INTERNATIONAL STANDARD

First edition 1996-l O-01

Information and documentation - Mathematical coded character set for bibliographic information interchange

Information et documentation - Jeu de caract&-es cod& mathgmatiques pour /es &changes d’informations bibliographiques

Reference number IS0 6862: 1996(E)

Foreword

IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies (IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be rep- resented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

International Standard IS0 6862 was prepared by Technical Committee lSO/TC 46, Information and documentation, Subcommittee SC 4, Com- puter applications in information and documentation.

Annex A of this International Standard is for information only.

0 IS0 1996

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from the publisher.

International Organization for Standardization Case postale 56 l CH-12 11 Geneve 20 l Swi tzerland

Printed in Switzerland

ii

INTERNATIONAL STANDARD @ IS0 IS0 6862:1996(E)

Information and documentation - Mathematical coded character set for bibliographic information interchange

1 Scope

1.1 This International Standard specifies a set of 188 graphic characters with their coded representations. It consists of code tables and a legend showing each graphic together with its name or meaning. Explana- tory notes are also included.

1.2 These characters, together with characters in the international reference version of IS0 646 (IS0 escape sequence ESC Z/8 4/O), in the extension of the Latin alphabet coded character set for bibliographic information interchange [ISO 5426111 and in the Greek alphabet coded character set for bibliographic infor- mation interchange [ISO 5428211 constitute a character set for the international exchange of bibliographic records including their annotations, incorporating symbols mainly from the following disciplines:

Algebra Arithmetic Calculus Cybernetics Geometry Hyperbolic functions Logic Mechanics Probability studies Set theory Statistics Topology Trigonometry Vectors

1.3 This International Standard is concerned with the transmission of mathematical characters in biblio- graphic records, not with their use in source docu- ments: the descriptions and comments in the legend are therefore neither prescriptive nor exhaustive. This means that there is no restriction against the use of a particular symbol in interchange of information in the form in which it appears in the data to be transmitted, even if its name or meaning as given in this Inter- national Standard does not cover its use in that par- ticular context.

2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards.

lSO/l EC 2022: 1994, lnforma tion technology - Character code structure and extension techniques.

IS0 2375:1985, Data processing - Procedure for registration of escape sequences.

1) Escape sequences: GO: ESC 218 5/O Gl : ESC 219 5/O G2: ESC 2/l 0 5/O G3: ESC 2/l 1 5/O

2) Escape sequences: GO: ESC 218 513 Gl : ESC 219 513 G2: ESC 2/l 0 513 G3: ESC 2/l 1 513

1

IS0 6862: 1996(E) @ IS0

3 Implementation

3.1 The implementation of this coded character set in physical media and for transmission, taking into account the need for error checking, is the subject of other International Standards (see annex A).

3.2 The implementation of this International Stan- dard is in accordance with the provisions of IS0 2022 and is identified by the escape sequences ESC (in accordance with IS0 2375).3)

3.3 The unassigned positions in the code tables are not to be utilized in the international exchange of bibliographic information.

3) The Registration Authority.

2

@ IS0 IS0 6862: 1996(E)

4 Code tables of mathematical coded characters

The mathematical character set is given in tables 1 and 2.

Table 1 - Basic set GO

0 a

6

0 m 0 m 0 m 1 m 1 m 1 m 1 m 0 m 0 m a m 0 m 1 m 1 m 1 m 1 m

n 34 n

0

0

n

0

m

0

n

0

n

0 m

0 m

0 m

1 I

1 m

1 m

1 m

1 m

1 m

1 m

1 m

jI 0

0 n I m 1 m 0 n 0 n 1 m 1 m cl m 0 m 1 m 1 m 0 n 0 n 1 n 1 n

m b 1

0

1 m

0 m

1 m

0 m

1

0 m

1 m

0

1

0

1 m

0

m

1 m

0 m

1 m

-

c

3 t/t

<

3 E V

n u A

3 v > < h C

1 t > l-

s > >

1

L

V 0

/ 00 > n n

n n

s JJI a h N 0

II Tl u

J

3

IS0 6862: 1996(E) @ IS0

Table 2 - Extension of basic set Gl

1

12 I 3

m

3

m

1

m

1 m

0

m

0

m

1 m

1 m

0 m

0 m

1 m

1

m

0 m

0 m

w

1 m

11 3 3'

1

0

1

0

1

0

1

0

1

0

1

0 m 1 m 0 m 1 m

;j

I m 3 n 3 m 0 - 1 n 1 m 1 m 1 m 0 m a w 0 m 0 m 1 m 1 m 1 m 7 m

14

j I

3 m 3 m 0 w 0 m 0 D 0

0 m 1

1 m 1

1 m 1 m 1 m 1 m 1 m

II a

0

/ \ - 0 0

\ oc

I A V

I= l l 0 n

r 3 E 3

2 /” Y J

0

7

P

R ,-.*.-.*.b.g.*, ,-.-.-.-.-.-.-a ,*.*.‘.-.*.***a ,a.‘.*.m.*.‘.ml ,*.‘.*.g.*.-.*, ,*.‘.e.*.-.g.*l WM

r

@ IS0 IS0 6862: 1996(E)

5 Legend A legend for tables 1 and 2 is given in table 3.

Table 3 - Legend

Position in

table 1

2/l

212

213

214

2/5

216

217

218

219

2110

2111

2112

2113

2114

2115

3/o

3/l

312

313

314

315

316

Graphics

/

I

I

-

0

cl

0

n

.

. .

x

+ -

‘L

z

- - -

<

5

Name or meaning

Negation : oblique

Negation: long bar

Negation: short bar

Negation : horizontal

Circle, overlay

Circle, anti-clockwise arrow

Circle, clockwise arrow

Anti-clockwise arrow

Superior dot

Superior double dot

Superior vector left

Superior hat

Superior V

Superior vector right

Clockwise arrow

Multiply

Plus or minus

Equivalent to

Asymptotic to

Identical with

Less than or equal to

Less than or greater than

Comments

Overlay character

Overlay character

Overlay character

Overlay character

Overlay character for integral, etc.

Overlay character for integral

Overlay character for integral

Overlay character

Overlay character

Overlay character

Overlay character

Overlay character

Overlay character

Overlay character

Overlay character

Also: negation, or proportional to

Also: approximately equal to

Coding

nego or I

negl or I

negs or I

negh or -

ciro

ciroa

ciroc

arroa

dots

ddots

arls

checkas

ckackas

arrs

arroc

times or x

plmin

sim

dsim

iden

It0

Iessgrtr

IS0 6862: 1996(E) @ IS0

Position in

table 1

317

318

319

3110

3111

3112

3113

3114

3115

4/o

4/l

412

413

414

415

416

417

418

419

4110

4111

4112

4113

4114

4115

Graphics Name or meaning Comments Coding

<

6

II

I-

A 0

(

II c . - .

- + w - w - - -

2

z >

9

-L

L

V 0 / 00

>

II

II

Table 3 (continueu’)

Less than or equivalent to lesssim

Much less than less2

Parallel to See also table 2 5/O: norm of a matrix

parr

Right angle Also : factorial rang

Increment incre

Degree deg

Left angle bracket labrak or <

Left open bracket lobrak or [

Sum of sum

Divide Alternative to IS0 646 div or I

Minus or plus minpl

Asymptotically equal to simeq

Similar to congr

Approximately equal to libra

Greater than or equal to gto

Greater than or less than grtrless

Greater than or equivalent to grtrsim

Much greater than grtr2

Orthogonal to Also: bottom element PerP

Angle aw

Backward finite difference operator Also: nabla operators nabla

Per mille perk

Angle bracket, right rabrak or >

Open bracket, right robrak or 1

Product prod

6

Table 3 (continued)

Position in

table 1

5/o

5/l

5/2

5/3

514

515

516

517

518

519

5110

5111

5112

5113

5114

5115

6/O

6/l

612

613

614

615

616

617

618

Graphics

+

c

c -

E

u

v

C

t

00

-

3

3 -

3

n 3 (zr 1

Name or meaning

Plus

Proper inclusion in set

Identity or inclusion in set

Set membership

Union of sets between limits

For all

Complement

Increases; exponent

Left arrow

Anti-clockwise

Mutually implies

Left arrow over right arrow

Functional relationship

Double arrow, upward

Is implied by

Infinity

Minus

Properly includes in set

Contains as subset

Contains

Intersection of classes or sets between limits

There exists

Empty set

Decreases

Approaches

Comments

Also : identity

Also : identical with

Coding

plus or +

lhook

lkkeq

mem

cup

inva

longc

arru

arrl

arrac

arrlr

Irarr

bararr

darru or A

darrl

infin

minus or -

rhook

rh keq

cant

hat

reve

bararc

arrd

arr

7

IS0 6862: 1996(E) @ IS0

Table 3 (continued)

I “YIbIVI.

in table I

Pncitinn

619

6110

6111

6112

6113

6114

6115

7/o

7/l

712

713

714

715

716

717

718

719

7110

7112

Name or meaning

Clockwise arrcc

Vertical relationship arrud

Right arrow over left arrow rlarr

Anti-parallel udarr

Double arrow, downward darrd

Implies darr

Radical square root rad

Prime minutes, feet prime or ’

Double prime Also : seconds, inches dprime or

Triple prime trprime

Logical or Also : disjunction checkd

Logical and Also : conjunction checku

Logical not lognot

Planck constant planck

Implies imply

Integral int

Double integral dint

Triple integral

Partial differentiation Prtl

Planck constant divided by 2 n: plan2pi

Aleph aleph

Composite function Also: small circle cirsm

Commsnf. Coding

trint

8

@ IS0 IS0 6862: 1996(E)

Table 3 (continued)

Position in

table 2

2/l

212

213

214

215

216

217

218

219

2110

2111

2112

2113

2114

2/15

3/o

3/l

312

313

314

315

316

317

3/a

319

Graphics Name or meaning

0

0 -

63

0 .

l

. .

. .

.

I

II

I --

I

.

+

+

3

#

2

.

B

L . . .

r c - u

Direct sum crplus

Symmetric difference crmin

Tensor product Also: Dyadic product, or Plethysm operator

zrtimes

Inner product Used with tensors zrdot

Therefore thrf

Because beta

Image of imbox

Original of origbox

Image of imline

Original of origline

Hermitian conjugate matrix herm

Direct sum dirsum

Most positive mpos

Homothetic homot

Element precedes under relation el rel

Not equal to nequ

Has an image hasim

Open angle bracket, left accbrale

Left floor Paired with right floor, 4/3 lfloor

Triple colon

Left ceiling Paired with right ceiling, 4/5

tripcol

lceil

Square subset .

Least upper bound

sqsub

Used for lattices lub

Long triangle ltril

Is dominated by cyrsim

Comments Coding

IS0 6862: 1996(E) @ IS0

Position in

table 2

3110

3111

3112

3113

3114

3115

4/o

4/l

412

413

414

415

416

417

418

419

4110

4/11

4112

4113

4114

4115

5/o

5/l

! Graphics

<

< --Y

. -

h -

Q

A

. . . .

P

J

-/\- -

1 7 - rl

5

> > /- . - v - - D

v

II

/

Table 3 (continued)

Name or meaning

Has a lower rank than

Is contained in or equal to

Symmetric difference

Estimates

Implied by

Triangle

Asymptotically equal to

Ratio

Open angle bracket, right

Right floor

Geometrically equivalent to

Right ceiling

Square superset

Greatest upper bound

Long triangle, underlined

Dominance

Has a higher rank than

Has rank higher than or equal to

Approaches the limit

Equiangular

Implies .

Hamilton operator

Norm of a matrix

Diagonal rule, to left

Comments

Also: corresponds to

Graphic positioned above base line

Graphic positioned above base line

Paired with left floor, 3/3

Paired with left ceiling, 315

Used for lattices

Also: contained in or equivalent to

Graphic positioned above base line

Also: curl of a vector; graphic positioned above base line

Coding

cyless

clyto

simdif

ests

ltriagl

triagl

dsimeq

ratio

aocbrak

rfloor

dlibra

rceil

sqsup

cm

ltrilb

cylsim

CY!P

limeq

heq

rtriagl

itriagl

nmat

diagl

40

@ IS0

Table 3 (continued)

Position in

table 2

512

513

514

515

516

517

518

519

5110

5111

5112

5113

5114

5115

6/O

6/l

612

613

614

615

616

617

618

619

6110

Graphics

T V

u

c

E

\

J

t

c

0

cl

Kl

0 I

\

\

A

n

3

3

/”

I

Name or meaning

Top element

Vector or sum

Sum or union of classes or sets

Is included in set

Is an element of

Arrow, NJ/V.

Arrow, S.W.

Half upward arrow

Crossed arrow, right

Curved arrow, right

Circle, spacing

Square

Rectangle

Lozenge

Magnitude of

Diagonal rule, to right

Difference

Vector product

Product of intersection of classes or sets

Includes in set

Such that

Arrow, N.E.

Arrow, S.E

Functional relationship, to right

On to map

Comments

Also: one to one map

Used with overlays

Also: D’Alembertain operator, or end of proof

Also: conjunction sign

Also: contains

Also : grows

Also : decays

Coding

top

checkd2

bcup

rcup

rbcup

arrnw

arrsw

hrru

narr

cyarr

circ

SW

rect

lo2

sline

diagr

diff

checku2

bhat

lcup

lbcup

arrne

arrse

zagarr

arr2

11

IS0 6862: 1996(E) @ IS0

6111

6112

6113

6114

6115

7/o

7/l

712

713

714

715

716

717

718

719

7110

7111

7112

7113

7114

Position in

table 2 Graphics Name or meaning Comments Coding

4-J

e

q

n

* . - - . . . . .

X

I

I=

1

4-r

t

tt

Table 3 (concluded)

Curved arrow, left cyarl

Dark circle bcir

End of proof bsqu

Parallelogram parlgr

Spherical angle spharg

Approximately equal to; is the image of

Geometric properties

image

prop

Varies as Also: proportional to varies

Curly vertical line cline

Statement is true Also: result in true

Assertion Also: reduced to assrt

Not parallel to

Crossed vertical bar

npar

nsline

Crossed arrow, to left narl

Functional relationship, to left zagarl

Equivalence Also : if and only if darrlr

Double arrow, up and down darrud

Inverted iota

Weierstrass elliptic function

Cross ratio

iiota

weirp

xrat

12

@ IS0 IS0 6862: 1996(E)

6 Explanatory notes

6.1 In general, separate shapes are considered to be individual characters. However, different font designs are not considered to require separate characters: where the shape, size or positioning of a character is meaningful within the citation, this will be specified by control characters.

6.2 Since characters have been assigned to the set on the grounds of shape rather than meaning, the absence of an appropriate definition by a symbol, or appearance of such a definition by another symbol, does not imply a restriction against the use of that symbol in interchange of information in the form in which it appears in the data to be transmitted.

6.3 Names were chosen based on a commonly accepted term describing a character’s shape or function.

For bibl iograph ic mathema tical characters that rep- resent several functions, a term descri bing their

shape was preferred. References from alternative names, such as those provided in IS0 31-l 1, have been given in the “Comments” column.

6.4 Characters already appearing in an established character set are not generally repeated in the mathematical character set. Exceptions are, in table 1 the characters 2/9, 2/l 0, 2/l 2, 2/13 (non-spacing), 3/l d 3/13, 4/13 (also found in IRV), 7/O, 7/l (also found in IS0 54261, 5/O and 6/O (used as minus only) (also found in IRV), 3/15 and 4/15 (in smaller form in IS0 5428), and in table 2, 6/O (used as magnitude only) (also found in IRV).

6.5 Negative and other modified symbols may be constructed by combining symbols from this and/or other character sets by the use of non-spacing overlay facilities in table 1, column 2 of this set or in other sets.

6.6 The codings given for each character in the legends are those recommended for use in environ- ments, such as teleprinter, which do not have access to the full character set.

13

IS0 6862: 1996( El

Annex A (informative)

PI

[51

Bibliography

IS0 31-I I :1992, Quantities and units - Part 1 I: 16% IS0 1177:1985, Information processing - Mathematical signs and symbols for use in the Character structure for start/stop and synchron- physical sciences and technology. ous character oriented transmission.

IS0 646: 1983, Information processing - /SO 7-bit coded change.

character set for information inter-

IS0 962:1974, Information processing - Im- plemen ta tion of th e 7-bit coded character set and its 7-bit and 8-bit extensions on g-track 12,7 mm (0.5 in) magnetic tape.

IS0 1113:1979, Information processing - Representation of the 7-bit coded character set on punched tape.

171

181

IS0 1155: 1978, Information processing - Use of longitudinal parity to ma tion messaaes.

detect errors in infor-

IS0 1745:1975, Information processing - Basic mode control procedures for data communi- cation sys terns.

IS0 5426:1983, Extension of the Latin alphabet coded character set for bibliographic information interchange.

IS0 5428:1984, Greek alphabet coded character set for bibliographic information interchange.

IS0 6586: 1980, Data processing - Implemen- tation of the IS0 7-bit and 8-bit coded character sets on punched cards.

14

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IS0 6862:1996(E) @ IS0

ICS 35.040 Descriptors: documentation, bibliographies, data processing, information interchange, graphic characters, character sets, coded character sets, mathematics.

Price based on 14 pages