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Mathematica 12.1.0 by Wolfram

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Mathematica 12.1.0 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 12 Features:

  • 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, user interfaces
  • Support for efficient datastructures such as sparse arrays, piecewise functions, etc
  • Support for emerging fields such as graph plotting and analysis, alternate input devices, 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

What’s New in Mathematica 12:

Changes in Mathematica 12.1.0:

  • Windows and Linux notebook interface updated with HiDPI support for thousands of icons and other assets
  • Windows and macOS interfaces now use Direct3D 11 and Metal API for improved rendering of 3D graphics
  • Sophisticated video framework for programmatic viewing, processing and analysis of a range of multimedia types
  • Spreadsheet-like viewing, editing and manipulation of tabular data with TableView
  • Detailed control of appearance, sorting, data storage and other options for Dataset
  • New DataStructure framework for efficient creation, storage and manipulation of common data structures
  • Compute asymptotic approximations and expansions for mathematical expressions with Asymptotic and DiscreteAsymptotic
  • Mathematical HeunG function representing the regular solution of the general Heun equation
  • Generate distributions over unordered classes with CategoricalDistribution
  • Use GeometricOptimization to find positive values that minimize the posynomial objective subject to given constraints
  • Plot functions, regions and vectors in the complex plane with ComplexRegionPlot, ComplexContourPlot, ComplexVectorPlot, etc.
  • Support for generating proofs from arbitrary predicates (first-order logic) with FindEquationalProof
  • Several improvements and new options for vector visualization
  • Artistically fill 2D polygons with HatchFilling and PatternFilling, and shade 3D objects with StippleShading, ToonShading, HatchShading and other new graphics directives
  • Improved support for geometric operations on geographic regions
  • Display values on maps as smoothly varying colors with GeoDensityPlot or as contours with GeoContourPlot
  • Explore the topology of meshes with MeshConnectivityGraph and NearestMeshCells
  • Train generative models on various types of data with NetGANOperator
  • Include anomaly detection in machine learning functions with AnomalyDetector
  • Set styled annotations for graphs and other objects with Annotate
  • Use Splice to automatically splice expressions into a list
  • Operate on subsets/sublists with functions such as SubsetCases, SubsetPosition, SubsetCount, etc.
  • Represent operator forms with OperatorApplied and CurryApplied, and use ReverseApplied to apply a function with arguments reversed
  • TimeRemaining for retrieving the seconds until a TimeConstrained computation will be terminated
  • DateInterval for representing time intervals continuously or at a given granularity, InfinitePast/InfiniteFuture for representing indefinite time intervals and MinDate/MaxDate for finding extrema in an interval or list of dates
  • View tree graphs of expressions at any level with ExpressionGraph
  • ExternalIdentifier for representing and referencing resources in external identifier systems
  • Search and retrieve values from Wikidata’s SPARQL endpoint with WikidataSearch and WikidataData
  • Support for Julia, Ruby and R languages through ExternalEvaluate
  • Identify molecular structures in an image with MoleculeRecognize
  • Upload files to an external storage such as Dropbox with ExternalStorageUpload
  • View and analyze ARK blockchain data and submit transactions
  • Combine and separate entity classes with UnionedEntityClass, IntersectedEntityClass and ComplementedEntityClass
  • Improved support for ZIP and TAR through CreateArchive and ExtractArchive
  • Securely store system passwords, secrets, keys, etc. locally with SystemCredential, and create digital file signatures from a given key with GenerateFileSignature
  • Paclet framework for representing, installing and managing local and remote paclets with functions such as PacletInstall, PacletFind, PacletSites, etc.
  • Improved support for MicrosoftSQL, MySQL and other relational databases
  • Solve the max-cut problem for a graph with FindMaximumCut
  • Use FaceAlign to align faces in images based on facial landmarks
  • FindImageText for detecting the regions of an image containing a character, word, line or block of text
  • Use SpeechCases and SpeechInterpreter to identify text and entities in spoken audio, and compare speech with a reference clip with SpeakerMatchQ
  • Use CharacterNormalize to convert text to various Unicode normalization forms
  • Support for user-provided CUDA Toolkits

Changes in Mathematica 12.0.0:

  • Optimization solvers such as LinearOptimization, QuadraticOptimization, SemidefiniteOptimization, etc. for optimizing convex functions over convex constraints, including vector inequalities such as VectorGreater for modeling vector-valued variables
  • Expanded asymptotics functionality, including asymptotic solutions to algebraic and difference equations and asymptotic approximations to sums
  • Added support for generating arbitrary constants in Integrate, Sum and Product
  • Improved elementary functions support for Integrate, support for large structured systems in Solve and Reduce, DSolve support for nonlinear first-order ODEs and extended coverage and support in FunctionDomain
  • Extended numerical PDE-solving capabilities of NDSolve to solve nonlinear PDEs over arbitrary-shaped regions with the finite element method, and automated idealized n-body interactions using NBodySimulation
  • Geometric capabilities have been further enhanced with the addition of general polygons with holes and polyhedra primitives, as well as improved support across the board
  • New framework to visualize Euclidean geometry and its theorems using GeometricScene and GeometricAssertion
  • Access built-in axiomatic theories for use in symbolic proofs with AxiomaticTheory
  • Visualize complex-valued data and functions using ComplexListPlot, plot real and imaginary components of a function using ReImPlot and plot the modulus of a complex function of a real variable colored by its argument using AbsArgPlot
  • Use Around to describe uncertainty in measured values, with built-in support in visualization functions
  • Create, analyze and modify chemical species using the Molecule function, and visualize structures in two and three dimensions with MoleculePlot and MoleculePlot3D
  • Represent geodetic vectors with GeoVector, and visualize geodetic vector fields using GeoVectorPlot and GeoStreamPlot
  • Generate randomly distributed geo positions in any region using RandomGeoPosition, and analyze distance, area and angular distortion of geo projections using GeoGridUnitDistance, GeoGridUnitArea and GeoGridDirectionDifference
  • Updated default appearance for GraphPlot visualizations, as well as new plot themes and updated properties
  • Color-processing functions such as FindMatchingColor, ImageRecolor and ColorDetect, all powered by the new ColorsNear wrapper to represent a color neighborhood
  • High-level recognition functions such as ImageCases, FacialFeatures, AudioIdentify and SpeechRecognize, and performance enhancements to FindFaces, FeatureSpacePlot, AudioMFCC, etc.
  • Performance improvements in audio analysis functions such as AudioIntervals and windowing functions such as HannWindow, and a new AudioAnnotate framework for annotating audio objects
  • Multi-language support for SpeechSynthesize, as well as improved discovery and searching of available voices through VoiceStyleData
  • ShortTimeFourier for computing and storing properties of short-time Fourier transforms, and InverseSpectrogram for approximating a signal from a magnitude spectrogram
  • The neural network framework has been enhanced with additional pre-trained models, new layers, new encoders and decoders, multi-GPU support and automatic early stopping of training to prevent overfitting
  • ClassifierMeasurements can now handle uncertainties and multi-class averaging, and the “NeuralNetwork” method for Classify has been vastly improved using a self-normalizing net
  • Learn a generalized probability distribution from arbitrary data using LearnDistribution, replace missing values in data by generated values using SynthesizeMissingValues and find anomalous examples in data using FindAnomalies
  • Interact with relational databases symbolically using RelationalDatabase, integrating out-of-core and in-memory techniques to access terabyte-scale data and automatically generating SQL code for popular databases
  • Query remote or in-memory RDF graph databases using SPARQL queries, and import/export RDF data from a variety of RDF formats
  • Support for “on-the-fly” properties, filtering and sorting, aggregation, combining types and sampling of classes in the entity framework
  • Expanded and enhanced data for built-in entities across all domains, including geographic, cultural and historic, life science and medical, financial, astronomical, earth science, transportation, engineering, linguistic and mathematical
  • Efficient partial import and other improvements in scientific formats such as “FITS” and “HDF5”, as well as tabular formats such as “CSV” and “XLS”
  • NumericArray for creating the most compact representation of a numeric array
  • Pass arguments to functions in any order or bracket structure with Curry, or map vector functions onto sublists of elements with SubsetMap
  • Information has been greatly extended and modernized to provide information on different object types
  • Initial version of Wolfram Compiler for translating portions of Wolfram Language code into optimized native machine code
  • Improvements to the external evaluation framework, including core performance enhancements, ExternalFunction to directly call external code and WebExecute to control web browsers
  • Create, sign and deploy custom blockchain transactions and interact with computational contracts using BlockchainTransaction, BlockchainTransactionSign, BlockchainTransactionSubmit and BlockchainContractValue
  • New Microcontroller Kit for automating the generation and deployment of code to microcontrollers
  • Bidirectional interface to the Unity game engine
  • Share notebooks to the Wolfram Cloud or via email without leaving the front end
  • Create, store and instantly access functions through the public Wolfram Function Repository and the ResourceFunction system

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