Mathematica

Mathematica 3D with Manipulate GUI: The ARCHITIME Design kinetic/dynamic wall reproduced in Wolfram Mathematica

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The parametric architecture company ARCHITIME Design has a wonderful kinetic/dynamic wall installation outside their office building. You can view their original videos of their installation at these links:

http://www.architime.ru/works/dynamic_wall_papushevo.htm

http://www.architime.ru/works/dynamic_wall/papushevo/animate.gif

Read more about 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 ProRes is buggy! WORKAROUND: To use transparency, export to PNG then use Mac Compressor or Handbrake to convert to ProRes4444

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

Dr Darren's thoughts on some problems with "Python culture" (and it isn't the fault of the language, per se, nor of the best Python language developers or commercial Python library developers)

100 Stars in Mathematica: Star #004: Alycone

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Science and Maths fun: 100 Stars in Wolfram Mathematica

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100 Stars in Mathematica: Star #001: The Cowherd Hikoboshi (Altair) and The Heavenly Weaver Girl (Vega)

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Science and Maths fun: 100 Stars in Wolfram Mathematica

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Science and Maths fun: 100 Stars in Wolfram Mathematica

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Buy Mathematica-generated 3D Maths Art in super high 16K resolution as quality Acrylic Float Frame mounted prints delivered worldwide!

Keywords

Mathematica isn't just brilliant for symbolic algebra, data analysis, and visualisation, it is a simply amazing tool for generating high quality Maths Art, such as these amazing colourful super high resolution 16K Maths Art images, which are available for purchase as quality Acrylic Float Frame mounted prints, delivered worldwide.

SysMLv1 Parametric Diagram of the Effectiveness-NTU Method for a finned tube cross flow air conditioner heat exchanger

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

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SysML Parametric Diagram

hex$E$GungorWinterton$1987$twophase$htc$horizontal as a single expression using ‘sym$’ markup

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

Gungor-Winterton method for boiling heat transfer 1987 as SysML Activity Diagram ('$SI$' Real convention version)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

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.

HelpF`: DownValues: sigsDown[f]: Signature(s) from ExpressionTree

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.

The Shah 1982 CHART correlation for saturated boiling heat transfer as SysML Activity Diagrams (1)

The Shah 1982 CHART correlation for saturated boiling heat transfer as SysML Activity Diagrams (2): Detailed view of the hex$SI$Shah$twophase$htc$combined SI Real convention function variant

hex$E$Shah$twophase$htc$combined as a single expression using ‘sym$’ markup

Gungor-Winterton method for boiling heat transfer 1987 as SysML Activity Diagram ('$SI$' Real convention version)

hex$E$GungorWinterton$1987$twophase$htc$horizontal as a single expression using ‘sym$’ markup

SysMLv1 Parametric Diagram of the Effectiveness-NTU Method for a finned tube cross flow air conditioner heat exchanger

‘$E$’, ‘$Q$’,‘$SI$’ and ‘$C$’ function variants: Simple demo using a trivial Psy` function

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

Psy` humid air physics package: Example: Sensible Heating results

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

Psy`humid air physics package: Example: Sensible Heating in SysMLv1

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

CONVENTION: ‘$EQ$’, ‘$E$’, ‘eq$’ and ‘sym$’: Examples from the Psy` Psychrometrics package

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

Webel: Mathematica: CONVENTION: A '$Q$' in a function variant name indicates that it is a variant where every argument is strictly either a Quantity or dimensionless Real. Compare with '$SI$' functions.

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SysML Activity Diagram

Psy`Psychrometrics package variables registry

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Overview of the Psy` package and the "one shot" MPsy humid air state class

The MPsy “one shot” humid air state class

MPsy object creation examples

Psychrometrics exercise references (and about some naming conventions)

Psy`Psychrometrics package variables registry

CONVENTION: ‘$EQ$’, ‘$E$’, ‘eq$’ and ‘sym$’: Examples from the Psy` Psychrometrics package

About the Psy` package Psychrometrics exercises slides (in this trail)

Psy` package equations/functions (some correspond to exercise cases)

Psy`humid air physics package: Example: Sensible Heating in SysMLv1

Psy` humid air physics package: Example: Sensible Heating results

‘$E$’, ‘$Q$’,‘$SI$’ and ‘$C$’ function variants: Simple demo using a trivial Psy` function

Apply to access the comprehensive PDF slide set accompanying the Webel Mathematica libraries technical slide trail

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

If you are interested in Mathematica, the Wolfram Language, or Systems Modeling Language v1 (SysML^®) you may be interested in accessing the very comprehensive accompanying

Apply to access the comprehensive

UD$EX$Component “database” demo (using a Wolfram Language EntityStore)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

UD$EX$Components as (quick) XML

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

SysML Block Definition Diagram (BDD)

Mathematica: Webel ADT pseudo classes: An EX$Val has concise methods for testing the type of its wrapped '$$' value: isR, isI, isB, isQ, isS. These may be used in ADT "constructor" type tests.

Mathematica: Webel ADT pseudo classes: There does not seem to be a way to register ::usage specific to a Webel ADT-Method (TagSetDelayed UpValue). The Webel libraries offer method documentation support via the HelpO` class/method registry.

Webel: Mathematica: The Method syntax for the user contributed MTools does not seem to support Method-specific ::usage. The Webel libraries offer method documentation support (including arguments and options) via the HelpO` class/method registry.

Webel: Mathematica: The Method syntax for the user contributed MTools does not seem to support Wolfram Language Options[]. The Webel MTools extensions offer options support via a Webel Options Association in combination with the HelpO` method registry.

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: Webel OpenXML: The XL$Cell value accessor XL$Cell⊙valReal has no units-awareness; prefer the US$Cell value accessor US$Cell⊙val, which can return a Quantity.

UUID-driven Once-caching. Example: XL$Cell value resolution with an XL$ResourcesMap

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

XL$Cell value resolution for “text” requires an XL$ResourcesMap (Real, Integer, and Boolean value resolution does not)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Overview of the Webel OpenXML libraries ADT Case Study

ADT hierarchy for the XL` package for reading unstructured data from OpenXML XLSM bundles

ADT hierarchy for the US` package with intermediate unstructured data and identification of data groups

ADT hierarchy for the EX`package for extracted structured data

ADT hierarchy for a typical Client Data (CD) layer for identifying structured data groups

Typical unstructured spreadsheet data imported into the XL layer

XL$Row and XL$Cell under the hood

XL$Cell value resolution for “text” requires an XL$ResourcesMap (Real, Integer, and Boolean value resolution does not)

UUID-driven Once-caching. Example: XL$Cell value resolution with an XL$ResourcesMap

XL$Cell with a VBA formula and XL$F

XL$RowList vs XL$Row vs XL$Cell

Spreadsheet “units indicator” HACKS do NOT use a units-aware Quantity algebra!

Units and Quantity extraction with US$Row

US$RowList spanned rows filling

US$RowList sub-list extraction

US$RowList & EX$RowMap column extraction and custom styled tables

US$RowList “section” extraction

UD` demo package for US$Section

UD` demo: Basic US$ValuesSection

US$ValuesSection to EX$RowMap

US$SectionMap auto-detection

Specific Component-aware sub-ADTs

Demo Component values extraction (but not yet as EX Component ADTs)

The demo UD$EX$Component for extracted structured EX Layer data

The US$SheetManager as a bridge between the US Layer and EX Layer

Extracted demo UD$EX$Component:Demo UD$EX$Components: Creative views in the UD$SheetManager

Demo UD$EX$Components analyser

UD$EX$Components as (quick) XML

UD$EX$Component “database” demo (using a Wolfram Language EntityStore)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

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SysML Internal Block Diagram (IBD)

Chained wrapped ADT pseudo Lists: Example: EX` package structured data ADTs

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

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SysML Block Definition Diagram (BDD)

Webel «adt:pseudo» elements in the SysMLv1 ADT model (2)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

MAll: isContractOf for PatternTest (easier contract checks for MTools)

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

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SysML Block Definition Diagram (BDD)

The MNestAllDemo class with MAll or MAllDemo as child

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

The MNestAllDemo class with optional MAll ‘obj’ child

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

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SysML Block Definition Diagram (BDD)

SysML Internal Block Diagram (IBD)

Webel: SysML4Mathematica: An '@~' prefix in a @pseudo function (OpaqueBehavior or Activity) represents a cast from any expression to a Type. Example: '@~OpenerView' casts from any expression to an OpenerView. '@Type~' casts from a specific Type.

Webel: Mathematica: The Webel MAll universal base class does not itself use Webel method options (but does offer some support for method options for extending classes)

SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Introduction to Webel Abstract Data Types (ADTs) with SysMLv1 models

Webel Abstract Data Types (ADTs) vs the user-contributed MTools for OO

Webel ADTs include inheritance (and aren’t actually formal ADTs)

Webel ADT hierarchy views as tree, graph, and SysML

Mini SysMLv1 BDD view of the Webel ADT Block

SysMLv1 Internal Block Diagram (IBD) of the Webel ADT base class

Webel ADT`package: Some ADT pseudo class utility functions in a ::usage help viewer. Diagnostic, help, and development functions.

Simple Webel ADT in the development view dV[adt] and class/methods help hC[adt]

Classes in the ADT` package: Extendable ADT pseudo classes have corresponding "definer functions"

Creating new ADTs that extend other classes using a definer function (and adt$addSuper)

Extending ADT sub-classes represented as SysML Blocks with redefined wrapped ‘$$’

Webel «adt:pseudo» elements in the SysMLv1 ADT model (1)

Webel «adt:pseudo» elements in the SysMLv1 ADT model (2)

Chained wrapped ADT pseudo Lists: Example: EX` package structured data ADTs

Chained wrapped ADT pseudos as a SysMLv1 Internal Block Diagram (IBD)

Clients of List ADTs don’t usually directly access the wrapped Lists (but can for testing with ADT⊙get which BREAKS ENCAPSULATION)

Webel ADT SysMLv1 Stereotypes

adt$graphHierarchy example: The EX` package for structured data

ADT finder functions and “methods” adt$findUp, adt$findUpArg, ADT⊙fM

ADT help functions and methods: adt$treeHierarchy (adt$tH), adt$hC, ADT⊙hC: Example: XL$Cell

ADT`: helpADT[class]: help on methods registered with HelpO`: Example: XL$Cell

adt$store, adt$fetch, and «adt:ref»: Example: Reference XL$ResourcesMap by ID in US$ResourcesHolder.

Var` package: e$var$table[] filtering by package

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Var` package Entity-based variable registry

Var` package: Demo variables in e$var$table[] view

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Var` package Entity-based variable registry

Webel: Mathematica: CONVENTION: An '$SI$' in a function variant name indicates that all arguments are SI Real convention (no Quantity arguments with units). An '$SI$' function can also be used to generate '$C$' compiled function variants.

Mathematica: CONVENTION: A prefix 'eq$' indicates a symbolic equation (typically using 'sym$' human-friendly markup "symbols")

Var` package: Extracted Associations

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Var` package Entity-based variable registry

Webel: Mathematica: CONVENTION: A '$C$' in a function name indicates that it is a compiled variant. Typically it is compiled from an '$E$' symbolic function or an '$SI$' Real convention function.

Webel: Mathematica: CONVENTION: An '$E$' in a function name indicates that it is symbolic (takes Blank expression arguments). An '$E$' function can also be used with Quantity inputs and can be used to generate '$C$' compiled function variants.

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SysML Package Diagram

Introduction to the Webel All` package and the MAll universal class extending MTools

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

Slide kind

SysML Block Definition Diagram (BDD)

Use an MOptsSet options group: Example: MAllDemo.methodWithOptsSet uses MOptsSetDemo

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

Slide kind

SysML Activity Diagram

SysML Block Definition Diagram (BDD)

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Introduction to the Webel All` package and the MAll universal class extending MTools

The Webel W`MOO` packages: MOO = MTools OO support utilities

The Webel MAll universal (intermediate) base class

MDemo`: Overview of demo classes for MAll & MOptsSet

MAll: All public Methods with signatures

MAll: methodHelp and methodFind: Short aliases mH and mF

MAll: Methods related to classes and contracts: Example: MDemoAll: From the MAll self-test GUI

MAll: isContractOf for PatternTest (easier contract checks for MTools)

The Webel MAll universal class for MTools integrates with the HelpO` method registry

HelpO`: Options management for MTools methods (lookup replaces OptionValue[])

The MAllDemo class with MOptsSetDemo

Registering method options using a Webel AOR (Argument, Options, Rules) Map

Use a method with an option via a Webel opts Association

MOptSet options groups: Example: MOptSetDemo

Use an MOptsSet options group: Example: MAllDemo.methodWithOptsSet uses MOptsSetDemo

An MOptSet can also be used in function Options[]

The MNestAllDemo class with optional MAll ‘obj’ child

The MNestAllDemo class with MAll or MAllDemo as child

Every MAll has a default gui[] for methods that don’t need arguments

Command GUI configuration and nesting: Example: MNestAllDemo

The MAll class has a self-tester GUI (for DEVELOPMENT use only)

Convention-based MDemoConfig with fields for ‘$opt$’ options (works with any MTools class but prefer MOptsSet or MOpt)

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SysML Block Definition Diagram (BDD)

The AOR Map (Attributes, Options, Rules) Association: Example: aor$f$helpClass

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

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SysML Block Definition Diagram (BDD)

The AOR Map (Arguments, Options, Rules): Integrated ::usage, HelpF`/HelpO` registration, and Options[] (without MTools)

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

Slide kind

SysML Block Definition Diagram (BDD)

Webel ODR (Options, Docs, Rules) as SysML

This content has been marked as discussing an ADVANCED topic!

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

HelpF`: OptionsPattern groups as SysML shared between functions

This content has been marked as discussing an ADVANCED topic!

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

Generate shared option groups using ‘$opt$’ helpers: wl$optsFromOpts, docsFromOpts, rulesFromOpts, and odrMap triplet

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

SysML: OptionsPattern[] “Generalizations” using Join:" Example: HelpM` helper classes new functions

This content has been marked as discussing an ADVANCED topic!

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

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SysML Block Definition Diagram (BDD)

About «pseudo» blocks (always prefixed with ‘@’)

This content has been marked as discussing an ADVANCED topic!

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions

Basic SysMLv1 example: The HelpM` package MTools classes as Blocks

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions

Slide kind

SysML Block Definition Diagram (BDD)

SysML Package Diagram

SECTION: The Webel Var` package Entity-based variable registry

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

About the Webel Var` package variables registry

Var` package variables registry example: Heat exchanger calculations (just p1 of 227 variables!)

Var` package variables registry example: Heat exchanger calculations (just p2 of 227 variables!)

Var` package: Special '$e$' field convention

Var` package: Package function ::usage overview

Var` package: “qualified name” String as key

Var` package: Register variables with e$var$add

Var` package: ‘sym$’ markup reused in ‘$E$’ functions

Var` package: Extracted Associations

Var` package: Demo variables in e$var$table[] view

Var` package: e$var$table[] filtering by package

HelpM`: Using the Webel MPackage helper with MFunction and MClass and the HelpF` and HelpO` help registries

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

Webel: Mathematica: CONVENTION: A '$doc$' prefix indicates a formatted documentation String helper. A '$doc$arg$' is for an argument, a '$doc$opt$' is for an option. A '$doc$ String may be used to create ::usage documentation via docF.

Doc` package ::usage help generation using the docV and docF functions (1)

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Doc` package ::usage help generation using the docV and docF functions (1)

Doc` package ::usage help generation using the docV and docF functions (2)

Why the Webel HelpF` & HelpO` registries?

The Webel HelpF` function registry

HelpF`example: helpFunction[$pac$HelpF, addFunction]

HelpF`example: helpPackage[$pac$HelpF]

HelpF`example: addFunction (1)

HelpF`example: addFunction (2)

Generate shared option groups using ‘$opt$’ helpers: wl$optsFromOpts, docsFromOpts, rulesFromOpts, and odrMap triplet

HelpF`: OptionsPattern groups as SysML shared between functions

Webel ODR (Options, Docs, Rules) as SysML

HelpF`: Pull Mathematica Options[] from a Webel HelpF` options superset

HelpF`: Pull Mathematica Options[] for a function registered with addFunction

HelpF`: usageF for ::usage generation example

HelpF`: UsageF ::usage generation: Example helpClass::usage

The HelpF` & TestF` packages: General query based help

HelpF`: packageFunctionTree[$pac]: Function ::usage help and signatures within a package

HelpF`: DownValues: sigsDown[f]: Signature(s) from ExpressionTree

HelpF`: Simple function DownValues inspector GUI: gui$helpDownStrings

HelpF`: gui$helpDownStrings signature display modes

TestF`: Simple package function DownValues vs ::usage checker

TestF`: Function search by argument number/kind to aid testing automation (1)

TestF`: Function search by argument number/kind to aid testing automation (2)

The Webel HelpO`package class and method registry

HelpO`: addClass: Register an MTools class by fully qualified package name

HelpO`: addMethod: MTools method registration example for the Webel MAll class and an object

HelpO`: Part of the help registry for the Webel MAll universal MTools class and some methods

HelpO`: Find help on a method of a Webel MAll universal class object

HelpM`: Using the MFunction and MMethod helper classes with MArg & MOpt

HelpM`: Using the Webel MFunction class and MArg & MOpt with HelpF`

HelpM`: Using the Webel MMethod class and MArg & MOpt with HelpO`

HelpM`: Use MFunction and MMethod with MArg & MOpt for ::usage (and consistent with the HelpF` and HelpO` registries)

HelpM`: Using the Webel MClass helper with the MMethod helper and the HelpO` help registry

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: A brief look at the Webel W`Base` utilities for Mathematica

Some Webel Utility` package functions

Gallery

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: A brief look at the Webel W`Base` utilities for Mathematica

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Webel coding and naming conventions for the Wolfram Language

Webel: Mathematica: CONVENTION: A '$t$' prefix indicates a String help holder with a "pseudo type" indicator (for human friendly documentation only). Used by the Doc`, HelpF`, and HelpO` packages.

The Webel ‘$t$’ “pseudo type” indicator String convention (for optional additional documentation only)

Gallery

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Webel coding and naming conventions for the Wolfram Language

The Webel ‘$pat$’ pattern helper convention for frequently used Patterns

Gallery

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Webel coding and naming conventions for the Wolfram Language

Webel: Mathematica: CONVENTION: A function's description (but not its signature, arguments, or options) may be captured as an '$info$f$' Stringhelp holder for use by the Doc` package for ::usage generation and the HelpF`& HelpO` help registry packages.

Webel ‘$info$f$’ prefix convention for function help holder Strings

Gallery

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: Webel coding and naming conventions for the Wolfram Language

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

The Webel '$opt$', 'rule$opt$', '$arg$', 'rule$arg$' and supporting '$k$' conventions for "help holders"

The Webel '$opt$' option "help holder" convention

Webel ‘$opt$grp$’ with grouping qualifier (where ‘grp$’ could be a package nickname)

Webel '$opt$' options help by function: Example: tableFunctionOptions[f]

Cleaner Options declarations!

Webel '$arg$' and '$opt$' support via the Doc` package

Functions from the W`Base`Doc` package

Make a Webel option help Rule relying on ‘$opt$’ naming conventions

Webel ‘$arg$’, ‘def$arg$’, and ‘rule$arg$’ convention

Make a Webel help Rule for a required ‘$arg$’ argument + conventions

Make a Webel argument help Rule with a default by convention OR override

Webel $arg$ convention help consistency checks

Webel ‘rule$arg$’ convention help consistency checks

Generate $doc$arg$ and $doc$opt$ Strings from Webel help Rules for use in ::usage

When to use explicit $arg$ help holders (in lower level utility packages)

Why not just generate all the '$arg$' and '$opt$' help holders (using ToExpression)?

Why not just use the Entity system for '$arg$' and '$opt$' help holders?

Association vs Class as SysML CASE: Webel $arg$ and $opt$ help

Association as SysML: CASE: Webel @RuleMap and @ArgsMap «pseudo» blocks. Very "fiddly" to represent in a SysML Block Definition Diagram!

Association as SysML: CASE: Webel @ArgMap «pseudo» block (slightly less "fiddly" as an Internal Block Diagram)

Easier ‘$arg$’ and ‘$opt$’ help Rules using the Webel MArg and MOpt helper classes and MTools for OO

Webel ‘$arg$’ help is much easier with the MArg class using MTools!

Webel ‘$opt$’ help is much easier with the MOpt class using MTools!

Webel ‘$opt$’ help even easier with makeOpt[$name] for MOpt!

HelpM`: Use Webel MOpt and MArg objects to create ‘$doc$’ Strings for ::usage help

SysML: OptionsPattern[] “Generalizations” using Join:" Example: HelpM` helper classes new functions

The AOR Map (Arguments, Options, Rules): Integrated ::usage, HelpF`/HelpO` registration, and Options[] (without MTools)

Webel: Mathematica: A help Rule 'rule$arg' for an '$arg$' (argument) accepts keys: '$k$help' (required), '$k$def' (required if $k$req = True not given), '$k$req' (True if $k$def not given), '$k$warn', '$k$tip', '$k$lab', '$k$type', '$k$mult' and '$k$pat'

Webel: Mathematica: CONVENTION: Where keys of Associations are Strings they are encapsulated as variables prefixed with '$k$' (promotes DRY and has many advantages, such as IDE prompting). Direct use of "Strings" as keys is WET and strongly discouraged!

Webel: Mathematica: CONVENTION: "pattern helpers" (which are not themselves Patterns) use the prefix '$pat$. Encapsulated Patterns use a 'pat$' prefix, and may use a '$pat$' pattern helper (such as an Alternatives).

Gallery

Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Section

SECTION: The Webel Mathematica libraries - INTRODUCTION - And the role of SysML

SECTION: A brief look at the Webel W`Base` utilities for Mathematica

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

The Webel W`Base`«M:Project» and «M:Paclet»

Overview of Webel utility W`Base` packages as SysMLv1 Blocks

Overview of Webel utilities W`Base` packages as SysML Usages

Detailed overview of Webel utilities W`Base` packages with usages

Webel W`Base` vs Git repository and Wolfram Player Pro encoded version

Some Webel Devel` package functions

Diagnostic message Print output switching between Mathematica and Wolfram Player Pro

Devel` package: check Function Symbol against ::usage

Devel` functions for ExpressionTree (basic)

Some Webel Utility` package functions

The Webel ‘$pac$’ convention and DEVEL loading echo diagnostics

Utility`package: stripOpt and stripOpts Delegating subsets of Options

Some Webel Display` package functions

The Webel ManGUI` package utilities for Manipulate GUIs

The Webel ManGUI` package has some shorthand '$man$' option aliases

Some Webel ManGUI` package functions

The Webel Units` library with short-cut variables for frequently used Units and their String identifiers

Webel ManGUI` examples: man$bool and man$group$pane

The Webel W`Moo` package group: Additional utilities for the user-contributed MTools paclet for classes & object orientation

Deployment folders for projects that depend on W`Base` and MTools OO (as SysML)

SECTION: Webel coding and naming conventions for the Wolfram Language

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

DRY not WET! "Don't Repeat Yourself!"

The Webel ‘$’ prefix convention for Strings and "String similar" Wolfram Language code

The Webel $k$ prefix convention for Association String keys

The Webel ‘$pat$’ pattern helper convention for frequently used Patterns

The Webel ‘$t$’ “pseudo type” indicator String convention (for optional additional documentation only)

Webel ‘$info$f$’ prefix convention for function help holder Strings

Webel ‘def$’ DRY default capture! Applicable to arguments and options.

SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

Modelling the Wolfram Language in SysML and SysML-friendly coding conventions.

Basic SysMLv1 example: The HelpM` package MTools classes as Blocks

SysML Stereotypes and icons used for Mathematica and Wolfram technologies

Wolfram Language vs SysMLv1

Parameter types in most SysML tools

Explicit vs implicit representation of expressions in SysML4Mathematica

Webel SysML4Mathematica: Some Wolfram Language Heads as SysMLv1 Blocks and ValueTypes

Concise {} for List and <||> for Association

Frequently used typed {} Lists

Frequently used String pair Lists

Association <||> vs Rule

Typed Association example: <||>$* maps String to any expression

“Active” OpaqueBehaviors corresponding to block Heads: Used in CallBehaviorActions

“Chained” Head and OpaqueBehavior Convenient for frequently used combinations

Example: Representation of a Webel MAll class MTools method as a SysML Activity Diagram

SysML Activities as function networks (simple contrived Real maths example)

SysML/UML ExpansionRegion for iteration (as adapted for use with Mathematica)

SysML Activity with @pseudo functions capturing Wolfram Language logic

The sigsUp/Down functions as a SysML BDD: With Options Block and pseudo functional indicators

The sigsUp function with OptionsPattern modelled as a SysML Activity (and with "pseudo functional" representation)

Extract Options from an OptionsPattern[] in a SysML Activity (1)

Extract Options from an OptionsPattern[] in a SysML Activity (2) DETAILED

About «pseudo» blocks (always prefixed with ‘@’)

SECTION: The Webel Mathematica libraries - INTRODUCTION - And the role of SysML

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Jump to first slide

DISCLAIMERS & CONCERNING TRADEMARKS

Sections

SECTION: The Webel Mathematica libraries - INTRODUCTION - And the role of SysML

SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions

SECTION: Webel coding and naming conventions for the Wolfram Language

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

SECTION: A brief look at the Webel W`Base` utilities for Mathematica

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

SECTION: The Webel Var` package Entity-based variable registry

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

[PUBLIC VERSION PENDING] SECTION: CASE STUDY: Applications of the Webel MTools class extensions to air conditioners and heat exchangers. With SysMLv1 models.

Service: Mathematica-driven spreadsheet data and equation migration to Wolfram Cloud or database or XML Schema or JSON with GUI and more.

Keywords

Please email or phone Webel IT Australia on +61 405 029 008 to enquire about our Mathematica-driven spreadsheet data and equation migration services!

Do you have have "siloed" data and VBA formulae and macros stuck in old spreadsheet files from Excel or LibreOffice Calc?

Buy Mathematica-generated Tessellation Art in 8K high resolution as quality Acrylic Float Frame mounted prints delivered worldwide!

Keywords

Mathematica isn't just brilliant for symbolic algebra, data analysis, and visualisation, it is a simply amazing tool for generating high quality Maths Art, such as these amazing colourful high resolution 8K Tessellation Art images, which are available for purchase as quality Acrylic Float Frame mounted prints, delivered worldwide. Includes both pure tessellations and tessellations combined with visual FX.

Mathematica: TIP: Start with With, update to Module as needed.

Mathematica: SUPER TIP: Use CreateUUID[] to trigger recalculation against Once[] to create a flexible optionally caching function! (May incur a memory penalty, consider also using a 'loc' persistence location.)

Mathematica: GOTCHA: The Problems Analysis review system of Mathematica Plugin for IntelliJ IDEA reports a declared Module variable used as a Table loop variable as an "Used local variable". DO NOT SIMPLY DELETE IT!

Mathematica: TIP/GOTCHA: When using a Table loop variable within a Module always declare a module variable for it or you can get very hard to track side-effects elsewhere in your project due to exposed scope. Yes, it's obvious (yet easy to miss).

Mathematica: Webel: A concise i:/o: notation is often used for indicating input/output cells in Mathematica notebooks in Webel's online help pages and tutorials, instead of 'In[n]:=' and 'Out[n]='. (Also learn how to hide them completely in notebooks.)

Mathematica: Webel ADT pseudo classes: POLICY: The ADT-Methods of an ADT-Class are created as TagSetDelayed UpValues using the 'signature' of the ADT-Class and its defining 'pattern' as 1st argument

Mathematica: Webel ADT pseudo classes: CONVENTION: PROVISIONAL: The infix operator for calling ADT-Methods on ADT "objects" is the CircleDot (⊙ in Notebooks). ISSUE: \[CircleDot] is NOT GOOD FOR USE IN IDEs!

Dr Darren of Webel IT Australia makes the case for better object-orientation for Mathematica using pseudo class ADTs without losing the super-functional power of the Wolfram Language

Gallery

Tutorial

Mathematica: POLICY NOTES for the Webel Abstract Data Type (ADT) pseudo classes with inheritance for the Wolfram Language

Section

Mathematica: Webel ADT pseudo classes: POLICY/DEFINITION: Every "hard coded" definer or defining client of a definer has a corresponding ADT ArchetypeClass. Example ("hard coded"): The definer 'my$def$MY$SmartList' has ArchetypeClass 'MY$SmartList'.

Mathematica: Webel ADT pseudo classes: TIP: Prefer the Decorator Pattern over multiple inheritance of ADT-Method UpValues! (But not because "inheritance is evil" per se, it isn't.) The base ADT libraries make heavy (and very useful) use in inheritance.

Mathematica: Webel ADT pseudo classes: A tricky POLICY & CONVENTION: Client packages MUST access the special "wrapped" primary '$$' via $ContextAliases! The recommended alias is "A`" (which stands of course for ADT).

Mathematica: Webel ADT pseudo classes: POLICY: Multiple inheritance is supported via ONE (only) ADT-Class and one or more ADT-MemberInterfaces (which have no ADT-Method UpValues)

Mathematica: Webel ADT pseudo classes: POLICY: Definer functions MUST return the self-declared or injected 'pattern' that determines the unique "ADT-signature" of the defined ADT class.

Mathematica: Webel ADT pseudo classes: ADTs that define membership of ADT-classes in a domain package have ADT-signature MemberInterface[$$:None] and MUST NOT populate ADT-method UpValues in their definers.

Mathematica: Webel ADT pseudo classes: NAMING CONVENTION: An UpValue that can be invoked on an ADT accepting its unique 'signature' pattern as (at least) 1st argument is called an 'ADT-Method'. They are NOT methods in the general object-oriented sense!

Mathematica: Webel ADT pseudo classes: There is an 'ADT' universal base that has no supers. It "blesses" every other sub-class ADT by populating it with some common ADT-Method UpValues against a signature pattern via the 'adt$def$All[]' definer function.

Mathematica: Webel ADT pseudo classes: DEFINITION/CONVENTION: Functions that populate ADTs with reusable ADT-method UpValues are called 'definers' and include '$def' in the name after a Package scope indicator: Example: adt$def$ADT, my$def$MY$CleverList

Mathematica: Webel ADT pseudo classes: POLICY: Every named concrete Abstract Data Type (ADT) has a ONE unique "signature" (which is the pattern passed to the "definer" functions). To vary a signature, define another unique ADT name.

Mathematica: Webel ADT pseudo classes: POLICY: The Abstract Data Types (ADTs) are stateless functional (although inheritance and overrides are supported), with no caching by default (although there is nice optional caching using CreateUUID[] and Once[]).

Mathematica: Webel ADT: The term 'Abstract Data Types (ADT)' is used informally (the Webel ADTs do not always adhere to strict definitions of ADTs). Please just think of it here as meaning a strong type or stateless "pseudo class".

Wolfram Player Pro zone (deployment environment for Mathematica Notebooks)

Keywords

Wolfram Player Pro is a low cost desktop application deployment solution for Mathematica Notebooks. It is "read only" w.r.t. new command lines, but end users can of course input data via Graphical User Interface (GUI) form elements. It supports truly rapid development GUIs that hide all of the complexity of the Wolfram Language.

Mathematica: Webel ADT pseudo classes: POLICY: The expression '$$' is reserved as the primary named parameter for the defining pattern of all ADT classes that extend the universal base 'ADT' class.

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 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: POLICY NOTES for the Webel Abstract Data Type (ADT) pseudo classes with inheritance for the Wolfram Language

Jump to first slide

Dr Darren of Webel IT Australia makes the case for better object-orientation for Mathematica using pseudo class ADTs without losing the super-functional power of the Wolfram Language

Sections

Mathematica: GOTCHA: The Module/With system (especially under rewriting when nested) can leave variables with a trailing '$' suffix, which may cause name clashes because the variables (expressions) are available later outside the scope of the Module/With!

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)!

TIP: SysMLv1: MagicDraw/Cameo: Activity Diagrams: Consider using the Pin display mode 'Name And Type Labels Inside' for 'Position of Labels'. Dr Darren swears by it!

Mathematica: TIP: Notebooks: Automatic Cell Grouping driving you up the wall? Try Manual Grouping and make it part of your workflow!

Webel: Psy/MPsy: Psychrometrics for Mathematica: '$HC' in a function name indicates pure sensible heating or cooling (with no change in water vapour content). Such functions may also be used in the pure sensible portion of a 2-step treatment.

Mathematica: The output form of Mathematica follows internal rules that may not always correspond exactly to how a human might typeset it.

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)

SysMLv1.x: Limitation: The 'body' (maths formula) of an OpaqueBehavior can't be synchronised (shared) with the 'constraint' of a ConstraintBlock (directly in the SysML model). Can lead to a WET (not DRY) model and breaks Single Source of Truth!

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 custom SysML ValueType 'Quantity' extends a custom ValueType '_' (representing a Mathematica '_' Blank). It DOES NOT also extend the SysML Real!

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

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

Slide kind

SysML Block Definition Diagram (BDD)

Webel: Psy/MPsy: Psychrometrics for Mathematica: Convention: Option variable names are prefixed with '$opt$psy'

Webel: Mathematica: CONVENTION: Option help holders use a String variable with the prefix '$opt$', a related '$info$opt$' String, a 'def$opt$' default value expression, and optional '$warn$opt$', '$tip$opt$', '$lab$opt$', and 'type$opt$' indicator ...

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.)

CoolProp: Mathematica wrapper: Psychrometrics (humid air): When obtaining the dew point temperature 'Tdp' at the pressure 'P', humidity ratio 'W', and dry bulb temperature 'Tdb', the 'Tdb' value will be "ignored" but MUST be within a sensible range!

Webel: Psy/MPsy: Psychrometrics for Mathematica: The default newPsy[tdb] builder accepts the pressure 'p' as an option, which defaults to sea level atmospheric pressure.

Webel: Psy/MPsy: Psychrometrics for Mathematica: The CoolProp "wrappers" of the Psy library in fact wrap lower-level wrappers (bindings) for CoolProp for Mathematica

Webel: Psy/MPsy: Psychrometrics for Mathematica: The default MPsy class is a readonly one-shot class that pre-builds many frequently used psychrometric properties (offered as public fields) using CoolProp, and also offers some value-adding methods.

Webel: Psy/MPsy: Psychrometrics for Mathematica: The default newPsy[tdb] builder requires the dry bulb temperature 'tdb', and one (only) of the relative humidity 'r', the humidity ratio 'w', or the wet bulb temperature 'twb' (as options).

Webel: SysML4Mathematica: SysML Parametric Diagrams are not well suited to modelling calculations with Blocks for MTools classes, or for modelling complex logic flow of Mathematica functions. Prefer SysML Activity Diagrams for those modelling cases.

The Webel SysML4Mathematica recipe for modelling Wolfram Language code in Systems Modeling Language (SysML) for Model-Based Systems Engineering

Keywords

New!

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!

SysML4Mathematica: Example 11 [B]: Total (qDotTot), sensible (qDotSen), and latent cooling (qDotLat) required for cooling air: Using Webel MPsy objects and SysML Activity Diagrams

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

Slide kind

SysML Activity Diagram

SysML4Mathematica: Example 11 [A] Total (qDotTot), sensible (qDotSen), and latent cooling (qDotLat) required for cooling air: Using CoolProp wrappers and SysML Parametric Diagrams

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

Slide kind

SysML Parametric Diagram

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.

SysML4Mathematica: Example 10: Condition and dehumidify air by chilling and condensing some moisture: Process table

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

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SysML Activity Diagram

SysML Parametric Diagram

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)

SysML4Mathematica: Example 09: Moisture added to air: Amount (mass)

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

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SysML Activity Diagram

SysML Parametric Diagram

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)

SysML4Mathematica: Example 08a: Humidification: Drying lumber with air: required volumetric air flow rate

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

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SysML Activity Diagram

SysML Parametric Diagram

SysML4Mathematica: Example 07: Sensible cooling: 'qDotSen' (-ve): energy transfer rate FROM humid air

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

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SysML Activity Diagram

SysML Parametric Diagram

Webel: Psy/MPsy: Psychrometrics for Mathematica: Most CoolProp wrappers can be invoked with the dry bulb temperature 'tdb', the pressure 'p', and one (only) of the relative humidity 'r', the humidity ratio 'w', or the wet bulb temperature 'twb'

Webel: Psy/MPsy: Psychrometrics for Mathematica: Due to Mathematica's units-aware Quantity algebra system it is irrelevant what units are used for the input Quantities for creation of the MPsy objects, as long as they are dimensionally consistent!

SysML4Mathematica: Example 06: Sensible heating: 'qSen' per mass (+ve): energy transfer TO humid air

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

Slide kind

SysML Activity Diagram

SysML Parametric Diagram

SysML4Mathematica: Example 05: Sensible heating: 'qSen' (+ve): energy transfer TO humid air

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

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SysML Activity Diagram

SysML Parametric Diagram

SysML4Mathematica: Psychrometrics (humid air physics) Air Conditioning scenarios in graphical Systems Modeling Language (SysMLv1.x) and Mathematica

Gallery

Tutorial

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Section

Slide kind

SysML Package Diagram

Mathematica: v13.2+: Division of one temperature by another will result in a numeric ratio given by the value of both temperatures in Kelvin.

Source

Wolfram Language (Mathematica) online help reference

Mathematica: v13.2+: Division by temperature units will produce a quantity equivalent to the temperature converted to Kelvin before division, with results canonically given in Kelvin.

Source

Wolfram Language (Mathematica) online help reference

Wolfram Language (Mathematica) online help reference

GOTCHA: Mathematica v13.2+: Operations on "DegreesFahrenheit" °F and "DegreesCelsius" °C are now performed using Kelvins (K). CASE: Naive percentage operation gives answer relative to Kelvins. Use "DegreesCelsiusDifference"/"DegreesFahrenheitDifference"!

Webel: Psy/MPsy: Psychrometrics for Mathematica: Transferred heat (energy "Q") has field names with lower case 'qTot', 'qSen', 'qLat'. Heat rates (energy per time) have field names 'qDotTot', 'qDotSen', 'qDotLat' (to avoid clashes with Mathematica core)

Webel: Psy/MPsy: Psychrometrics for Mathematica: Relative humidity is indicated by a lower case 'r' and measured as a Real fraction (rather than as a Percentage). [Some tables and plots do SHOW the relative humidity as a Percentage.]

Mathematica: Notebooks: Automatic Cell Grouping mode can be a "royal pain", turn it off by setting Cell > Grouping > Manual Grouping

Webel: Psy/MPsy: Psychrometrics for Mathematica: Humidity ratio (absolute humidity) is indicated by a lower case 'w' and measured in mass (water) / mass (dry air) units, so the SI and IP representations are equal Real (without an explicit unit system)

TRAIL: Air Conditioning Psychrometrics (vs CED Engineering course): Example results (only) in Mathematica and SysML using the Webel Psy package and MPsy class

Jump to first slide

Example 01: Values from 'tdb' and relative humidity 'r'

Sections

GOTCHA: Mathematica: Specific enthalpy conversion J/kg to Btu/lb: Does not consider a possible "total" enthalpy reference offset vs 0 °C or 0 °F respectively

Mathematica: HOWTO: Add every element of one list to the end of another list

[FIXED in v2022Refresh1]: BUG: MagicDraw/Cameo: 19SP3/v2022xGolden: Activity Diagrams: Pin display mode 'Position of Labels' does not stick, label positions in Diagrams have sometimes moved after re-opening a project [and "FIX"]

ARCHIVAL (2022): This content is now considered historical only!

The Webel Recipe for SysML-friendly Wolfram Language coding in Mathematica

Keywords

Keywords

Webel:MathematicaSysML

Mathematica

Wolfram

SysML

Systems Modeling Language

Model-Based Systems Engineering

MD SysML

MagicDraw

MagicDraw SysML

MagicDraw UML

Unified Modeling Language

UML

CATIA Magic

CATIA Magic:v2022xGolden

Cameo Systems Modeler

Magic Model Analyst [Cameo Simulation Toolkit]

functional programming

As part of a long term project developed, initially during work for a client, Webel IT Australia in partnership with GreenSoft Pty Ltd is developing a very complex Mathematica application with substantial SysML modelling support.

Mathematica: Wolfram Player Pro 13.1: NotebookDelete[] does not work

Mathematica: v13.1: There is an undocumented command MessagesNotebook[]

Mathematica: GOTCHA: Print[] from Manipulate always goes to the Messages console notebook

Mathematica: 'Through' is your more functional friend.

THE BIG TIP: You brain has many facets: code + graphical engineering is greater than either alone

TIP: Mathematica: Use of For is often a hint that Map, Table, Scan, or something else more functional could be used. But don't stress over it!

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: TIP: Protecting against computations breaking verbosely because of Null, None, Undefined. And about using Undefined as a return policy.

Mathematica: The Webel Units` package has Quantity variables for frequently used units using a naming convention 'unit$[Symbol]' or 'unit[DescriptiveName]' or unit[Acronym], each with a corresponding '$unit...' for the units identifier String(s).

Mathematica: Use of UnitConvert (or even just multiplication or division by a unit Quantity) MASSIVELY slows the calculations down!

Mathematica: Compile won't work with a Quantity with units

CoolProp: HOWTO reproduce a pressure vs specific enthalpy chart in Mathematica. Example: R32 refrigerant.

Mathematica: TIP: The ThermodynamicData function of Mathematica uses NIST's RefProp under the hood.

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)

Mathematica: MTools: Argument Pattern strong type matching does not intrinsically respect inheritance (makes implementing design-by-contract and some Design Patterns less convenient). But you can use PatternTests with Webel MAll extensions.

Webel + Mathematica + MTools + SysML

Mathematica: LINKS: Manipulating Strings and using RegularExpression

Mathematica: GOTCHA: Null is tricky!

Mathematica: Wolfram Workbench: Basic variable name refactoring is not supported. (Or just use the IntelliJ IDEA Plugin for Mathematica, which does variable and function renaming well.)

Mathematica: Objectica 3rd-party commercial package for OO in Mathematica. Earth calling Objectica, do you still exist?

Mathematica: Wolfram Workbench: Sometimes the Outline view gets completely out of sync with the .m or .wl Package code

Mathematica: Wolfram Workbench: Sometimes the code syntax checking goes haywire (with red nearly everywhere) for no good reason (even when the code load and runs fine in Mathematica). WORKAROUND: Just restart Eclipse.

Webel vs Mathematica: The Very Good, The Bad, and The Ugly

Mathematica: TIP: Try //Dataset on just about anything and be amazed! Click on nearly anything to navigate through nearly anything in impressively interactive human-readable format.

Mathematica: How mimic pattern matching of arguments for pseudo "Boolean" (including providing a default)?

Mathematica: The awesome Quantity system for values with units is everything the SysMLv1.x Quantity/Unit system should have been (and hopefully SysMLv2 will be). But it comes at a high performance cost!

Daikin Australia air conditioning

Mathematica: TIPS for living with the user-contributed MTools for Object-Orientation (until a vendor-supported OO solution is eventually provided)

Wolfram Workbench for Mathematica: Limitation: Using more than one '$' sign within function names blocks navigation on function usages.

Mathematica: GOTCHA: EntityFunction can only return a scalar.

Mathematica: Some links on Object-Orientation (or the lack thereof)

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

Mathematica: TIP: LINKS: Filename chooser dialogs

GOTCHA/BUG: Cameo Simulation Toolkit v2021xR1 + Mathematica: Delegation to Mathematica from ConstraintBlocks FAILS if any of the input or output parameters are larger than 99999 because they get interpreted as 1.0e5 and that trips something! Aarrrggggh!

LINKS: Wolfram Workbench for Mathematica (or just use the far superior IntelliJ IDEA Plugin)

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

Mathematica: HOWTO Autoload the simplest possible .m or .wl Package file with a few custom functions

Mathematica + Magic Model Analyst (Cameo Simulation Toolkit) for SysML Parametrics: GOTCHA: You must use a regular '=' on the SysML side, not the Mathematica '==' (or it will be intepreted as a constraint condition to test, not an equation to solve).

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

Mathematica: TIP: Package Editor mode: Use cell division between every function in .wl library files to make them more readable (and to make it easier to apply at least some degree automated code formatting per function).

Webel: Mathematica is functional programming on steroids (and has nearly everything else, except for decent in-built OO support, although you can make some progress with Abstract Data Types and even some inheritance).

Webel: Mathematica: WISHLIST: Support for EXTRACTABLE structured documentation for individual arguments of functions RIGHT IN/NEAR THE CODE. Yes it is needed, really it is. (And ::usage support for "methods" would be nice too.)

Webel: Mathematica: WISHLIST: Support for decent vendor-supported, built-in, fully fledged, IDE-friendly, object-orientation (OO)! [With or without the use of state, which is a choice, not obligatory, and OO doesn't throw functional away]

Mathematica: Webel: You CAN/MAY use $ in variable names and function names - just not as the first character before a Capital - and it's extremely useful. You won't get sent to Azkaban prison if do you use a $ character!

Mathematica: Having trouble clearing a variable with complex formatting? Try =.

Mathematica: HOWTO Manage test data for functions using rules across multiple functions (and about the Webel '$0' variable suffix convention for substitution targets).

Mathematica: HOWTO: Strip an option from an OptionsPattern[] sequence before passing down (propagating) to a function with fewer options

Mathematica: Nasser M. Abbasi's cheat sheet

Mathematica: HOWTO Convert a list into a Sequence of arguments to a function (where each of the arguments to the function corresponds to a list item)

Mathematica: HOWTO Create collapsible control groups in Manipulate GUIs

Mathematica: TIP: OverDot: Type CTRL & and then . to enter an OverDot directly

Mathematica: TIP: OverBar: Type CTRL & and then _ to enter an OverBar directly

Mathematica: v12.3.1.0: How to obtain values of physical constants

Mathematica: GOTCHA: MMA distinguishes between Kelvins and KelvinsDifference

MagicDraw/Cameo 19SP3/v2022xGolden: [FIXED in v2022xRefresh1]: Activity Diagrams: Pin display mode 'Position of Labels' does not work correctly for 'Name And Type Labels Inside', only shows the Name inside (not the Label) [and WORKAROUND]

ARCHIVAL (2022): This content is now considered historical only!

Q: What types of simulation, execution, and calculation are available for SysML with MagicDraw/Cameo?

Keywords

Keywords

simulation

calculation

mathematics

Mathematica

Maple

MATLAB

SysML

Model-Based Systems Engineering

MBSE

Systems Modeling Language

Cameo Systems Modeler

MD SysML

MagicDraw SysML

MagicDraw UML

fUML

There are a number of ways of simulating and executing various aspects of Systems Modeling Language v1 (SysML^®), and they are not just novelties! They also really help your models become more robust, logical, and organised.

There is "internal" tool simulation of Activities and StateMachines based on fUML (or variations of it).

External simulation: Languages and tools: SysML vs SysPhS vs Modelica vs Simulink

Gallery

Tutorial

MINI TRAIL: Some recommended tools for getting started with Model-Based Systems Engineering with SysML and simulation with Modelica and/or Simulink

Section

Wolfram SystemModeler zone

Keywords

Keywords

Wolfram

Modelica

Mathematica

Wolfram SystemModeler

simulation

execution

NEWS: SysML Extension for Physical Interaction and Signal Flow Simulation (SysPhS): New technology assessment trail: TRAIL: SysPhS-1.1 specification body figures in MagicDraw/Cameo SysML vs Modelica [using Wolfram SystemsModeler]

NEWS: SysML Extension for Physical Interaction and Signal Flow Simulation (SysPhS): New techn

MagicDraw/Cameo support for the SysML Parametric Diagram and ConstraintBlocks for equations and mathematics is excellent, and it integrates with powerful maths engines such as Mathematica. It CAN be used on industrial strength real-world projects.

Mathematica and Wolfram Language zone

Keywords

Keywords

mathematics

symbolic algebra

Mathematica

Wolfram

Wolfram Language

data visualisation

data

data mapping

data analysis

graphics

animation

physics

simulation

graph

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.

Service: Wolfram Mathematica: Modelling, data analysis, mapping, transformation, and visualisation, including end-user GUIs

Keywords

Keywords

service

data

data analysis

data mapping

data transformation

data visualisation

animation

image processing

3D

3D modelling

Wolfram

Wolfram Language

Wolfram Player Pro

Mathematica

symbolic algebra

numerical analysis

equation

XML Schema

XML

simulation

Webel IT Australia are experts in applications of the powerful Wolfram Mathematica technical computing system to symbolic algebra, equation analysis, numerical analysis, physics and engineering simulations, data analysis and transformation, plotting, generative graphics, 3D modelling, animation, image processing, and rapid desktop GUI development for end users for deployment to Wolfram Player Pro, or as Wolfram Cloud applications.

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