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Mathematica 13.1.0 by Wolfram

Mathematica is a general computing environment, organizing many algorithmic, visualization, and user interface capabilities within a document-like user interface paradigm.

It was originally conceived by Stephen Wolfram, developed by a team of mathematicians and programmers that he assembled and led, and it is sold by his company Wolfram Research.

Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications.

Mathematica combines powerful computing software with a convenient user interface. It is this range of capabilities – many world-leading in their own right – that makes Mathematica uniquely capable as a “one-stop-shop” for you or your organization’s technical work.

The features include symbolic and high-performance numeric computation, 2D and 3D data visualization, broad programming capabilities, and one-step creation of web documents. Mathematica’s notebook format allows for the generation of cross-platform, fully customisable files that provide professional mathematical typesetting and publication-quality layout of electronic and printed media.

Wolfram Mathematica 13 Features:
  • A vast web of mathematical, visualization, graphics, and general programming functions, typically with state-of-the-art implementations
  • Ability to instantly create user interfaces to arbitrary computations by just specifying parameters
  • Integrated computable data sources, from chemistry and pure mathematics to city locations and country statistics
  • Highly general interface that allows the uniform manipulation and intermingling of graphics, programs, and user interfaces
  • Support for efficient data structures such as sparse arrays, piecewise functions, etc
  • Support for emerging fields such as graph plotting and analysis, alternate input devices, and new data formats
  • Ability to create and publish programs that run on the free Mathematica Player

Wolfram Mathematica is split into two parts, the “kernel” and the “front end”. The kernel is the algorithmic engine for performing computations. The front end provides a convenient human interface for creating and manipulating programmatic structures, allowing graphics, mathematics, programs, text, and user interfaces can be freely edited and intermingled.

It also provides debugging capabilities, a presentation environment, and interfaces to USB controllers like gamepads. The two communicate via the MathLink protocol. It is possible to use the kernel on one computer and the front end on another, although this is not how most people use Mathematica.

Key Elements:

  • Notebook Document System
  • Complex Analysis
  • Volumes of Knowledge
  • Typesetting
  • Symbolic and Numeric Computations
  • Graphics
  • Application Development
  • Programmable Palettes
  • Special-Purpose Interfaces
  • Programming Language
  • Interactive Help Browser
Changes in Mathematica 13.1.0:
  • Version 13.1 includes 90 completely new functions – plus 203 functions with substantial updates, new user interface features and enhanced compiler functionality.
  • Thread arrays at deep levels of other arrays with Threaded
  • New language convenience functions for list manipulation: DeleteElements, DeleteAdjacentDuplicates, SymmetricDifference and UniqueElements
  • Added functional programming convenience functions: ReplaceAt, MapApply, Until and SameAs
  • Compute change of variables in integrals and differential equations with IntegrateChangeVariables and DSolveChangeVariables
  • Support for fractional derivatives and fractional differential equations with FractionalD, CaputoD and an update to DSolve
  • Compute derivatives of implicitly defined functions using ImplicitD
  • Added several new types of structured arrays: PermutationMatrix, BlockDiagonalMatrix, LowerTriangularMatrix, UpperTriangularMatrix, BlockLowerTriangularMatrix and BlockUpperTriangularMatrix
  • Interval evaluation via CenteredInterval or Interval added to multiple special mathematical functions
  • Plot ratios of quantities with TernaryListPlot
  • Enhanced support for the ScalingFunctions option in visualization functions, and added NominalScale and OrdinalScale
  • VoronoiMesh now supports 3D Voronoi decompositions
  • Reconstruct 1D, 2D and 3D meshes from point clouds using ReconstructionMesh
  • EstimatedPointNormals can estimate normals to points in a point cloud
  • Added functions for operations on graphs: GraphProduct, GraphJoin and graphs
  • Emoji and more multilingual support
  • Create 2D drop shadow effects with DropShadowing
  • Several new shaders for graphics were added: FlatShading, GouraudShading and PhongShading
  • Interactive video recording from webcams and other devices with VideoCapture
  • Interactive screen video recording with VideoScreenCapture
  • New machine learning functions to plot impact of features on a model result: FeatureValueImpactPlot, FeatureImpactPlot, CumulativeFeatureImpactPlot and FeatureValueDependencyPlot
  • New tree-related functions RootTree, UnlabeledTree, TreeLeafCount and numerous options to style and label trees
  • Represent a family of chemical reactions symbolically with PatternReaction and apply such a reaction to a set of molecules with ApplyReaction
  • Perform chemical conversions with ChemicalConvert
  • ModelPredictiveController performs explicit constrained MPC controller design with 1-, 2- and ∞-norms
  • DiscreteInputOutputModel implements a general nonlinear input-output model
  • New functions for type declaration and type specification syntax in compiled code and libraries: TypeDeclaration, CompiledExpressionDeclaration, LibraryFunctionDeclaration and TypeSpecifier
  • Expanded support for type representation in compiled code with ForAllType, LiteralType, TypeEvaluate, CreateTypeInstance and TypeOf
  • Call the evaluator from compiled code with InertEvaluate
  • Create and dereference pointers for interacting with external libraries with ToRawPointer and FromRawPointer
  • Added an “ExprStruct” data structure that represents an expression that can be modified without evaluation
  • QuestionGenerator and QuestionSelector add further support for question & answer interfaces
  • New default toolbar, annotation overlay and custom guide page creation
  • All new and updated features since 13

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