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ISO 10303-50:2002

(Main)

Industrial automation systems and integration — Product data representation and exchange — Part 50: Integrated generic resource: Mathematical constructs

Industrial automation systems and integration — Product data representation and exchange — Part 50: Integrated generic resource: Mathematical constructs

This part of ISO 10303 specifies the resource constructs for the explicit representation of mathematical structures and data related to properties of a product. The following are within the scope of this part of ISO 10303: multi-dimensional tables; mathematical expressions; mathematical functions; mathematical spaces. The following are outside the scope of this part of ISO 10303: context of application; physical units; non-mathematical semantics.

Systèmes d'automatisation industrielle et intégration — Représentation et échange de données de produits — Partie 50: Ressources génériques intégrées: Constructions mathématiques

General Information

Status
Published
Publication Date
15-May-2002
ICS
25.040.40 - Industrial process measurement and control
Technical Committee
ISO/TC 184/SC 4 - Industrial data
Drafting Committee
ISO/TC 184/SC 4/WG 12 - STEP product modelling and resources
Current Stage
9020 - International Standard under periodical review
Start Date
15-Oct-2024
Completion Date
15-Oct-2024
Ref Project

Relations

Consolidated By
ISO 13079:2011 - Laboratory glass and plastics ware — Tubes for the measurement of the erythrocyte sedimentation rate by the Westergren method
Effective Date
06-Jun-2022
Corrected By
ISO 10303-50:2002/Cor 2:2014 - Industrial automation systems and integration — Product data representation and exchange — Part 50: Integrated generic resource: Mathematical constructs — Technical Corrigendum 2
Effective Date
26-Nov-2021

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ISO 10303-50:2002 - Industrial automation systems and integration -- Product data representation and exchangeISO 10303-50:2002 - Industrial automation systems and integration -- Product data representation and exchange
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ISO 10303-50:2002 - Industrial automation systems and integration -- Product data representation and exchange
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INTERNATIONAL ISO
STANDARD 10303-50
First edition
2002-05-01
Industrial automation systems and
integration — Product data representation
and exchange —
Part 50:
Integrated generic resource: Mathematical
constructs
Systèmes d'automatisation industrielle et intégration — Représentation
et échange de données de produits —
Partie 50: Ressources génériques intégrées: Constructions mathématiques

Reference number
©
ISO 2002
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©  ISO 2002
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ii  © ISO 2002 – All rights reserved

Contents Page
1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Terms, definitions, and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.1 Terms defined in ISO 10303-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.2 Other terms and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.3 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Mathematical functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.1 Introduction .8
4.2 Fundamental concepts and assumptions .8
4.2.1 Mathematical function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2.2 Mathematical object or value . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2.3 Mathematical expression . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2.4 Mathematical space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2.5 Mathematical tuple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2.6 Function domains and ranges . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2.7 Spaces of one-tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2.8 Array function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2.9 Table function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2.10 Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2.11 Inputs and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.12 Function evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2.13 Function application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Mathematical functions schema constant definitions . . . . . . . . . . . . . . . 14
4.3.1 schema prefix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3.2 the elementary spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3.3 the empty space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3.4 real intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3.5 tuple spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.3.6 empty values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.4 Mathematical functions schema type definitions . . . . . . . . . . . . . . . . . . 17
4.4.1 nonnegative integer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4.2 positive integer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4.3 zero or one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4.4 one or two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4.5 local names for simple types . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4.6 maths simple atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4.7 maths atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4.8 atom based tuple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4.9 atom based value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4.10 maths tuple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4.11 maths value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4.12 maths expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4.13 maths function select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4.14 input selector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4.15 elementary space enumerators . . . . . . . . . . . . . . . . . . . . . . . . 22
4.4.16 ordering type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4.17 lower upper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4.18 symmetry type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4.19 elementary function enumerators . . . . . . . . . . . . . . . . . . . . . . . 25
4.4.20 open closed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.21 space constraint type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.22 repackage options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4.23 extension options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4.24 maths enum atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.25 dotted express identifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.26 express identifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.27 product space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.28 tuple space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4.29 maths space or function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4.30 real interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5 Mathematical functions schema entity definitions . . . . . . . . . . . . . . . . . 36
4.5.1 quantifier expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.5.2 dependent variable definition . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5.3 bound variable semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5.4 free variable semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5.5 complex number literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5.6 logical literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.5.7 binary literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.5.8 maths enum literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.5.9 real tuple literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5.10 integer tuple literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5.11 atom based literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5.12 maths tuple literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.5.13 maths variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.5.14 maths real variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5.15 maths integer variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5.16 maths boolean variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5.17 maths string variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5.18 function application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5.19 maths space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5.20 elementary space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5.21 finite integer interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5.22 integer interval from min . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
interval to max . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5.23 integer
4.5.24 finite real interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5.25 real interval from min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5.26 real interval to max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5.27 cartesian complex number region . . . . . . . . . . . . . . . . . . . . . . . 49
4.5.28 polar complex number region . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5.29 finite space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5.30 uniform product space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.5.31 listed product space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5.32 extended tuple space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.5.33 function space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.34 maths function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.35 finite function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.36 constant function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5.37 selector function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.38 elementary function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5.39 restriction function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
iv © ISO 2002 — All rights reserved

4.5.40 repackaging function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5.41 reindexed array function. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.42 series composed function . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.43 parallel composed function . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.44 explicit table function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5.45 listed real data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.5.46 listed integer data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5.47 listed logical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5.48 listed string data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5.49 listed complex number data . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.5.50 listed data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.51 externally listed data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.52 linearized table function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.53 standard table function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.54 regular table function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5.55 triangular matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.56 strict triangular matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.57 symmetric matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.5.58 symmetric banded matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5.59 banded matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.60 basic sparse matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5.61 homogeneous linear function . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.5.62 general linear function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.63 b spline basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5.64 b spline function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.65 rationalize function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5.66 partial derivative function . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.67 partial derivative expression . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.5.68 definite integral function . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.5.69 definite integral expression . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5.70 abstracted expression function . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5.71 expression denoted function . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5.72 imported point function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.5.73 imported curve function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.5.74 imported surface function . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
volume function . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.5.75 imported
4.5.76 application defined function . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.5.77 mathematical description . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6 Mathematical functions schema function definitions . . . . . . . . . . . . . . . 104
4.6.1 all members of es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.6.2 any space satisfies . . . . . . . . . . . . .
...

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ISO 10303-1:2024(Main)
Industrial automation systems and integration — Product data representation and exchange — Part 1: Overview and fundamental principles

This document provides an overview of the ISO 10303 series. This document defines the architectural principles of product information representation and exchange used in the ISO 10303 series. It specifies the characteristics of the various sets of parts in the ISO 10303 series and the relationships among them. The following are within the scope of this document: — scope statement for the ISO 10303 series as a whole; — overview of the ISO 10303 series; — architectures of the ISO 10303 series; — structure of the ISO 10303 series; — overview of data specification methods used in the ISO 10303 series; NOTE This includes the EXPRESS data specification language and graphical presentation of product information models. — introduction to the ISO 10303 series: — integrated resources (IRs); — application interpreted constructs (AICs); — application modules (AMs); — application domain models (ADMs); — Core model; — business object models (deprecated); — application protocols (APs); — implementation methods; — usage guides; — conformance testing methodology and framework; — abstract test suites (ATSs); — scheme for identification of schemas and other information objects defined in the ISO 10303 series.

  • Standard
    23 pages
    English language
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ISO
ISO/TS 23301:2023(Main)
STEP geometry visualization services

This document defines a set of metadata to support the audit trail of the transformation of a geometry definition, while it is distributed and shared in supply-chains, to ensure the traceability of geometric model data. It also defines a set of web services based on the utilisation of these metadata. The following are within the scope of this document: — metadata definitions for geometry transformation audit trail: — syntax for storing these metadata in geometry data sets in various formats; — conformance level for implementers and business processes; — definitions of web services to query the geometric model data set and its associated metadata. The following are outside the scope of this document: — service specifications for CAD operations; — specifications of a cybersecurity infrastructure to enable web services; — the technical implementation of a STEP geometry services client or server; — any geometric model definition; — any product and manufacturing information (PMI) definition; — archiving.

  • Technical specification
    30 pages
    English language
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ISO
ISO/TR 20123:2023(Main)
Automation systems and integration — Industrial data — Nuclear digital ecosystem specifications

This document provides: — a review and summary of the adoption of digital methods and technology in the national nuclear sectors; — a summary of the state of the art of some of the standards supporting the digital representation and interoperability of industrial data; — orientation on the use of these standards for model-based systems engineering (MBSE) in order to achieve a nuclear digital ecosystem (NDE); — a high-level roadmap of the stages by which this ecosystem can be achieved, taking into account the maturity of the actors of the ecosystem, their relationships and the added value of using advanced standards. NOTE The complete reports from the participating entities are presented in Annexes A to G. This document includes the following: — the systems composing the nuclear facilities and their input, output, and other products resulting from interactions in the nuclear system or with its environment; — the material accounting and the corresponding requirements; — waste management: all types of nuclear waste produced during processes and activities, and their properties are considered for a seamless management of information in the whole value chain of the nuclear ecosystem.

  • Technical report
    87 pages
    English language
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ISO
ISO/TR 3151-1:2023(Main)
Visualization elements of PLM-MES interface — Part 1: Overview

This document outlines the visualization elements for data exchange between the Product Lifecycle Management and Manufacturing Execution System (PLM-MES) or Manufacturing Operations Management (MOM). The following are within the scope of this document: — the need for a PLM-MES interface; — the technical elements that make up the PLM-MES interface; — the visualization elements of the PLM-MES interface. The following is outside the scope of this document: — application of the PLM-MES interface and its visualization elements.

  • Technical report
    29 pages
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