Mathematica 8 adds a number of dramatic improvements to its core algorithms, with a new generation of methods for globally solving equations and inequalities, either symbolically or numerically. New symbolic-numeric methods allow you to numerically integrate a wide class of highly oscillatory functions automatically. Mathematica 8 reaches a new high-water mark in exact linear algebra performance, and also includes a number of additions to the world's largest collection of special functions.

• Solve can solve equations and inequalities over complexes, reals, and integers. »
• NSolve can solve equations and inequalities over complexes and reals. »
• Solve and NSolve have new advanced methods for solving transcendental equations.
• Solve and NSolve have new advanced methods for finding real solutions to high-degree polynomials.
• New conditionally valid expressions for representing partial functions. »
• New generation of fast, exact linear algebra. »
• New hybrid symbolic-numeric method for integrating highly oscillatory functions. »
• New special functions for probability and statistics. »

Compute with Conditionally Valid Solutions »	Find Parametrized Real Solutions of Systems of Equations »	Solve Transcendental Equations Numerically »
Solve High-Degree Real Polynomial Equations Numerically »	Conditionally Valid Expressions »	Fast Determinant Computation for Integer Matrices »
Fast Inverse Computation for Integer Matrices »	Fast Solving of Systems of Linear Equations with Integer Coefficients »	Fast Null Space Computation for Integer Matrices »
Solve a Numerical Integration Challenge Problem »	Integrate Sums, Products, and Compositions of Oscillatory Functions »	Integrate Multidimensional Highly Oscillatory Functions »
Compute Binormal Probability over a Polygon »	Sublevel Sets for RankedMin »	Eigenfunctions of the Laplace Equation »
Compute Values of High-Order Derivatives Directly »	Perform Numerical Hankel Transform »

RELATED FUNCTIONS

Solve  NSolve  ConditionalExpression  NIntegrate  LinearSolve  NullSpace  MatrixRank  Inverse  LeastSquares  PseudoInverse  Det  Dot  MarcumQ  OwenT  WignerD  BellY  RankedMin  RankedMax