New in Version 5Mathematica 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. Numerical Computation• 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. Symbolic Computation• 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. Interfaces• 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. Notebook Interface• 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.
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