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MathType MTEF v.3 (Equation Editor 3.x)

Abstract

This document describes MTEF, the binary equation format used by Equation Editor 3.x (all platforms). MTEF was embedded in OLE equation objects produced by the legacy Equation Editor, as well as in all the file formats in which Equation Editor could save equations. The methods used by Equation Editor and MathType to embed this information in such files are described in a separate document. See How MTEF is Stored in Files and Objects.

Introduction

This document describes the binary equation format used by Equation Editor 3.x (all platforms). Although MTEF is not the most friendly medium for defining equations, there have been so many requests for this information, we decided to publish it anyway. We must warn the reader that it is not an easy format to understand and, more importantly, MathType is not at all forgiving in its processing of it. This means that if you send MathType MTEF with errors, it might crash. At a minimum, you will get an equation with formatting problems. Also, it is a binary format. This means that you can't use character strings to represent equations and it makes creating MTEF a little harder with programming languages like Visual Basic.

How MathType stores an equation description in an OLE equation object, a file, or on the clipboard is not described here. Please see the document on MathType MTEF Storage for more information on this subject.

Header

MTEF version history:

MTEF data exists in the following versions:

  • 0 MathType for the Mac 1.x (this format is not described here)

  • 1 MathType for the Mac 2.x and MathType for Windows 1.x

  • 2 MathType 3.x and Equation Editor 1.x

  • 3 Equation Editor 3.x (the format described here)

  • 4 MathType 3.5

  • 5 MathType 4.0 and later

Version 2 differs from version 1 only in the format of the header.

MTEF header (version 1):

The version 1 header consists of a single byte version number. This number is 1 if the MTEF was generated on the Mac or 101 if it was generated by the Windows version.

MTEF header (version 2 and later):

The version 2 header consists of a 5-byte header:

  • byte description value 0 MTEF version 3 1 generating platform 0 for Mac, 1 for Windows 2 generating product 0 for MathType, 1 for Equation Editor 3 product version 3 4 product subversion 0

MTEF byte stream

This section describes the actual MTEF data following the header. MTEF data consists of a series of records. Each record starts with a tag byte containing the record type and some flag bits. The overall structure is:

Most MTEF values are bytes. Word values (16-bit) are written low-order byte followed by high-order byte. All dimensional values are expressed in MathType’s internal units, 32nds of a point (A point is 1/72 inch).

Tag byte structure:

Each tag byte consists of a record type in the low-order 4 bits and option flags in the high-order 4 bits. The following record types are used:

value

symbol

description

0

END

end of MTEF, pile, line, embellishment list, or template

1

LINE

line (slot) record

2

CHAR

character record

3

TMPL

template record

4

PILE

pile (vertical stack of lines) record

5

MATRIX

matrix record

6

EMBELL

character embellishment (e.g. hat, prime) record

7

RULER

ruler (tab-stop location) record

8

FONT

font name record

9

SIZE

general size record

10

FULL

full size record

11

SUB

subscript size record

12

SUB2

sub-subscript size record

13

SYM

symbol size record

14

SUBSYM

sub-symbol size record

Option values:

The option flag values are record-dependent:

value

symbol

description

Option flag values for all equation structure records:

0x8

xfLMOVE

nudge values follow tag

Option flag values for CHAR records:

0x1

xfAUTO

character is a candidate for function recognition

0x2

xfEMBELL

character is followed by an embellishment list

Option flag values for LINE records:

0x1

xfNULL

line is a placeholder only

0x4

xfLSPACE

line spacing value follows tag

Option flag values for LINE and PILE records:

0x2

xfRULER

RULER record follows LINE or PILE record

Nudge values:

LINE, CHAR, TMPL, PILE, MATRIX, and EMBELL records may store the result of nudging (small offsets applied by the user). A nudged record has the xfLMOVE flag (0x8) set in the tag byte and the tag byte is followed immediately by the nudge offset. The nudge offset consists of either two bytes or six, depending on the amount of offset. If –128 < dx < +128 and –128 < dy < +128, then the offsets are stored as two bytes, dx followed by dy, where each value is biased by 128. Otherwise, two bytes of 128 are stored, followed by the (unbiased) offsets, dx and dy, stored as 16-bit values.

Typeface values:

CHAR records contain a typeface value (biased by 128). If the value is positive, it represents one of MathType’s styles:

value

symbol

1

fnTEXT

2

fnFUNCTION

3

fnVARIABLE

4

fnLCGREEK

5

fnUCGREEK

6

fnSYMBOL

7

fnVECTOR

8

fnNUMBER

9

fnUSER1

10

fnUSER2

11

fnMTEXTRA

12

fnTEXT_FE

If the value is negative, it represents an explicit font as specified by a FONT record.

Object lists:

LINE, CHAR, TMPL, PILE, MATRIX, and RULER records are followed by object lists that define contents of each equation structure. Each object list contains a sequence of records of any type and terminated by an END record. In a special case for LINE records, if there are no objects in the list, the xfNULL flag will be set in the tag byte and the object list is omitted entirely (i.e. no END record). Although there are no restrictions made by the MTEF format on what record types may occur in any particular list, the user interface prevents certain things from happening. For example, the object list defining the contents of a pile contains only LINE records.

Record details

END record (0):

Contains just the tag byte. No flags are defined.

LINE record (1):

Consists of:

  • tag (1)

  • [nudge] if xfLMOVE is set

  • [line spacing] if xfLSPACE is set

  • [RULER record] if xfRULER is set

  • object list contents of line (a single pile, characters and templates, or nothing)

The line spacing value, if present, is the distance between the baseline of this line and the line above it.

CHAR record (2):

Consists of:

  • tag (2)

  • [nudge] if xfLMOVE is set

  • [typeface] typeface value (see FONT below) + 128

  • [character] 16-bit character value (encoding depends on typeface)

  • [embellishment list] if xfEMBELL is set (embellishments)

Associated with every font is an encoding (a one-to-one mapping between character value and glyph; e.g. ASCII). The character represented by the character value is determined according to the encoding of the typeface value. The 16-bit character value is a Unicode value if the font is a text font or a font index if the font is symbolic.

TMPL record (3):

Consists of:

  • tag (3)

  • [nudge] if xfLMOVE is set

  • [selector] template selector code

  • [variation] template variation code

  • [options] template-specific options

  • [subobject list] either a single character (e.g. sigma in a summation) and/or lines

The template selector and variation codes determine the class of the template and various properties of the template, such as which subobjects can be deleted by the user (see Template Selectors and Variations for a list). The class of a template determines the order and meaning of each of its subobjects (see Template Subobject Order).

The template-specific options field is only used for integrals and fence templates:

Integral template option field values:

0

fixed-size integral;

1

the integral expands vertically to fit its contents.

Fence template option field values (fence alignment):

0

center fence on math axis, place math axis of contents on math axis of containing line (default);

1

center fence on contents, place math axis of contents on math axis of containing line;

2

center fence on contents, center contents on math axis of containing line.

PILE record (4):

Consists of:

  • tag (4)

  • [nudge] if xfLMOVE is set

  • [halign] horizontal alignment

  • [valign] vertical alignment

  • [RULER record] if xfRULER is set

  • [object list] list of lines contained by the pile

Horizontal alignment:

1

left justification

2

centered

3

right justification

4

relational operator alignment

5

decimal point alignment

Vertical alignment:

0

alignment with baseline of top line

1

alignment with baseline of center line

2

alignment with baseline of bottom line

3

vertical centering

MATRIX record (5):

Consists of:

  • tag (5)

  • [nudge] if xfLMOVE is set

  • [valign] vertical alignment of matrix within container

  • [h_just] horizontal alignment within columns

  • [v_just] vertical alignment within columns

  • [rows] number of rows

  • [cols] number of columns

  • [row_parts] row partition line types

  • [col_parts] column partition line types

  • [object list] list of lines, one for each element of the matrix, in order from left-to-right and top-to-bottom

The values for valign, h_just, and v_just are described in PILE above.

The row partition line type list consists of two-bit values for each possible partition line (one more than the number of rows), rounded out to the nearest byte. Each value determines the line style of the corresponding partition line (0 for none, 1 for solid, 2 for dashed, or 3 for dotted). Similarly for the column partition lines.

EMBELL record (6):

Consists of:

  • tag (6)

  • nudge] if xfLMOVE is set

  • [embell] embellishment type

The embellishment types are:

value

symbol

description

2

embDOT

single dot

3

embDDOT

double dot

4

embTDOT

triple dot

5

embPRIME

single prime

6

embDPRIME

double prime

7

embBPRIME

backwards prime (left of character)

8

embTILDE

tilde

9

embHAT

hat (circumflex)

10

embNOT

diagonal slash through character

11

embRARROW

right arrow

12

embLARROW

left arrow

13

embBARROW

double-headed arrow

14

embR1ARROW

right single-barbed arrow

15

embL1ARROW

left single-barbed arrow

16

embMBAR

mid-height horizontal bar

17

embOBAR

over-bar

18

embTPRIME

triple prime

19

embFROWN

over-arc, concave downward

20

embSMILE

over-arc, concave upward

RULER record (7):

Consists of:

  • tag (7)

  • [n_stops] number of tab-stops

  • [tab-stop list] tab-stops in order from left-to-right

Each tab stop is described by a tab-stop type (0 for left, 1 for center, 2 for right, 3 for equal, 4 for decimal), followed by a 16-bit offset from the left end of the slot or pile with which it is associated.

FONT record (8):

Consists of:

  • tag (8)

  • [tface] typeface number

  • [style] 1 for italic and/or 2 for bold

  • [name] font name (null-terminated)

This record associates a typeface number with an explicit font and style. The typeface number is the negative (which makes it positive) of the typeface value (unbiased) that appears in CHAR records that might follow a given FONT record. For example, a 3 in the FONT record corresponds to 125 (-3 + 128) in the CHAR record.

SIZE record (9):

Consists of one of the following cases:

if lsize < 0 (explicit point size):

  • tag (9)

  • 101

  • -lsize (16 bits)

else if –128 < dsize < +128:

  • tag (9)

  • lsize

  • dsize + 128

else: (large delta)

  • tag (9)

  • 100

  • lsize

  • dsize (16 bits)

Sizes in MathType are represented as a pair of values, lsize and dsize. Lsize stands for "logical size", dsize for "delta size". If it is negative, it is an explicit point size (in 32nds of a point) negated and dsize is ignored. Otherwise, lsize is one of the following typesize values and dsize is a delta from that size:

value

symbol

description

0

szFULL

full

1

szSUB

subscript

2

szSUB2

sub-subscript

3

szSYM

symbol

4

szSUBSYM

sub-symbol

5

szUSER1

user 1

6

szUSER2

user 2

TYPESIZE records (10-14):

Consists of:

  • tag (10-14)

These records are just short ways of specifying a simple typesize where dsize is zero. The tag value represents an lsize + 10. So if the tag value is 10, it means equation content following it will be Full size (szFULL), tag value 11 means szSUB, and so on.

Template selectors and variations

This section shows the selector and variation codes for all the templates. The symbols shown here are internal identifiers in MathType and are for reference only. The class names can be used to determine the order of subobjects in the list following the template tag (see Template Subobject Order).

selector

symbol

description

class

0

tmANGLE

angle brackets

ParBoxClass

:::

variation

symbol

description

:::

0

tvBANGLE

both left and right

:::

1

tvLANGLE

left only

:::

2

tvRANGLE

right only

1

tmPAREN

parentheses

ParBoxClass

:::

variation

symbol

description

:::

0

tvBPAREN

both left and right

:::

1

tvLPAREN

left only

:::

2

tvRPAREN

right only

2

tmBRACE

braces (curly brackets)

ParBoxClass

:::

variation

symbol

description

:::

0

tvBBRACE

both left and right

:::

1

tvLBRACE

left only

:::

2

tvRBRACE

right only

3

tmBRACK

square brackets

ParBoxClass

:::

variation

symbol

description

:::

0

tvBBRACK

both left and right

:::

1

tvLBRACK

left only

:::

2

tvRBRACK

right only

4

tmBAR

vertical bars

ParBoxClass

:::

variation

symbol

description

:::

0

tvBBAR

both left and right

:::

1

tvLBAR

left only

:::

2

tvRBAR

right only

5

tmDBAR

double vertical bars

ParBoxClass

:::

variation

symbol

description

:::

0

tvBDBAR

both left and right

:::

1

tvLDBAR

left only

:::

2

tvRDBAR

right only

6

tmFLOOR

floor brackets

ParBoxClass

7

tmCEILING

ceiling brackets

ParBoxClass

8

tmLBLB

left brace, left brace

ParBoxClass

9

tmRBRB

right brace, right brace

ParBoxClass

10

tmRBLB

right brace, left brace

ParBoxClass

11

tmLBRP

left brace, right parenthesis

ParBoxClass

12

tmLPRB

left parenthesis, right brace

ParBoxClass

13

tmROOT

radical

RootBoxClass

:::

variation

symbol

description

:::

0

tvSQROOT

square root

:::

1

tvNTHROOT

nth root

14

tmFRACT

fractions

FracBoxClass

:::

variation

symbol

description

:::

0

tvFFRACT

full-size slots

:::

1

tvPFRACT

subscript-size slots (piece fraction)

15

tmSCRIPT

subscript/superscript

ScrBoxClass

:::

variation

symbol

description

:::

0

tvSUPER

superscript

:::

1

tvSUB

subscript

:::

2

tvSUBSUP

both

16

tmUBAR

underbar

BarBoxClass

:::

variation

symbol

description

:::

0

tvSUBAR

single underbar

:::

1

tvDUBAR

double underbar

17

tmOBAR

overbar

BarBoxClass

:::

variation

symbol

description

:::

0

tvSOBAR

single overbar

:::

1

tvDOBAR

double overbar

18

tmLARROW

left-pointing arrow

ArroBoxClass

:::

variation

symbol

description

:::

0

tvLTARROW

box on top

:::

1

tvLBARROW

box on bottom

19

tmRARROW

right-pointing arrow

ArroBoxClass

:::

variation

symbol

description

:::

0

tvRTARROW

box on top

:::

1

tvRBARROW

box on bottom

20

tmBARROW

left- and right-pointing arrow

ArroBoxClass

:::

variation

symbol

description

:::

0

tvBTARROW

box on top

:::

1

tvBBARROW

box on bottom

21

tmSINT

single integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvNSINT

no limits

:::

1

tvLSINT

lower limit only

:::

2

tvBSINT

both limits

:::

3

tvNCINT

contour, no limits

:::

4

tvLCINT

contour, lower limit only

22

tmDINT

double integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvNDINT

no limits

:::

1

tvLDINT

lower limit only

:::

2

tvNAINT

area, no limits

:::

3

tvLAINT

area, lower limit only

23

tmTINT

triple integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvNTINT

no limits

:::

1

tvLTINT

lower limit only

:::

2

tvNVINT

volume, no limits

:::

3

tvLVINT

volume, lower limit only

24

tmSSINT

single summation-style integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvBSSINT

both limits

:::

1

tvLSSINT

lower limit only

:::

2

tvLCSINT

contour, lower limit only

25

tmDSINT

double summation-style integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLASINT

area, lower limit only

:::

1

tvLDSINT

lower limit only

26

tmTSINT

triple summation-style integral

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLVSINT

volume, lower limit only

:::

1

tvLTSINT

lower limit only

27

tmUHBRACE

upper horizontal brace

HBrBoxClass

28

tmLHBRACE

lower horizontal brace

HBrBoxClass

29

tmSUM

summation

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLSUM

lower only

:::

1

tvBSUM

both upper and lower limits

:::

2

tvNSUM

no limits

30

tmISUM

summation (integral-style limits)

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLISUM

lower only

:::

1

tvBISUM

both upper and lower limits

31

tmPROD

product

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLPROD

lower only

:::

1

tvBPROD

both upper and lower limits

:::

2

tvNPROD

no limits

32

tmIPROD

product (integral-style limits)

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLIPROD

lower only

:::

1

tvBIPROD

both upper and lower limits

33

tmCOPROD

coproduct

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLCOPROD

lower only

:::

1

tvBCOPROD

both upper and lower limits

:::

2

tvNCOPROD

no limits

34

tmICOPROD

coproduct (integral-style limits)

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLICOPROD

lower only

:::

1

tvBICOPROD

both upper and lower limits

35

tmUNION

union

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLUNION

lower only

:::

1

tvBUNION

both upper and lower limits

:::

2

tvNUNION

no limits

36

tmIUNION

union (integral-style limits)

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLIUNION

lower only

:::

1

tvBIUNION

both upper and lower limits

37

tmINTER

intersection

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLINTER

lower only

:::

1

tvBINTER

both upper and lower limits

:::

2

tvNINTER

no limits

38

tmIINTER

intersection (integral-style limits)

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvLIINTER

lower only

:::

1

tvBIINTER

both upper and lower limits

39

tmLIM

limit

LimBoxClass

:::

variation

symbol

description

:::

0

tvULIM

upper limit

:::

1

tvLLIM

lower limit

:::

2

tvBLIM

both upper and lower limits

40

tmLDIV

long division

LDivBoxClass

:::

variation

symbol

description

:::

0

tvLDIVW

with upper slot

:::

1

tvLDIVWO

without upper slot

41

tmSLFRACT

slash fractions

SlashBoxClass

:::

variation

symbol

description

:::

0

tvSLFNORM

normal

:::

1

tvSLFBASE

slots on baseline

:::

2

tvSLFSUB

subscript-sized slots

42

tmINTOP

big integral-style operators

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvUINTOP

upper limit

:::

1

tvLINTOP

lower limit

:::

2

tvBINTOP

both upper and lower limits

43

tmSUMOP

big summation-style operators

BigOpBoxClass

:::

variation

symbol

description

:::

0

tvUSUMOP

upper limit

:::

1

tvLSUMOP

lower limit

:::

2

tvBSUMOP

both upper and lower limits

44

tmLSCRIPT

leading sub- and superscripts

ScrBoxClass

:::

variation

symbol

description

:::

0

tvLSUPER

superscript

:::

1

tvLSUB

subscript

:::

2

tvLSUBSUP

subscript and superscript

45

tmDIRAC

Dirac delta

DiracBoxClass

:::

variation

symbol

description

:::

0

tvBDIRAC

both left and right slots

:::

1

tvLDIRAC

left slot only

:::

2

tvRDIRAC

right slot only

46

tmUARROW

under arrow

VectorBoxClass

:::

variation

symbol

description

:::

0

tvLUARROW

left-pointing

:::

1

tvRUARROW

right-pointing

:::

2

tvDUARROW

double-headed (left and right)

47

tmOARROW

over arrow

VectorBoxClass

:::

variation

symbol

description

:::

0

tvLOARROW

left-pointing

:::

1

tvROARROW

right-pointing

:::

2

tvDOARROW

double-headed (left and right)

48

tmOARC

over arc

ArcBoxClass

Template subobject order

The following list shows the order of subobjects for each template class:

ArcBoxClass vector notation

  • main slot

ArroBoxClass expanding arrows

  • main slot

  • arrow character

BarBoxClass over-bars and under-bars

  • main slot

BigOpBoxClass integrals, summations, products, etc.

  • main slot (summand, integrand)

  • upper slot

  • lower slot

  • large operator character

DiracBoxClass three-part bracket structure

  • left slot

  • right slot

  • left angle bracket (optional)

  • vertical bar

  • right angle bracket (optional)

FracBoxClass fractions with a horizontal bar

  • numerator slot

  • denominator slot

HBrBoxClass horizontal expanding braces

  • main slot

  • small slot

  • brace character

LDivBoxClass long division

  • dividend slot

  • quotient slot

LimBoxClass limits

  • main slot

  • lower slot

  • upper slot

ParBoxClass parenthesized or bracketed slots

  • main slot

  • left fence character (optional)

  • right fence character (optional)

RootBoxClass radical sign

  • main slot

  • radicand slot

ScrBoxClass subscripts and superscripts

  • subscript slot

  • superscript slot

SlashBoxClass fractions with a diagonal bar

  • numerator slot

  • denominator slot

VectorBoxClass box with upper or lower arrow

  • main slot

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