Mathematica and Wolfram Language zone

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Please email or phone Webel IT Australia on +61 405 029 008 to enquire about our Mathematica services!
Webel IT Australia offers professional consultancy services for applications of the incredibly powerful  Wolfram Mathematica to mathematical modelling, data analysis and visualisation, 3D modelling and animation, systems modelling, and physics modelling. Mathematica can also be used for rapid development of GUI applications within Mathematica Notebooks that can be deployed in Wolfram Player Pro to capture Mathematica-driven solutions conveniently for end users, for development of Wolfram Cloud web applications, and for RESTful web services.

Service: Wolfram Mathematica: Modelling, data analysis, mapping, transformation, and visualisation, including end-user GUIs
Service: Mathematica-driven spreadsheet data and formula migration to Wolfram Cloud, database, XML Schema or JSON with GUI or web app

New! A comprehensive technical slide trail on the Webel libraries for Mathematica and Webel SysML4Mathematica (v1):

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.
Dr Darren says:
Ever wondered why Wolfram Mathematica users are so very enthusiastic about it? It's because as far as capabilities are concerned and the power of the underlying Wolfram Language and Mathematica Notebooks for scientific computing it is in a league of its own. Nothing else comes even vaguely close for integrated symbolic algebra (actual mathematics and equations), numerics, data analysis, data manipulation, data transformation, visualisation, integration with other data source, the ability to import/export a wide range of data formats and other data sources, realistic simulation creation, rapid parametrically controlled GUI creation, integration with Natural Language Processing (NLP), and the Wolfram technology ecosystem including Wolfram|Alpha is simply extraordinary.

Did you know? Mathematica can call Python and Python libraries directly in Mathematica Notebooks and can also call Java via J/Link directly in Notebooks!

Did you know? Mathematica can compile many Wolfram Language functions to highly optimised C language code for rapid execution.

Mathematica: Webel: You get compelling incremental value out of Mathematica even if you don't yet command all of the syntax and massive powers of the Wolfram Language!
Mathematica can be used as an external maths engine for SysML Parametrics!
Visit also: Mathematica and Wolfram SystemModeler tips, issues, and wishlist tracking
Visit also: The Webel SysML4Mathematica recipe for modelling Wolfram Language code in Systems Modeling Language (SysML) for Model-Based Systems Engineering
NEWS: New trail demonstrating applications of Mathematica, SysML/MBSE, and CoolProp to Psychrometrics (humid air physics): TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class
Visit also: TIP: Mathematica: Webel's ultimate guide to using Abstract Data Types to create "pseudo classes" (strong types) with inheritance for the Wolfram Language, all modelled in SysML!
TIP: Mathematica: The IntelliJ IDEA Plugin for Mathematica is HEAPS better than the Eclipse-based Wolfram Workbench (at least for the Wolfram Language as used by Webel projects)!
Webel on Mathematica and the Wolfram Language vs Python. Python is not even close, not even vaguely close, it's not in the same league, as the Wolfram Language and Mathematica!
Mathematica is also brilliant for creating Maths Art!
Buy Mathematica-generated Tessellation Art in 8K high resolution as quality Acrylic Float Frame mounted prints delivered worldwide!
Buy Mathematica-generated 3D Maths Art in super high 16K resolution as quality Acrylic Float Frame mounted prints delivered worldwide!
And the techniques used for creation of the stunning scenes shown under the links above is also used by Webel IT Australia for advanced parametric 3D modelling of devices for industry and building projects using Webel's own custom library for enhancing the amazing visualisation and 3D modelling capabilities of Mathematica.
Visit the Wolfram Mathematica home page to learn about "the world's definitive system for modern technical computing":
Notes
Relevant snippets (from other sources)
Visit also
Service: Wolfram Mathematica: Modelling, data analysis, mapping, transformation, and visualisation, including end-user GUIs
Service: Mathematica-driven spreadsheet data and formula migration to Wolfram Cloud, database, XML Schema or JSON with GUI or web app
Wolfram SystemModeler zone
Mathematica and Wolfram SystemModeler tips, issues, and wishlist tracking
Visit also (backlinks)
Software engineering reference zone
Dr Darren's links for Lambdas vs Closures for coding languages and formal Lambda Calculus
Visuals: Amazing super long play Maths Art 3D video creating using scenes generated by Wolfram Mathematica and combined with FX!
Mathematica (v14.2): Now supports export to ProRes with VideoTransparency on M1 Max/Silicon with "PRORES-AW" or "PRORES-KS"
Mathematica 3D with Manipulate GUI: The ARCHITIME Design kinetic/dynamic wall reproduced in Wolfram Mathematica
Mathematica: GOTCHA: If you pull an EntityStore from a CloudObject with PersistentSymbol it caches and will not update if invoked again even if the CloudObject for the EntityStore has changed. Use instead CloudGet.
Mathematica: GOTCHA/LIMITATION: Changing the value of an Entity in an expression-based EntityStore loaded from a CloudObject does not update the CloudObject. You have to push the EntityStore back to the CloudObject. It is not like a "live" connection.
Mathematica: GOTCHA/LIMITATION: RelationalDatabase and DatabaseReference are NOT supported in the Wolfram Cloud for "public" accounts, not even for Premium Plan (Commercial)! It is only optionally offered on the Wolfram Enterprise Private Cloud (EPC).
Mathematica: GOTCHA: Setting the value of a property of an Entity using EntityValue[e,"property"] where 'e' is an Entity does NOT work with a relational database backed EntityStore, which undermines half the point of a relational database bridge!
ISSUE: Mathematica (v14.1): Known Apple BUG: macOS Ventura: M1 Max/Silicon: Export to "PRORES422-AVF" or "PRORES4444-AVF" is buggy! [Since Mathematica v14.2 you can use "PRORES-AW" or "PRORES-KS" instead]
TIP: Mathematica: To Export a ListAnimation without the controls (and without possible frame drops) Export the List of frames directly (not the output of ListAnimation)
TIP: Mathematica: HOWTO Get the (approximate) bounding box of any Graphics3D object for use in PlotRange. Use Charting`get3DPlotRange
Science and Maths fun: 100 Stars in Wolfram Mathematica
Buy Mathematica-generated 3D Maths Art in super high 16K resolution as quality Acrylic Float Frame mounted prints delivered worldwide!
Webel: SysML4Mathematica: A custom stereotype «M:Paclet» applied to a SysML Package denotes a Wolfram Package Paclet. An «M:Package» is a specialisation of SysMLv1 Block and denotes a Wolfram Language Package.
Webel: SysML4Mathematica: A SysML/UML Usage (keyword «uses») is used to indicate a Wolfram Package Needs import, where an «M:Package» is a specialisation of Block (not a SysML/UML Package) and denotes a Wolfram Language Package.
Webel: SysML4Mathematica: Activity Diagrams used purely for analysis and as development aids are not required to show every ControlFlow, may omit InitialNode and ActivityFinalNode, and are not required to fully validate in SysML tools or execute.
Webel: SysML4Mathematica: An OptionsPattern[] may be represented by an «M:OptionsPattern» SysMLv1 Block with «M:Opt» properties. An «M:Opt» property represents an Options[] Rule IMPLICITLY (an «M:Opt» does not use the Rule block modelling recipe).
Mathematica: CONVENTION: A prefix 'eq$' indicates a symbolic equation (typically using 'sym$' human-friendly markup "symbols")
SysML Stereotypes and icons used for Mathematica and Wolfram technologies
Service: Mathematica-driven spreadsheet data and formula migration to Wolfram Cloud, database, XML Schema or JSON with GUI or web app
Buy Mathematica-generated Tessellation Art in 8K high resolution as quality Acrylic Float Frame mounted prints delivered worldwide!
Mathematica: Webel: You get compelling incremental value out of Mathematica even if you don't yet command all of the syntax and massive powers of the Wolfram Language!
Webel: Mathematica: CONVENTION: A prefix '$doc' indicates a documentation String for each primary variable/quantity (argument or output)
Webel: Mathematica: CONVENTION: A prefix 'sym$' indicates a markup variable "symbol" for a documented variable. It need not be a String, but each referenced part MUST be a String - not a Mathematica Symbol - to avoid namespace clashes!
Webel: SysML4Mathematica: Does every bit of the Mathematica code need to be modelled in SysML? No. Typically just the main function parameters and their interdependencies, data structures, and main code logic. Except for special or educational purposes.
Webel: SysML4Mathematica: POLICY: Handle flow sign changes via a single negative (not duplicated and "adjusted" algebra). This strategy may come at a very slight performance cost (for benefit of more robustness).
Cameo Simulation Toolkit: You can use Mathematica as an external maths engine to share maths between an OpaqueBehavior and a ConstraintBlock using custom auto-loaded Mathematica functions (keeps a project nice and DRY and respects Single Source of Truth)
HOWTO: MagicDraw/Cameo: v2022Refresh1: JDK 11 download compatible with the modelling tools AND Apple Silicon (ARM) machines (such as M1 Max)
Webel: SysML4Mathematica: SysML Activities and SysML Activity Diagrams CAN represent some functional programming paradigms (sort of). You can type Parameters by encapsulations of functions and pass them to/from InputPins/OutputPins of Actions.
Webel: SysML4Mathematica: TIP: Representing Mathematica Paclets and their inter-dependencies as SysML Packages modelled in SysML Package Diagrams can really help you organise your Wolfram Language code on complex projects!
Webel: SysML4Mathematica: TIP: Representing Mathematica functions as SysML ConstraintBlocks modelled in Block Definition Diagram (BDD) overviews can really help you organise and document your Wolfram Language code on complex projects!
Webel: SysML4Mathematica: TIP: Representing Mathematica functions as SysML ConstraintBlocks modelled in SysML Parametric Diagrams and as Activities in SysML Activity Diagrams is super for analysing the dependencies between functions and their arguments!
Webel: SysML4Mathematica: TIP: Exported SysML Diagrams can be embedded in Mathematica Notebooks!
Webel: SysML4Mathematica: Convention: A Mathematica Blank '_' (which pattern-matches any Expression) is represented by a custom SysML ValueType '_'
SysML4Mathematica: Example: Block Definition Diagram overview of ConstraintBlocks, their parameters, and ConstraintBlock usages representing lower-level Webel Psy library Psychrometrics functions and CoolProp wrapper usages
Webel: SysML4Mathematica: An Association used as the Type of an argument or return is represented by a Block '<||>'. A List used as as the Type of an argument or return is represented by a Block '{}'. (Extending types may adapt the notation.)
The Webel SysML4Mathematica recipe for modelling Wolfram Language code in Systems Modeling Language (SysML) for Model-Based Systems Engineering
SysML/UML: MagicDraw/Cameo: GOTCHA: Connecting a typed OutputPin to an untyped (UNSPECIFIED) InputPin with an ObjectFlow changes the type of the InputPin
Webel: SysML4Mathematica: Convention: A '$E' in a function name indicates that all parameters (arguments and return) are Mathematica '_' expressions. However, when representing such functions as Activities they may end up getting strongly typed in tools!
Webel: SysML4Mathematica: When modelling the main logic flow of Mathematica code with Activity Diagrams it isn't necessary to model every Mathematica construct. Placeholder Actions, OpaqueActions , and OpaqueBehaviors (as CallBehaviorActions) may be used.
Webel: SysML4Mathematica: Cameo Systems Modeler: Can perform calculations with a custom Quantity ValueType (for Mathematica) directly, but DOES NOT perform units-aware algebra (no automatic conversions)
Webel: SysML4Mathematica: An '@' prefix in the name of a Block indicates a data structure (such as an Association or List) that does not have a corresponding MTools class or a Webel Abstract Data Type (ADT) "pseudo class" in the Wolfram Language code.
Webel: SysML4Mathematica: An '@' prefix in the name of a ConstraintBlock, Activity, or OpaqueBehavior indicates that it is a "@pseudo" function not represented directly in the Wolfram Language or Webel code libraries (typically for minor maths or logic)
TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class
The Webel Recipe for SysML-friendly Wolfram Language coding in Mathematica
Mathematica: Wolfram Player Pro 13.1: NotebookDelete[] does not work
Mathematica: v13.1: There is an undocumented command MessagesNotebook[]
Mathematica: 'Through' is your more functional friend.
THE BIG TIP: You brain has many facets: code + graphical engineering is greater than either alone
The integration between Wolfram Workbench and Mathematica is partly gammy (as of latest versions 2022-08-23)
Mathematica: TIP: Wolfram Notebooks are the best testing environment I've ever used!
Mathematica: ISSUE with all Entity operations on MMAv13.0.0.0 vs macOS Monterey 12.3 or 12.4 ["solved" by upgrade to MMA 13.1.0.0]
CoolProp: Mathematica: Mac: HOWTO get CoolProp for Mathematica running on Apple M1 Max and Mathematica13
Mathematica: CoolProp wrapper binaries don't seem to be maintained past CoolProp 5.1.1 (and the PhaseSI and 2-args Props1SI functions do not work)
Webel + Mathematica + MTools + SysML
Mathematica: LINKS: Manipulating Strings and using RegularExpression
Mathematica: GOTCHA: Null is tricky!
Webel vs Mathematica: The Very Good, The Bad, and The Ugly
Mathematica: How mimic pattern matching of arguments for pseudo "Boolean" (including providing a default)?
Mathematica: The Entity system: useful links
Mathematica: TIP: How to change a value within an Association inline within a Module (like pass by reference)
Mathematica: GOTCHA: Package usages (Needs) are not transitive
Mathematica: HOWTO Find the value of a symbol in all contexts
HOWTO access custom (user-defined) Mathematica functions using Mathematica v13.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1
HOWTO use Mathematica v12.3.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1
External simulation: Languages and tools: SysML vs SysPhS vs Modelica vs Simulink
MINI TRAIL: Some recommended tools for getting started with Model-Based Systems Engineering with SysML and simulation with Modelica and/or Simulink
Modelica zone
Maple zone
Service: Wolfram Mathematica: Modelling, data analysis, mapping, transformation, and visualisation, including end-user GUIs
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Wolfram Mathematica
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