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 iTeh STpourA /esN &changesDAR Ddinformations PRE VbibliographiquesIEW (standards.iteh.ai)

ISO 6862:1996 https://standards.iteh.ai/catalog/standards/sist/dfc1ce59-129a-4cc6-85b3- d492e83bb54b/iso-6862-1996

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 ileastTe 75h %S Tof theA NmemberDA RbodiesD PcastingRE VIEW a vote. (standards.iteh.ai) International Standard IS0 6862 was prepared by Technical Committee lSO/TC 46, Information and documentation, SubcommitteeISO 68 62:1SC996 4, Com- puter applications in informationh ttpands://s tadocumentation.ndards.iteh.ai/ca talog/standards/sist/dfc1ce59-129a-4cc6-85b3- d492e83bb54b/iso-6862-1996 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 1.3 This International Standard is concerned with the transmission of mathematical characters in biblio- 1.1 This International Standard specifies a set of 188 graphic records, not with their use in source docu- graphic characters with their coded representations. It ments: the descriptions and comments in the legend consists of code tables and a legend showing each are therefore neither prescriptive nor exhaustive. This graphic together with its name or meaning. Explana- means that there is no restriction against the use of a tory notes are also included. particular in interchange of information in the form in which it appears in the data to be transmitted, 1.2 These characters, together with characters in even if its name or meaning as given in this Inter- the international reference version of IS0 646 (IS0 national Standard does not cover its use in that par- escape sequence ESC Z/8 4/O),iT ein hthe SextensionTAN ofD theA RDticular PR context.EVI EW Latin alphabet coded character set for(s tbibliographicandar ds.iteh.ai) information interchange [ISO 5426111 and in the Greek alphabet coded character set for bibliographic infor- ISO 6862:1996 mation interchange [ISO 5428211 constitute a character 2 Normative references set for the international httpexchanges://standa rds.ofite h.bibliographicai/catalog/stan dards/sist/dfc1ce59-129a-4cc6-85b3- records including their annotations, incorporatingd492e83bb5 4b/iso-6862-1996 symbols mainly from the following disciplines: The following standards contain provisions which, through reference in this text, constitute provisions of Algebra this International Standard. At the time of publication, Arithmetic the editions indicated were valid. All standards are Calculus subject to revision, and parties to agreements based Cybernetics on this International Standard are encouraged to Geometry investigate the possibility of applying the most recent Hyperbolic functions editions of the standards indicated below. Members Logic of IEC and IS0 maintain registers of currently valid Mechanics International Standards. Probability studies Set theory lSO/l EC 2022: 1994, lnforma tion technology - Statistics Character code structure and extension techniques. Topology Trigonometry IS0 2375:1985, Data processing - Procedure for Vectors 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 3.2 The implementation of this International Stan- dard is in accordance with the provisions of IS0 2022 3.1 The implementation of this coded character set and is identified by the escape sequences ESC (in in physical media and for transmission, taking into accordance with IS0 2375).3) account the need for error checking, is the subject of other International Standards (see annex A). 3.3 The unassigned positions in the code tables are not to be utilized in the international exchange of bibliographic information.

iTeh STANDARD PREVIEW (standards.iteh.ai)

ISO 6862:1996 https://standards.iteh.ai/catalog/standards/sist/dfc1ce59-129a-4cc6-85b3- d492e83bb54b/iso-6862-1996

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 n m 6 34 jI b1 n - 0 0 0

0 0 0 1 c n m n m t/t 0 0 I 0 < 3 m m m m 0 0 1i T1 eh STANDARD PREVIEEW 3 V n m m m

0 1 0 0 (standards.iteh.ai) A n m n m u n 0 1 0 1 ISO 6862:1996 https://standards.iteh.ai/catalog/standards/sist/dfc1ce59-129a-4ccv6-8 5b3-3 m m n d492e83bb54b/iso-6862-1996 0 1 1 0 > < C h m m m m 0 1 1 1 > l- t 1 m m m m 1 0 cl 0 > I m m s 1 0 0 1 1 n n m m m 1 a 1 0 L s m m m JJI 1 0 1 1 V II a m m m m 0 1 1 0 0 /00 Tl h m m n m 1 1 0 1 > u N m m n m 1 1 1 0 n 0 m m n m 1 1 1 1 n m J m n m

3 IS0 6862: 1996(E) @ IS0

Table 2 - Extension of basic set Gl

1

14 ;j 12 311 a I I 3 3' j I II 0 m m

- 3 3 3 1 / \ 0 0 m n m

3 3 1 0 \ oc m m m 0 0 1 1 V A I w - m l l 0 0 1 0 0 n I= m n m 0 1 0 1 iTeh STANDARrD PREVIEW3 D m m (standards.iteh.ai) 0 1 1 0 E 3 m m ISO 6862:1996 0 1 1 1h ttps://standards.iteh.ai/catalog/standards/sist/dfc1ce59-1229 a-4cc/6-”8 5b3-Y m m m d492e83bb54b/iso-6862-1996 1 0 0 0 J m m 1 a 0 1 r m w m 1 0 1 0 m m

1 0 1 1 0 m m m 1 1 0 0 7 m m m m 1 1 0 1 P m m m m 1 1 0 R m m w m ,-.-.-.-.-.-.-a,-.*.-.*.b.g.*, ,a.,*.*.‘.*.m.*.‘.-.*.***a‘.ml 1 7 1 1 ,*.‘.e.*.-.g.*l.*.g.*.-.*, m m m m WM @ IS0 IS0 6862: 1996(E)

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

Position in Graphics Name or meaning Comments Coding table 1

2/l / : oblique Overlay character nego or I

212 I Negation: long Overlay character negl or I

213 I Negation: short bar Overlay character negs or I

214 - Negation : horizontal Overlay character negh or -

2/5 0 Circle, overlay Overlay character for ciro integral, etc.

216 cl Circle, anti-clockwise Overlay character for integral ciroa

217 0 iTCircle,eh clockwiseSTA NarrowD ARD PREVOverlayIE characterW for integral ciroc 218 n Anti-clockwise(s taarrownd ards.iteh.ai)Overlay character arroa

219 . Superior ISO 6862:1996 Overlay character dots https://standards.iteh.ai/catalog/standards/sist/dfc1ce59-129a-4cc6-85b3- 2110 . . Superior doubled4 92dote8 3bb54b/iso-6862-1996 Overlay character ddots

2111 Superior vector left Overlay character arls

2112 Superior hat Overlay character checkas

2113 Superior V Overlay character ckackas

2114 Superior vector right Overlay character arrs

2115 Clockwise arrow Overlay character arroc

3/o x Multiply times or x

3/l -+ Plus or minus plmin

312 ‘L Equivalent to Also: negation, or sim proportional to

313 z Asymptotic to Also: approximately equal to dsim

- 314 - Identical with iden

315 < Less than or equal to It0

316 5 Less than or greater than Iessgrtr IS0 6862: 1996(E) @ IS0

Table 3 (continueu’)

Position in Graphics Name or meaning Comments Coding table 1

317 < Less than or equivalent to lesssim

318 6 Much less than less2

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

3110 I- Right angle Also : factorial rang

3111 A Increment incre

3112 0 Degree deg

3113 ( Left angle labrak or <

3114 II Left open bracket lobrak or [

3115 c Sum of sum . iTeh STANDARD PREVIEW 4/o -. Divide Alternative to IS0 646 div or I - (standards.iteh.ai) 4/l + Minus or plus minpl w ISO 6862:1996 412 - Asymptoticallyhttps://standa rds.equaliteh. ai/toc atalog/standards/sist/dfc1ce59-129a-4cc6-85b3- simeq w d492e83bb54b/iso-6862-1996 413 - Similar to congr

414 - Approximately equal to libra

415 2 Greater than or equal to gto

416 z Greater than or less than grtrless

417 > Greater than or equivalent to grtrsim

418 9 Much greater than grtr2

419 -L Orthogonal to Also: bottom PerP

4110 L Angle aw

4111 V Backward finite difference operator Also: nabla operators nabla

0 4112 /00 perk

4113 > Angle bracket, right rabrak or >

4114 II Open bracket, right robrak or 1

4115 II Product prod

6 Table 3 (continued)

Position Coding in Graphics Name or meaning Comments table 1

plus or + 5/o + Plus

lhook 5/l c Proper inclusion in set

lkkeq 5/2 c- Identity or inclusion in set Also : identity

mem 5/3 E Set membership

514 u of sets between limits cup

inva 515 v For all

516 C longc

arru 517 t Increases; exponent

arrl 518 Left arrow

iTeh STANDARD PREVIEW arrac 519 Anti-clockwise(s tandards.iteh.ai) 5110 Mutually implies arrlr ISO 6862:1996 5111 https://sLefttan daarrowrds.i teoverh.ai/ carighttalo garrow/stand ards/sist/dfc1ce59-129a-4cc6-85b3- Irarr d492e83bb54b/iso-6862-1996 5112 Functional relationship bararr

5113 Double arrow, upward darru or A

5114 Is implied by darrl

5115 00 Infinity infin

minus or - 6/O - Minus

rhook 6/l 3 Properly includes in set Also : identical with

612 -3 Contains as rh keq

613 3 Contains cant

614 n Intersection of classes or sets hat between limits reve 615 3 There exists

bararc 616 (zr arrd 617 1 Decreases

618 Approaches arr

7 IS0 6862: 1996(E) @ IS0

Table 3 (continued)

IPncitinn “YIbIVI. in Name or meaning Coding table I Commsnf. 619 Clockwise arrcc

6110 Vertical relationship arrud

6111 Right arrow over left arrow rlarr

6112 Anti-parallel udarr

6113 Double arrow, downward darrd

6114 Implies darr

6115 Radical square root rad

7/o minutes, feet prime or ’

7/l Double prime Also : seconds, inches dprime or

712 Triplei Tprimeeh STANDARD PREVIEW trprime (standards.iteh.ai) 713 Logical or Also : disjunction checkd ISO 6862:1996 714 Logicalhttps:/ /standand ards.iteh.ai/catalog/standards/sist/dfc1Alsoce5 9: -conjunction129a-4cc 6-85b3- checku d492e83bb54b/iso-6862-1996 715 Logical not lognot

716 Planck constant planck

717 Implies imply

718 Integral int

719 Double integral dint

7110 Triple integral trint

Partial differentiation Prtl

7112 Planck constant divided by 2 n: plan2pi

Aleph aleph

Composite function Also: small circle cirsm

8 @ IS0 IS0 6862: 1996(E)

Table 3 (continued)

Position in Graphics Name or meaning Comments Coding table 2

2/l 0 Direct sum crplus

212 0- Symmetric difference crmin

213 63 Tensor product Also: Dyadic product, or zrtimes Plethysm operator

214 0. Inner product Used with tensors zrdot

l thrf 215 . . Therefore

. . 216 . Because beta

imbox 217 I Image of

origbox 218 II Original of

219 Image of imline

iTeh STANDARD PREVIEW origline 2110 Original of( standards.iteh.ai) I -- herm 2111 I Hermitian conjugate matrix ISO 6862:1996 . Direct sum dirsum 2112 + https://standards.iteh.ai/catalog/standards/sist/dfc1ce59-129a-4cc6-85b3- d492e83bb54b/iso-6862-1996 2113 Most positive mpos

homot 2114 + Homothetic

Element precedes under relation el rel 2/15 3

Not equal to nequ 3/o #

2 hasim 3/l . Has an image

accbrale 312 B Open angle bracket, left

313 L Left floor Paired with right floor, 4/3 lfloor . 314 . Triple colon tripcol

Paired with right ceiling, 4/5 lceil 315 r Left ceiling

sqsub 316 -c Square subset . 317 u Least upper bound Used for lattices lub

3/a Long triangle ltril

319 Is dominated by cyrsim