New in Version 5
Mathematica Version 5 introduces important extensions to the Mathematica system, especially in scope and scalability of numeric and symbolic computation. Building on the core language and extensive algorithm knowledge base of Mathematica, Version 5 introduces a new generation of advanced algorithms for a wide range of numeric and symbolic operations.
• Major optimization of dense numerical linear algebra.
• New optimized sparse numerical linear algebra.
• Support for optimized arbitrary-precision linear algebra.
• Generalized eigenvalues and singular value decomposition.
• LinearSolveFunction for repeated linear-system solving.
• norms for vectors and matrices.
• Built-in MatrixRank for exact and approximate matrices.
• Support for large-scale linear programming, with interior point methods.
• New methods and array variable support in FindRoot and FindMinimum.
• FindFit for full nonlinear curve fitting.
• Constrained global optimization with NMinimize.
• Support for -dimensional PDEs in NDSolve.
• Support for differential-algebraic equations in NDSolve.
• Support for vector and array-valued functions in NDSolve.
• Highly extensive collection of automatically accessible algorithms in NDSolve.
• Finer precision and accuracy control for arbitrary-precision numbers.
• Higher-efficiency big number arithmetic, including processor-specific optimization.
• Enhanced algorithms for number-theoretical operations including GCD and FactorInteger.
• Direct support for high-performance basic statistics functions.
• Solutions to mixed systems of equations and inequalities in Reduce.
• Complete solving of polynomial systems over real or complex numbers.
• Solving large classes of Diophantine equations.
• ForAll and Exists quantifiers and quantifier elimination.
• Representation of discrete and continuous algebraic and transcendental solution sets.
• FindInstance for finding instances of solutions over different domains.
• Exact constrained minimization over real and integer domains.
• Integrated support for assumptions using Assuming and Refine.
• RSolve for solving recurrence equations.
• Support for nonlinear, partial and difference equations and systems.
• Full solutions to systems of rational ordinary differential equations.
• Support for differential-algebraic equations.
• CoefficientArrays for converting systems of equations to tensors.
Programming and Core System
• Integrated language support for sparse arrays.
• New list programming with Sow and Reap.
• EvaluationMonitor and StepMonitor for algorithm monitoring.
• Enhanced timing measurement, including AbsoluteTiming.
• Major performance enhancements for MathLink.
• Optimization for 64-bit operating systems and architectures.
• Support for computations in full 64-bit address spaces.
• Support for more than 50 import and export formats.
• High-efficiency import and export of tabular data.
• PNG, SVG and DICOM graphics and imaging formats.
• Import and export of sparse matrix formats.
• MPS linear programming format.
• Cascading style sheets and XHTML for notebook exporting.
• Preview version of .NET/Link for integration with .NET.
• Enhanced Help Browser design.
• Automatic copy/paste switching for Windows.
• Enhanced support for slide show presentation.
• AuthorTools support for notebook diffs.
Standard Add-on Packages
• Statistical plots and graphics.
• Algebraic number fields.
New in Versions 4.1 and 4.2
• Enhanced pattern matching of sequence objects.
• Enhanced optimizer for built-in Mathematica compiler.
• Enhanced continued fraction computation.
• Greatly enhanced DSolve.
• Additional TraditionalForm formats.
• Efficiency increases for multivariate polynomial operations.
• Support for import and export of DXF, STL, FITS and STDS data formats.
• Full support for CSV format import and export.
• Support for UTF character encodings.
• Extensive support for XML, including SymbolicXML subsystem and NotebookML.
• Native support for evaluation and formatting of Nand and Nor.
• High-efficiency CellularAutomaton function.
• J/Link MathLink-based Java capabilities.
• MathMLForm and extended MathML support.
• Extended simplification of Floor, Erf, ProductLog and related functions.
• Integration over regions defined by inequalities.
• Integration of piecewise functions.
• Standard package for visualization of regions defined by inequalities.
• ANOVA standard add-on package.
• Enhanced Combinatorica add-on package.
• AuthorTools notebook authoring environment.