over Algebraic Number Fields Polynomials Modulo Primes Complex Polynomial Systems TUTORIAL COLLECTION Advanced Algebra MORE ABOUT Polynomial Equations Diophantine Equations Linear Algebra & Matrices Algebraic Number Fields RELATED LINKS Demonstrations related to Polynomial Systems (The Wolfram Demonstrations Project)