Simulation methods and systems are described for topology and shape optimization of a geometrical representation of a physical object being modeled. An initial geometry of the physical object is represented. Equation data representing physical properties for portions of an initial geometry are defined. User inputs are received through a GUI for optimization settings and user selections of portions of the geometry being optimized. For topology optimization, various material properties and solver settings may be defined. For shape optimization, various solver settings and optimization objective may be defined. A discretized model is generated of the physical object. Solutions of the topology or shape optimization are generated and updated values are determined. Iterative operations are then performed for solving the topology or shape optimization objective expressions. The solutions are stored and graphical representations of the solutions may be generated.
G06F 30/17 - Mechanical parametric or variational design
G06F 30/12 - Geometric CAD characterised by design entry means specially adapted for CAD, e.g. graphical user interfaces [GUI] specially adapted for CAD
G06T 17/10 - Volume description, e.g. cylinders, cubes or using CSG [Constructive Solid Geometry]
G06T 17/20 - Wire-frame description, e.g. polygonalisation or tessellation
2.
System and method for adding and defining perfectly matched layers for a model of a physical system
A graphical user interface includes GUI elements configured for defining discretized base geometry data for a model of a physical system, receiving a first input representing a user instruction to add a perfectly matched layer to the model, receiving a second input representing the user selection of boundaries that define a base geometry, and receiving a third input representing extra geometry meshing instructions. Extra geometry line segment data is discretized representing an outward direction of a PML from the boundary according to the extra geometry meshing instructions. Weak form expressions representing a wave-related phenomena are formed based on received PML settings and physics settings parameterized using discretized base geometry data and discretized extra geometry data. Matrix data are generated based on the formed weak form expressions. A solution to a simulation of the wave-related phenomena of the model is generated based on the formed weak form expressions. A graphical representation of the solution is generated for display on the GUI.
Simulation methods and systems are described for topology and shape optimization of a geometrical representation of a physical object being modeled. An initial geometry of the physical object is represented. Equation data representing physical properties for portions of an initial geometry are defined. User inputs are received through a GUI for optimization settings and user selections of portions of the geometry being optimized. For topology optimization, various material properties and solver settings may be defined. For shape optimization, various solver settings and optimization objective may be defined. A discretized model is generated of the physical object. Solutions of the topology or shape optimization are generated and updated values are determined. Iterative operations are then performed for solving the topology or shape optimization objective expressions. The solutions are stored and graphical representations of the solutions may be generated.
G06F 30/17 - Mechanical parametric or variational design
G06T 17/10 - Volume description, e.g. cylinders, cubes or using CSG [Constructive Solid Geometry]
G06T 17/20 - Wire-frame description, e.g. polygonalisation or tessellation
G06F 30/12 - Geometric CAD characterised by design entry means specially adapted for CAD, e.g. graphical user interfaces [GUI] specially adapted for CAD
4.
System and method for accessing settings in a multiphysics modeling system using a model tree
A system and method for implementing, on one or more processors, a bidirectional link between a design system and a multiphysics modeling system includes establishing via a communications link a connection between the design system and the multiphysics modeling system. Instructions are communicated via the communication link that include commands for generating a geometric representation in the design system based on parameters communicated from the multiphysics modeling system. One or more memory components can be configured to store a design system dynamic link library and a multiphysics modeling system dynamic link library. A controller can be operative to detect an installation of the design system, and implement via the dynamic link libraries, bidirectional communications of instructions between the design system and the multiphysics modeling system.
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. The processor is adapted to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of models of physical systems. Geometry data representing geometry subroutines and call data representing geometry subroutine calls are added to the embedded multiphysics model data structure. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing a form feature, or (ii) second data representing an action feature. A customized application data structure is generated providing a customized modeling of the physical systems using a modeling operation, a geometry of the one or more models of physical systems, an application feature, and a geometry subroutine. The customized application data structure is configured for distribution to end users as an application executed by an application runtime engine.
Systems and methods for determining finite elements in physics simulation systems for modeling physical systems using common geometry shape function spaces
Systems and methods for modeling physical systems include displaying geometric representation of a physical system on a physics simulation system. User-selection inputs received indicate, for mesh elements, selections of dependent variable shape function spaces representing dependent variables. Geometry shape function space options for simulating the physical system are determined that are common to mesh elements and include a serendipity shape function space of second order or higher. A determined geometry shape function space option is a subset of a combination of the dependent variable shape function spaces and satisfies accuracy criteria based on an accuracy ordering of shape function spaces. A finite element mesh for the physical system is created based on the mesh elements, a selected geometry shape function space, and the selection of dependent variable shape function spaces. A solution to a finite element simulation of the physical system being modeled is generated and the geometric representation displayed.
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. The processor is adapted to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of models of physical systems. Geometry data representing geometry subroutines and call data representing geometry subroutine calls are added to the embedded multiphysics model data structure. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing a form feature, or (ii) second data representing an action feature. A customized application data structure is generated providing a customized modeling of the physical systems using a modeling operation, a geometry of the one or more models of physical systems, an application feature, and a geometry subroutine. The customized application data structure is configured for distribution to end users as an application executed by an application runtime engine.
Systems and methods include preparing instances of physics modeling applications for use over a computer network based on expected use by a user of a modeling system. A server system remote from the user is configured to implement the acts of (i) determining an expected usage of the physics modeling applications, (ii) pre-launching an inactive application server and pre-loading an inactive instance of physics modeling applications, that meets pre-determined statistical usage criteria, onto the pre-launched application server, and (iii) sending at least a portion of the instance of the physics modeling application, wherein the pre-launching and/or pre-loading provide a reduced startup time of the pre-launched inactive application servers and the pre-loaded instance of the physics modeling application.
G06Q 10/04 - Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
G06F 30/20 - Design optimisation, verification or simulation
A system and method for implementing, on one or more processors, a bidirectional link between a design system and a multiphysics modeling system includes establishing via a communications link a connection between the design system and the multiphysics modeling system. Instructions are communicated via the communication link that include commands for generating a geometric representation in the design system based on parameters communicated from the multiphysics modeling system. One or more memory components can be configured to store a design system dynamic link library and a multiphysics modeling system dynamic link library. A controller can be operative to detect an installation of the design system, and implement via the dynamic link libraries, bidirectional communications of instructions between the design system and the multiphysics modeling system.
A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. The processor is adapted to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of models of physical systems. Geometry data representing geometry subroutines and call data representing geometry subroutine calls are added to the embedded multiphysics model data structure. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing a form feature, or (ii) second data representing an action feature. A customized application data structure is generated providing a customized modeling of the physical systems using a modeling operation, a geometry of the one or more models of physical systems, an application feature, and a geometry subroutine. The customized application data structure is configured for distribution to end users as an application executed by an application runtime engine.
Systems and methods for generating a model tree structure for a multiphysics modeling system include the acts of transmitting a plurality of selectable physics options for association with at least one of combined systems. An input associated with a selection of at least one of the plurality of selectable physics options is received. One or more selectable study options are transmitted for association with the combined systems. An input associated with a selection of at least one of the one or more selectable study options is received. In response to receiving the input associated with the selection at least one of the one or more selectable study options, a model tree structure is generated using the one or more processing units. The model tree structure includes a plurality of selectable nodes including one or more parent nodes and one or more child nodes. The selectable nodes include fields storing physical quantities and operations for modeling the combined systems.
G06F 17/30 - Information retrieval; Database structures therefor
13.
SYSTEMS AND METHODS FOR CREATING USER INTERFACES FOR GUIDING THE CREATION OF MODELING APPLICATIONS FOR FORMING AND SOLVING PROBLEMS IN A MULTIPHYSICS MODELING SYSTEM
Systems and methods generate a modified application data structure that provides a customized modeling of physical systems in response to customized user inputs received via application feature(s) for new window form(s). The modified application data structure is generated from guided user inputs received through application builder wizard graphical user interface(s). The systems and methods include embedding a multiphysics model data structure in an initial application data structure and defining new window form(s). Window form data representing the defined new window forms is added to the initial application data structure. User-selectable application feature options are displayed in the application builder wizard graphical user interface(s) and application feature data is added to the initial application data structure to create a modified application data structure. The added application features can include data representing widget(s), form feature(s), and command sequence(s).
Systems and methods for creating user interfaces for guiding the creation of modeling applications for forming and solving problems in a multiphysics modeling system
Systems and methods generate a modified application data structure that provides a customized modeling of physical systems in response to customized user inputs received via application feature(s) for new window form(s). The modified application data structure is generated from guided user inputs received through application builder wizard graphical user interface(s). The systems and methods include embedding a multiphysics model data structure in an initial application data structure and defining new window form(s). Window form data representing the defined new window forms is added to the initial application data structure. User-selectable application feature options are displayed in the application builder wizard graphical user interface(s) and application feature data is added to the initial application data structure to create a modified application data structure. The added application features can include data representing widget(s), form feature(s), and command sequence(s).
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. The processor is adapted to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of models of physical systems. Geometry data representing geometry subroutines and call data representing geometry subroutine calls are added to the embedded multiphysics model data structure. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing a form feature, or (ii) second data representing an action feature. A customized application data structure is generated providing a customized modeling of the physical systems using a modeling operation, a geometry of the one or more models of physical systems, an application feature, and a geometry subroutine.
An apparatus for generating an application data structure includes a physical computing system comprising processor(s), input device(s), display(s), and memor(ies). The memory includes executable instructions that cause a processor to perform the acts of embedding a multiphysics model data structure for a physical system in an application data structure. Application features are determined to add to the application data structure. First data is added representing a form feature for the application features for the model of the physical system. Second data is added representing at an action feature for the application features. The second data is associated with at least one modeling operation to define a sequence of operations for modeling the physical system. The application data structure is updated including the added first and second data and the associating defining the sequence of operations. The updated application data structure is stored on the memory device(s).
Systems and methods for generating a physics interface data structure via a graphical user interface include processing user inputs received via one or more user input devices. The inputs correspond to one or more variables, one or more physics properties, one or more physics features, one or more feature equations for physics features, one or more feature equations for physics properties, one or more solver settings, and one or more output result features. The user inputs are received via selection menus or user editable fields. A physics interface data structure comprising the user inputs is generated. A physics interface corresponding to the generated physics interface data structure is displayed in a graphical user interface. The physics interface data structure is stored on a physical memory devices.
G06F 3/048 - Interaction techniques based on graphical user interfaces [GUI]
G06G 7/50 - Analogue computers for specific processes, systems, or devices, e.g. simulators for distribution networks, e.g. for fluids
G06G 7/40 - Arrangements for performing computing operations, e.g. amplifiers specially adapted therefor for solving of equations of differential or integral equations of partial differential equations
18.
System and apparatus for accessing a multiphysics modeling system via a design system user interface
Systems and methods for controlling settings of a design system include receiving, via a communications interface, identifying data associated with a multiphysics modeling system. Instructions are transmitted via the communication interface or another interface. The instructions include model settings related to a multiphysics model at least partially residing in the multiphysics modeling system. Model results are received that are at least partially derived from the transmitted model settings. At least a portion of the received model results are displayed in a graphical user interface associated with the design system.
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. The processor is adapted to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of models of physical systems. Geometry data representing geometry subroutines and call data representing geometry subroutine calls are added to the embedded multiphysics model data structure. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing a form feature, or (ii) second data representing an action feature. A customized application data structure is generated providing a customized modeling of the physical systems using a modeling operation, a geometry of the one or more models of physical systems, an application feature, and a geometry subroutine.
An apparatus for generating an application data structure includes a physical computing system comprising processor(s), input device(s), display(s), and memor(ies). The memory includes executable instructions that cause a processor to perform the acts of embedding a multiphysics model data structure for a physical system in an application data structure. Application features are determined to add to the application data structure. First data is added representing a form feature for the application features for the model of the physical system. Second data is added representing at an action feature for the application features. The second data is associated with at least one modeling operation to define a sequence of operations for modeling the physical system. The application data structure is updated including the added first and second data and the associating defining the sequence of operations. The updated application data structure is stored on the memory device(s).
A system generates a customized application data structure for modeling physical systems. The system includes a processor, an input device, optionally a display device, and a memory device. One or more processors are adapted, during use, to embed a multiphysics model data structure in the application data structure. The multiphysics model data structure comprises a representation of one or more models of physical systems. Data representing application features are added to the application data structure. Each application feature comprises one or more of (i) first data representing at least one form feature, and/or (ii) second data representing at least one action feature. A customized application data structure is generated providing, when executed, a customized modeling of the physical systems using the at least one modeling operation, the at least one geometry of at least a part of the one or more models of physical systems, and at least one application feature.
Systems and methods for controlling settings of a design system include receiving, via a communications interface, identifying data associated with a multiphysics modeling system. Instructions are transmitted via the communication interface or another interface. The instructions include model settings related to a multiphysics model at least partially residing in the multiphysics modeling system. Model results are received that are at least partially derived from the transmitted model settings. At least a portion of the received model results are displayed in a graphical user interface associated with the design system.
A system and method for implementing, on one or more processors, a bidirectional link between a design system and a multiphysics modeling system includes establishing via a communications link a connection between the design system and the multiphysics modeling system. Instructions are communicated via the communication link that include commands for generating a geometric representation in the design system based on parameters communicated from the multiphysics modeling system. One or more memory components can be configured to store a design system dynamic link library and a multiphysics modeling system dynamic link library. A controller can be operative to detect an installation of the design system, and implement via the dynamic link libraries, bidirectional communications of instructions between the design system and the multiphysics modeling system.
09 - Scientific and electric apparatus and instruments
Goods & Services
Computer software, namely, software for use in providing a graphical user interface and connection between Finite Element Analysis (FEA) based mathematical software and CAD software, and FEA based mathematical software and general mathematical technical computing software packages
09 - Scientific and electric apparatus and instruments
Goods & Services
Computer software for performing technical mathematical calculations in the fields of mathematics, engineering, and science, and manuals and instruction handbooks sold together as a unit; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of computer-aided engineering and design; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of virtual prototyping and experiments; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of multiphysics modeling, simulation, and optimization; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of reaction engineering modeling, simulation, and optimization
09 - Scientific and electric apparatus and instruments
Goods & Services
(1) Computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science, and manuals and instruction handbooks sold together as a unit; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of computer-aided engineering and design; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of virtual prototyping and experiments; computer graphics software; computer software to model, simulate, optimize, control, test and analyze physics-based systems in the fields of multiphysics modeling, simulation, and optimization; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of reaction engineering modeling, simulation and optimization.
09 - Scientific and electric apparatus and instruments
42 - Scientific, technological and industrial services, research and design
45 - Legal and security services; personal services for individuals.
Goods & Services
Computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science, and manuals and instruction handbooks sold together as a unit; computer software for use in the fields of computer-aided engineering and design; computer software for use in the fields of virtual prototyping and experiments; computer graphics software; computer software for use in the fields of multiphysics modeling, simulation, and optimization; computer software for use in the fields of reaction engineering modeling, simulation, and optimization. Computer programming for others; computer consulting and technical support services, namely, assisting clients in running models and providing analysis of simulation results; providing maintenance and repair to computer software applications; providing updates to computer software applications; computer software consultation; technical support services, namely, troubleshooting in the nature of diagnosing and repairing computer software problems; providing temporary use of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; providing temporary use of computer software for use in the fields of multiphysics modeling, simulation, and optimization; providing temporary use of computer software for use in the fields of reaction engineering modeling, simulation, and optimization; leasing of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; leasing of computer software for use in the fields of multiphysics modeling, simulation, and optimization; leasing of computer software for use in the fields of reaction engineering modeling, simulation, and optimization; research and development in the field of computer software. Licensing of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; licensing of computer software for use in the fields of multiphysics modeling, simulation, and optimization; licensing of computer software for use in the fields of reaction engineering modeling, simulation, and optimization.
09 - Scientific and electric apparatus and instruments
41 - Education, entertainment, sporting and cultural services
42 - Scientific, technological and industrial services, research and design
45 - Legal and security services; personal services for individuals.
Goods & Services
(1) Computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science, and manuals and instruction handbooks sold together as a unit; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of computer-aided engineering and design; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of virtual prototyping and experiments; computer software to model, simulate, optimize, control, test and analyze physics-based systems in the fields of multiphysics modeling, simulation, and optimization; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of reaction engineering modeling, simulation and optimization.
(2) Computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science, and manuals and instruction handbooks sold together as a unit; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of computer-aided engineering and design; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of virtual prototyping and experiments; computer software to model, simulate, optimize, control, test and analyze physics-based systems in the fields of multiphysics modeling, simulation, and optimization; computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of reaction engineering modeling, simulation and optimization. (1) Educational services, namely, conducting classes, seminars, conferences, and workshops in the fields of computer programming, mathematics, engineering, multiphysics, and reaction engineering; computer training services, namely, computer training in the fields of computer programming, mathematics, engineering, multiphysics, and reaction engineering; computer consulting and technical support services, namely, assisting clients in running models and providing analysis of simulation results; providing maintenance and repair to computer software applications; providing updates to computer software applications; computer software consultation; technical support services, namely, troubleshooting in the nature of diagnosing and repairing computer software problems; providing temporary use of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; providing temporary use of computer software for use in the fields of multiphysics modeling, simulation, and optimization; providing temporary use of computer software for use in the fields of reaction engineering modeling, simulation, and optimization; licensing of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; licensing of computer software for use in the fields of multiphysics modeling, simulation, and optimization; licensing of computer software for use in the fields of reaction engineering modeling, simulation, and optimization; research and development in the field of computer software.
(2) Educational services, namely, conducting classes, seminars, conferences, and workshops in the fields of computer programming, mathematics, engineering, multiphysics, and reaction engineering; computer training services, namely, computer training in the fields of computer programming, mathematics, engineering, multiphysics, and reaction engineering; computer consulting and technical support services, namely, assisting clients in running models and providing analysis of simulation results; providing maintenance and repair to computer software applications; providing updates to computer software applications; computer software consultation; technical support services, namely, troubleshooting in the nature of diagnosing and repairing computer software problems; computer services, namely, providing temporary use of non-downloadable computer software for performing technical mathematical calculations for use in the fields of mathematics, engineering, and science; providing temporary use of non-downloadable computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of multiphysics modeling, simulation, and optimization; providing temporary use of non-downloadable computer software to model, simulate, optimize, control, test, and analyze physics-based systems in the fields of reaction engineering modeling, simulation, and optimization; licensing of computer software for technical mathematical calculations for use in the fields of mathematics, engineering, and science; licensing of computer software for use in the fields of multiphysics modeling, simulation, and optimization; licensing of computer software for use in the fields of reaction engineering modeling, simulation, and optimization.
09 - Scientific and electric apparatus and instruments
Goods & Services
(1) Computer software, namely, software for use in providing a graphical user interface and connection between Finite Element Analysis (FEA) based mathematical software and computer aided design software, and FEA based mathematical software and general mathematical technical computing software packages, namely, providing interactive access to geometric descriptions and properties defined using computer aided design software in Finite Element Analysis (FEA) based mathematical software, to mathematic and programmatic functions defined using general mathematical technical computing software in FEA based mathematical software, and to FEA based mathematical software properties, quantities, boundary conditions, and graphical user interface components in a computer aided design software or a general mathematical technical computing software package
09 - Scientific and electric apparatus and instruments
41 - Education, entertainment, sporting and cultural services
42 - Scientific, technological and industrial services, research and design
Goods & Services
Computer software for technical mathematical calculations for use in the field of mathematics, engineering and science, and manuals and instruction handbooks sold together as a unit Educational services, namely, conducting classes, seminars and workshops in the field of computer programming; computer training services, namely, computer training in the field of computer programming Computer programming for others; computer consulting and technical support services, namely, assisting clients in running models and providing analysis of simulation results
31.
System and method for graphically creating models for simulating systems of reacting species
A system and method for generating a model for simulating systems of reacting species comprising receiving a plurality of reaction formulas, determining a reaction rate expression for each of the received reaction formulas, and generating a model for simulating systems of reacting species using the received reaction formulas and the determined reaction rate expressions. The invention further relates to pruning the reaction list to deactivate one or more reactions in the reaction list based on one or more criteria, such as threshold criteria. A graphical user interface may also be used in connection with the present invention in various ways. An output based on the generated model may be displayed, wherein the output displays the composition and temperature dependence of the system of reacting species. Material and energy balances may also be generated for the reacting species as input to a solver of partial differential equations.
09 - Scientific and electric apparatus and instruments
16 - Paper, cardboard and goods made from these materials
42 - Scientific, technological and industrial services, research and design
Goods & Services
Computer software for mathematical calculations. Manuals, handbooks, printed matters and printed publications all concerning computer software for mathematical calculations. Design and development of computer hardware and software for mathematical calculations.
09 - Scientific and electric apparatus and instruments
16 - Paper, cardboard and goods made from these materials
42 - Scientific, technological and industrial services, research and design
Goods & Services
Computer software for mathematical calculations. Manuals, handbooks, printed matters and printed publications all concerning computer software for mathematical calculations. Design and development of computer hardware and software for mathematical calculations.
09 - Scientific and electric apparatus and instruments
Goods & Services
(1) Computer software for performing technical mathematical calculations for use in the field of mathematics, engineering and science, and manuals and instruction handbooks sold together as a unit.
09 - Scientific and electric apparatus and instruments
Goods & Services
(1) Computer software for performing technical mathematical calculations for use in the field of mathematics, engineering and science, and manuals and instruction handbooks sold together as a unit.
09 - Scientific and electric apparatus and instruments
16 - Paper, cardboard and goods made from these materials
41 - Education, entertainment, sporting and cultural services
Goods & Services
(1) Computer software for technical mathematical calculations for use in the field of mathematics, engineering and science; manuals, handbooks, printed publications all concerning computer software; paper, tapes and cards for the recordal of computer programmes. (1) Computer programming and education services, namely the teaching and training of computer programming
