Mathematica

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!

[STUB] TRAIL: Mathematica: The Webel recipe for Abstract Data Type (ADT) pseudo classes with inheritance for the Wolfram Language

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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

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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: COMING SOON! Webel's ultimate guide to using Abstract Data Types to create pseudo-classes WITH INHERITANCE in Wolfram Language, all modelled in SysML! [There's already some examples and some detailed policy notes.]

TIP: Mathematica: The IntelliJ IDEA Plugin for Mathematica is HEAPS better than the Eclipse-based Wolfram Workbench!

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: SysML4Mathematica: Convention: A prefix '$doc' indicates a documentation String for each primary variable/quantity (argument or output)

Webel: SysML4Mathematica: 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 raw 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: Yes, SysML Activities and SysML Activity Diagrams CAN represent functional programming paradigms! 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

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Tutorial

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

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SysML Block Definition Diagram (BDD)

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

Webel Best Practice: Mathematica: Options are encapsulated as a String variable with the prefix '$opt', and have a related '$info$opt$' String (help), '$lab$opt' String (label), a 'def$opt' default value expression, and an optional '$warn$opt' String.

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 '{}'.

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

Webel IT Australia is developing a recipe for modelling Wolfram Language code for Mathematica graphically in Systems Modeling Language v1 (SysML^®), so far primarily for SysMLv1.6 and SysMLv1.7, but a version of the recipe for SysMLv2 is foreseen.

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

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Tutorial

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

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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

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Tutorial

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

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SysML Parametric Diagram

Webel: SysML4Mathematica: When modelling the logic flow of Mathematica code with Activity diagrams it is not necessary to model every single Mathematica construct. Placeholder OpaqueBehaviors (used via CallBehaviorActions) and OpaqueActions may be used.

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

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Tutorial

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

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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)

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Tutorial

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

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SysML Activity Diagram

SysML Parametric Diagram

Webel: SysML4Mathematica: An '@' prefix in the name of a Block indicates a Mathematica data structure (such as an Association or List) that is not represented by an MTools class in the Mathematica code

Webel: SysML4Mathematica: An '@' prefix in the name of a ConstraintBlock, Activity, or OpaqueBehavior indicates that it is not represented by a dedicated function in a Mathematica code library (typically for minor maths or logic)

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

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Tutorial

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

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SysML Activity Diagram

SysML Parametric Diagram

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

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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

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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

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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

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"]

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

Keywords

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.

Webel: Mathematica: TIP: Maintain a Package library of Quantity variables for frequently used units using a naming convention unit$[unitSymbol] and unit[DescriptiveName] or unit[Acronym]

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 matching does not respect inheritance (undermines design-by-contract and heaps of Design Patterns)

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 (although its the 3rd decade of the 21st century)

Mathematica: The slightly less painful ultimate list of links on Object-Orientation (or the lack thereof) and a public plea to Wolfram Research

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 to functions RIGHT IN/NEAR THE CODE. Yes it is needed. Really it is.

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]

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

Keywords

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

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Tutorial

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

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Wolfram SystemModeler zone

Keywords

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

NEWS: SysML Extension for Physical Interaction and Signal Flow Simulation (SysP

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 zone

Keywords

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, systems modelling, and physics modelling.

Service: Wolfram Mathematica: Data analysis, mapping, transformation, and visualisation

Keywords

Webel IT Australia are experts in applications of the powerful Wolfram Mathematica system for 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 deployment to Wolfram Player Pro.

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