MathType MTEF v.5 (MathType 4.0 and later)

Abstract

This document describes MTEF, the binary equation format used by MathType 4.0 and later (all platforms). MTEF is embedded in OLE equation objects produced by MathType, as well as in all the file formats in which MathType can save equations. The methods used by 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 MathType 4.0 and later (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.

This document sometimes refers to MathType's internal names for values (e.g. parmLINESPACE). These are given for reference purposes and are handy for reducing errors when such values are communicated by humans.

Header

MTEF version history:

MTEF data exists in the following versions:

0MathType for Mac 1.x (this format is not described here)
1MathType for Mac 2.x and MathType for Windows 1.x
2MathType 3.x and Equation Editor 1.x
3Equation Editor 3.x (this format is not described here)
4MathType 3.5
5MathType 4.0 and later

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

Header record:

The MTEF version 5 header contains:

length in bytes descriptionvalue
1 MTEF version5
1 generating platform0 for Mac, 1 for Windows
1 generating product0 for MathType, 1 for Equation Editor
1 product version4 or later
1 product subversion0 (or ???)
length of app key application keynull-terminated string identifying the writing application
(e.g. "DSMT4" for the Wiris version of MathType)
1 equation optionsif bit 0 is set, equation is inline, else display equation
other bits are unused and must be 0

MTEF Byte Stream

This section describes the actual MTEF data following the header.

Records:

MTEF data consists of a series of records. Each record starts with a record type byte and an options byte, then is followed by data specific to the record.

The overall structure of an MTEF stream is:

  • MTEF header
  • equation preferences (size, style, spacing), preceded by the definition records to which they refer
  • initial SIZE record
  • PILE or LINE record
  • contents of PILE or LINE
  • END record

Once the header has been read, reading of the MTEF stream should be driven by reading the next record type and then acting on it. If a given record depends on data that is not contained within the record itself, such data is defined by records that precede it.

Record types:

The following record types are used:

valuesymboldescription
0ENDend of MTEF, pile, line, embellishment list, or template
1LINEline (slot)
2CHARcharacter
3TMPLtemplate
4PILEpile (vertical stack of lines)
5MATRIXmatrix
6EMBELLcharacter embellishment (e.g. hat, prime)
7RULERruler (tab-stop location)
8FONT_STYLE_DEFfont/char style definition
9SIZEgeneral size
10FULLfull size
11SUBsubscript size
12SUB2sub-subscript size
13SYMsymbol size
14SUBSYMsub-symbol size
15COLORcolor
16COLOR_DEFcolor definition
17FONT_DEFfont definition
18EQN_PREFSequation preferences (sizes, styles, spacing)
19ENCODING_DEFencoding definition
≥ 100FUTUREfor future expansion (see below)

If the record type is 100 or greater, it represents a record that will be defined in a future version of MTEF. For now, readers can assume that an unsigned integer follows the record type and is the number of bytes following it in the record (i.e. it doesn't include the record type and length). This makes it easy for software that reads MTEF to skip these records. Although it might be handy if all records had such a length value, it will only be present on future expansion records (i.e. those with record types ≥ 100).

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 line record will have the mtefOPT_LINE_NULL option set, in which case 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.

Definition records:

Some of MTEF's records (FONT_STYLE_DEF, FONT_DEF, COLOR_DEF, and ENCODING_DEF) do not represent equation structure themselves but are referred to by equation structure records. The definition records in an MTEF stream are assigned indices, starting at 1 (except for ENCODING_DEFs, which start at 5), in the order they appear in the stream. Records which refer to these definitions do so using the index value of the definition. Definition records always appear in the stream before their first reference.

Option values:

Each MTEF 5 record starts with a type byte followed by an option byte. This is different from earlier versions of MTEF where the option flags were stored in the upper 4 bits of the type byte.

The option flag values are record-dependent:

valuesymboldescription
Option flag values for all equation structure records:
0×08mtefOPT_NUDGEnudge values follow tag
Option flag values for CHAR records:
0×01mtefOPT_CHAR_EMBELLcharacter is followed by an embellishment list
0×02mtefOPT_CHAR_FUNC_STARTcharacter starts a function (sin, cos, etc.)
0×04mtefOPT_CHAR_ENC_CHAR_8character is written with an 8-bit encoded value
0×10mtefOPT_CHAR_ENC_CHAR_16character is written with an 16-bit encoded value
0×20mtefOPT_CHAR_ENC_NO_MTCODEcharacter is written without an 16-bit MTCode value
Option flag values for LINE records:
0×01mtefOPT_LINE_NULLline is a placeholder only (i.e. not displayed)
0×04mtefOPT_LINE_LSPACEline spacing value follows tag
Option flag values for LINE and PILE records:
0×02mtefOPT_LP_RULERRULER record follows LINE or PILE record
Option flag values for COLOR_DEF records:
0×01mtefCOLOR_CMYKcolor model is CMYK, else RGB
0×02mtefCOLOR_SPOTcolor is a spot color, else a process color
0×04mtefCOLOR_NAMEcolor has a name, else no name

Dimensional units:

All dimensional values are expressed in MathType's internal units, 32nds of a printer's point (a point is 1/72 inch).

Signed integer values:

Signed values are written as follows:

range of valuealgorithm
-128 ≤ value < 127 value = value + 128
written as a single byte
value < -128 or
value ≥ 127		value = value + 32768
written as 3 bytes:
byte 1: 255
byte 2: low byte of value
byte 3: high byte of value

Unsigned integer values:

Unsigned values are written as follows:

range of valuealgorithm
value < 255written as a single byte
value ≥ 255written as 3 bytes:
byte 1: 255
byte 2: low byte of value
byte 3: high byte of value

Simple 16-bit integer values:

Some values are written as 16-bits even if the value would fit in a byte. In this case, the value is written low byte followed by high byte.

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 mtefOPT_NUDGE option (0×8) and the option 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 has 128 added to it before it is written. Otherwise, two bytes of 128 are stored, followed by the offsets, dx and dy, stored as 16-bit values, low byte followed by high byte.

Typeface values:

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

valuesymbol
1fnTEXT
2fnFUNCTION
3fnVARIABLE
4fnLCGREEK
5fnUCGREEK
6fnSYMBOL
7fnVECTOR
8fnNUMBER
9fnUSER1
10fnUSER2
11fnMTEXTRA
12fnTEXT_FE
22fnEXPAND
23fnMARKER
24fnSPACE

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

Typesize values:

Typesize values (sometimes referred to as lsizes) are used in several MTEF records. Not all values may be valid in a particular record. Their meaning is as follows:

valuesymboldescription
0szFULL full
1szSUB subscript
2szSUB2 sub-subscript
3szSYM symbol
4szSUBSYM sub-symbol
5szUSER1 user 1
6szUSER2 user 2
7szDELTA delta increment

Character style values:

Character styles are represented by a single byte, bit 0 indicates bold and bit 1 indicates italic. In other words:

0plain
1bold
2italic
3bold and italic

Horizontal alignment values:

Horizontal alignment values are used in several MTEF records. Not all values may be valid in a particular record. Their meaning is as follows:

1left justification
2centered
3right justification
4relational operator alignment
5decimal point alignment

Vertical alignment values:

Vertical alignment values are used in several MTEF records. Not all values may be valid in a particular record. Their meaning is as follows:

0alignment with baseline of top line
1alignment with baseline of center line
2alignment with baseline of bottom line
3vertical centering 4 alignment with the math axis (center of +,-, brace points, etc.)

Dimension arrays:

In the EQN_PREFS record, sizes and spacing values are both written as dimension arrays. These arrays are used to record the particular settings from the Define Sizes and Define Spacing dialogs used to define the equation. Instead of recording each value as a number, the dimension array captures each value as a character string. This ensures the user always sees the value just as entered, rather than possibly modified by rounding and/or truncation in conversion (e.g. so "2.0 inches" doesn't turn into "1.999 inches").

Each array is written as a single byte count of dimensions in the array, followed by a "nibble stream" containing the dimensions. Each nibble is a 4-bit value, packed 2 per byte. The upper 4 bits of each byte precedes the lower 4 bits. If the array contains an odd number of nibbles, an additional 0 nibble is written to round out the stream to whole bytes.

Each dimension in the array consists of a units nibble (see first table below), followed by a nibble for each character in the value string (see second table below), terminated by a 0×F nibble. The following table shows how each units nibble is interpreted:

0inches
1centimeters
2points
3picas
4percentage

The following table shows how each nibble in a value string is interpreted:

0×0-0×9decimal digit
0×Adecimal point
0×Bminus sign
0×Fend of value string

Record Details

The following details the individual records in MTEF. All values are single bytes unless indicated otherwise.

END record (0):

Consists of:

There is no option byte.

LINE record (1):

Consists of:

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:

The character value itself is represented by one or more values. The presence or absence of these value is indicated by options and appear in this order:

16-bit integer MTCode valuepresent unless the mtefOPT_CHAR_ENC_NO_MTCODE option is set
8-bit font positionpresent if the mtefOPT_CHAR_ENC_CHAR_8 option is set
16-bit integer font positionpresent if the mtefOPT_CHAR_ENC_CHAR_16 option is set

The MTCode value defines the character independent of its font. MTCode is a superset of Unicode and is described in MTCode Encoding Tables. The 8-bit and 16-bit font positions are mutually exclusive but may both be absent. This is the position of the character within its font. Some of the common font encodings are given in Font Encoding Tables.

TMPL record (3):

Consists of:

  • record type (3)
  • options
  • [nudge] if mtefOPT_NUDGE is set
  • [selector] template selector code
  • [variation] template variation code (1 or 2 bytes; see below)
  • [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 Templates). The class of a template determines the order and meaning of each of its subobjects (see Template subobject order).

The variation code may be 1 or 2 bytes long. If the first byte value has the high bit set (0×80), the next byte is read and combined with the first according to this formula:

    variation code = (byte1 & 0×7F)  |  (byte2 << 8)

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

Fence template option field values (fence alignment):
0center fence on math axis, place math axis of contents on math axis of containing line (default);
1center fence on contents, place math axis of contents on math axis of containing line;
2center fence on contents, center contents on math axis of containing line.
Warning: the expanding integral property is duplicated in the integral templates variation codes (see Limit variations). On reading, MathType only looks at the variation code.
Integral template option field values:
0fixed-size integral;
1the integral expands vertically to fit its contents.

PILE record (4):

Consists of:

MATRIX record (5):

Consists of:

  • record type (5)
  • options
  • [nudge] if mtefOPT_NUDGE 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 (see below)
  • [col_parts] column partition line types (see below)
  • [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:

The embellishment types are:

valuesymboldescription
2emb1DOTover single dot
3emb2DOTover double dot
4emb3DOTover triple dot
5emb1PRIMEsingle prime
6emb2PRIMEdouble prime
7embBPRIMEbackwards prime (left of character)
8embTILDEtilde
9embHAThat (circumflex)
10embNOTdiagonal slash through character
11embRARROWover right arrow
12embLARROWover left arrow
13embBARROWover both arrow (left and right)
14embR1ARROWover right single-barbed arrow
15embL1ARROWover left single-barbed arrow
16embMBARmid-height horizontal bar
17embOBARover-bar
18emb3PRIMEtriple prime
19embFROWNover-arc, concave downward
20embSMILEover-arc, concave upward
21embX_BARSdouble diagonal bars
22embUP_BARbottom-left to top-right diagonal bar
23embDOWN_BARtop-left to bottom-right diagonal bar
24emb4DOTover quad dot
25embU_1DOTunder single dot
26embU_2DOTunder double dot
27embU_3DOTunder triple dot
28embU_4DOTunder quad dot
29embU_BARunder bar
30embU_TILDEunder tilde (~)
31embU_FROWNunder arc (ends point down)
32embU_SMILEunder arc (ends point up)
33embU_RARROWunder right arrow
34embU_LARROWunder left arrow
35embU_BARROWunder both arrow (left and right)
36embU_R1ARROWunder right arrow (1 barb)
37embU_L1ARROWunder left arrow (1 barb)

RULER record (7):

Consists of:

  • record type (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 integer offset from the left end of the slot or pile with which it is associated.

FONT_STYLE_DEF record (8):

Consists of:

This record associates a character style with a font. See Definition records.

SIZE record (9):

Consists of one of the following cases:

if lsize < 0 (explicit point size):

else if -128 < dsize < +128:

else: (large delta)

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 a typesize value and dsize is a delta from that size:

Simple typesizes, without a delta value, are written using the records described in the next section.

Typesize records (10-14):

Consists of:

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. See typesize.

COLOR records (15):

Consists of:

The appearance of this record in the stream indicates that all following equation records (until the next COLOR record) have the color defined by the indicated COLOR_DEF record.

COLOR_DEF records (16):

Consists of:

  • record type (16)
  • [options] model is RGB unless mtefCOLOR_CMYK bit is set; type is process unless mtefCOLOR_SPOT bit is set; color is unnamed unless mtefCOLOR_NAME bit is set
  • [color values] if RGB, 3 values (red, green, blue); if CMYK, 4 values (cyan, magenta, yellow, black); see below for details
  • [name] null-terminated color name; appears only if mtefCOLOR_NAME option is set

This record defines a color (see Definition records). Each color value is written as a 16-bit integer that ranges between 0 and 1000 where 0 is the absence of the color and 1000 is a fully saturated color. So, an RGB color definition for black has all three components at 0.

FONT_DEF records (17):

Consists of:

This record associates an font encoding with a font name. See Definition records.

EQN_PREFS records (18):

Consists of:

When reading arrays, the number of values may be less than or greater than expected. MTEF readers should be driven by the array count. If the array is shorter than expected, assume defaults for the missing values. If the array is longer than expected, the extra values must be skipped to stay in sync with the MTEF stream.

Spacing values are written in the following order:

0parmLINESPACELine spacing
1parmMATRIXROWMatrix row spacing
2parmMATRIXCOLMatrix column spacing
3parmSUPHEIGHTSuperscript height
4parmSUBDEPTHSubscript depth
5parmSUBSUPGAPSub/superscript gap
6parmLIMHEIGHTLimit height
7parmLIMDEPTHLimit depth
8parmLIMSPACELimit line spacing
9parmFRACTHEIGHTNumerator height
10parmFRACTDEPTHDenominator depth
11parmFRACTOVERFraction bar overhang
12parmFRACTTHICKFraction bar thickness
13parmFRACTTHICK2Sub-fraction bar thickness
14parmFRACTGAPSlash/diagonal fraction gap
15parmFENCEOVERFence overhang
16parmOPERSPACINGOperator spacing (% of normal)
17parmNONOPERSPACINGNon-operator spacing (% of normal)
18parmCHARWIDTHCharacter width adjustment
19parmMINGAPMinimum gap
20parmVRADGAPRadical gap (vertical)
21parmHRADGAPRadical gap (horizontal)
22parmRADWIDTHRadical width (% of normal)
23parmEMBELLGAPEmbellishment gap
24parmPRIMEHEIGHTPrime Height
25parmBOX_STROKE_THICKBox stroke thickness
26parmSTRIKE_THRU_THICKStrike-through thickness
27parmMATRIX_PART_THICKMatrix partition line thickness
28parmRAD_THICKRadical stroke thickness
29parmHORIZ_FENCE_GAPHorizontal fence gap

The style definition array is written as a single byte count followed by that number of style definitions. The order is defined by Typeface values, however only fnTEXT through fnTEXT_FE are written. Each style definition is written as an unsigned integer that is 0 if the style is unused in the equation or is the index of the corresponding FONT_DEF record. If the style is used (not 0), it is followed by a single byte character style.

ENCODING_DEF records (19):

Consists of:

  • record type (19)
  • [name] null-terminated encoding name

This record defines (see Definition records) a font encoding and is referred to by a FONT_DEF record. In order to reduce the size of the MTEF stream, the following 4 encodings are predefined:

ENCODING_DEF indexencoding name
1MTCode
2Unknown
3Symbol
4MTExtra

This means that the first ENCODING_DEF record in the MTEF stream is considered to have an index of 5. See Extending MathType's font and character information and MathType's character encodings for more information on font encodings.

Templates

This section shows the selector and variation codes for all the templates. The class names can be used to determine the order of subobjects in the list following the template tag (see Template subobject order).

Limit variations:

The following variation codes apply to all templates whose class is BigOpBoxClass or LimBoxClass:

variation bitssymboldescription
0×0001tvBO_LOWERlower limit is present
0×0002tvBO_UPPERupper limit is present
0×0040tvBO_SUMsummation-style limit positions, else integral-style

Template selectors and variations:

Fences (parentheses, etc.):
selectorsymboldescriptionclass
0tmANGLEangle bracketsParBoxClass
1tmPARENparenthesesParBoxClass
2tmBRACEbraces (curly brackets)ParBoxClass
3tmBRACKsquare bracketsParBoxClass
4tmBARvertical barsParBoxClass
5tmDBARdouble vertical barsParBoxClass
6tmFLOORfloor bracketsParBoxClass
7tmCEILINGceiling bracketsParBoxClass
8tmOBRACKopen (white) bracketsParBoxClass
variationsvariation bitssymboldescription
0×0001tvFENCE_Lleft fence is present
0×0002tvFENCE_Rright fence is present
Intervals:
selectorsymboldescriptionclass
9tmINTERVALunmatched brackets and parenthesesParBoxClass
variationsvariation bitssymboldescription
0×0000tvINTV_LEFT_LPleft fence is left parenthesis
0×0001tvINTV_LEFT_RPleft fence is right parenthesis
0×0002tvINTV_LEFT_LBleft fence is left bracket
0×0003tvINTV_LEFT_RBleft fence is right bracket
0×0000tvINTV_RIGHT_LPright fence is left parenthesis
0×0010tvINTV_RIGHT_RPright fence is right parenthesis
0×0020tvINTV_RIGHT_LBright fence is left bracket
0×0030tvINTV_RIGHT_RBright fence is right bracket
Radicals (square and nth roots):
selectorsymboldescriptionclass
10tmROOTradicalRootBoxClass
variationsvariationsymboldescription
0tvROOT_SQsquare root
1tvROOT_NTHnth root
Fractions:
selectorsymboldescriptionclass
11tmFRACTfractions
variationsvariation bitssymboldescription
0×0001tvFR_SMALLsubscript-size slots (piece fraction)
0×0002tvFR_SLASHfraction bar is a slash
0×0004tvFR_BASEnum. and denom. are baseline aligned
Over and Underbars:
selectorsymboldescriptionclass
12tmUBARunderbarBarBoxClass
13tmOBARoverbarBarBoxClass
variationsvariation bitssymboldescription
0×0001tvBAR_DOUBLEbar is doubled, else single
Arrows:
selectorsymboldescriptionclass
14tmARROWarrowArroBoxClass
variationsvariationsymboldescription
0×0000tvAR_SINGLEsingle arrow
0×0001tvAR_DOUBLEdouble arrow
0×0002tvAR_HARPOONharpoon
0×0004tvAR_TOPtop slot is present
0×0008tvAR_BOTTOMbottom slot is present
0×0010tvAR_LEFTif single, arrow points left
0×0020tvAR_RIGHTif single, arrow points right
0×0010tvAR_LOSif double or harpoon, large over small
0×0020tvAR_SOLif double or harpoon, small over large
Integrals (see Limit Variations):
selectorsymboldescriptionclass
15tmINTEGintegralBigOpBoxClass
variationsvariationsymboldescription
0×0001tvINT_1single integral sign
0×0002tvINT_2double integral sign
0×0003tvINT_3triple integral sign
0×0004tvINT_LOOPhas loop w/o arrows
0×0008tvINT_CW_LOOPhas clockwise loop
0×000CtvINT_CCW_LOOPhas counter-clockwise loop
0×0100tvINT_EXPANDintegral signs expand
Sums, products, coproducts, unions, intersections, etc. (see Limit Variations):
selectorsymboldescriptionclass
16tmSUMsumBigOpBoxClass
17tmPRODproductBigOpBoxClass
18tmCOPRODcoproductBigOpBoxClass
19tmUNIONunionBigOpBoxClass
20tmINTERintersectionBigOpBoxClass
21tmINTOPintegral-style big operatorBigOpBoxClass
22tmSUMOPsummation-style big operatorBigOpBoxClass
Limits (see Limit Variations):
selectorsymboldescriptionclass
23tmLIMlimitsLimBoxClass
variationsvariationsymboldescription
0tvSUBARsingle underbar
1tvDUBARdouble underbar
Horizontal braces and brackets:
selectorsymboldescriptionclass
24tmHBRACEhorizontal braceHFenceBoxClass
25tmHBRACKhorizontal bracketHFenceBoxClass
variationsvariationsymboldescription
0×0001tvHB_TOPslot is on the top, else on the bottom
Long division:
selectorsymboldescriptionclass
26tmLDIVlong divisionLDivBoxClass
variationsvariationsymboldescription
0×0001tvLD_UPPERupper slot is present
Subscripts and superscripts:
selectorsymboldescriptionclass
27tmSUBsubscriptScrBoxClass
28tmSUPsuperscriptScrBoxClass
29tmSUBSUPsubscript and superscriptScrBoxClass
variationsvariationsymboldescription
0×0001tvSU_PRECEDESscript precedes scripted item,
else follows
Dirac bra-ket notation:
selectorsymboldescriptionclass
30tmDIRACbra-ket notationDiracBoxClass
variationsvariationsymboldescription
0×0001tvDI_LEFTleft part is present
0×0002tvDI_RIGHTright part is present
Vectors:
selectorsymboldescriptionclass
31tmVECvectorHatBoxClass
variationsvariationsymboldescription
0×0001tvVE_LEFTarrow points left
0×0002tvVE_RIGHTarrow points right
0×0004tvVE_UNDERarrow under slot, else over slot
0×0008tvVE_HARPOONharpoon
Hats, arcs, tilde, joint status:
selectorsymboldescriptionclass
32tmTILDEtilde over charactersHatBoxClass
33tmHAThat over charactersHatBoxClass
34tmARCarc over charactersHatBoxClass
35tmJSTATUSjoint status constructHatBoxClass
Overstrikes (cross-outs):
selectorsymboldescriptionclass
36tmSTRIKEoverstrike (cross-out)StrikeBoxClass
variationsvariationsymboldescription
0×0001tvST_HORIZline is horizontal, else slashes
0×0002tvST_UPif slashes, slash from lower-left to upper-right is present
0×0004tvST_DOWNif slashes, slash from upper-left to lower-right is present
Boxes:
selectorsymboldescriptionclass
37tmBOXboxTBoxBoxClass
variationsvariationsymboldescription
0×0001tvBX_ROUNDcorners are round, else square
0×0002tvBX_LEFTleft side is present
0×0004tvBX_RIGHTright side is present
0×0008tvBX_TOPtop side is present
0×0010tvBX_BOTTOMbottom side is present

Template subobject order:

Template subobjects appear in object lists in the order that matches the movement of the insertion point within a template in the MathType user interface. For template classes that have more than one slot, the following list shows the order of subobjects for all templates with that class:

ArroBoxClass: expanding arrows

  • main slot
  • arrow character

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

HFenceBoxClass 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

Example

In order to illustrate MTEF with a concrete example, in this section will examine the MTEF byte stream in detail for the quadratic formula:

For this equation, MathType 7.0 for Windows generates the following MTEF:

byte positionbyte valuemeaningrecord
00×00005, 0×05MTEF versionheader
10×00011, 0×01Windows
20×00020, 0×00MathType
30×00037, 0×07MT major version
40×00040, 0×00MT minor version
50×000568, 0×44, 'D'application key
60×000683, 0×53, 'S'
70×000777, 0×4D, 'M'
80×000884, 0×54, 'T'
90×000955, 0×37, '7'
100×000A0, 0×00
110×000B0, 0×00equation options
120×000C19, 0×13record typeENCODING_DEF
encoding #5
130×000D87, 0×57, 'W'encoding name
"WinAllBasicCodePages"
140×000E105, 0×69, 'i'
150×000F110, 0×6E, 'n'
160×001065, 0×41, 'A'
170×0011108, 0×6C, 'l'
180×0012108, 0×6C, 'l'
190×001366, 0×42, 'B'
200×001497, 0×61, 'a'
210×0015115, 0×73, 's'
220×0016105, 0×69, 'i'
230×001799, 0×63, 'c'
240×001867, 0×43, 'C'
250×0019111, 0×6F, 'o'
260×001A100, 0×64, 'd'
270×001B101, 0×65, 'e'
280×001C80, 0×50, 'P'
290×001D97, 0×61, 'a'
300×001E103, 0×67, 'g'
310×001F101, 0×65, 'e'
320×0020115, 0×73, 's'
330×00210, 0×00
340×002217, 0×11record typeFONT_DEF
font def #1
350×00235, 0×05index of encoding
WinAllBasicCodePages
360×002484, 0×54, 'T'font name
"Times New Roman"
370×0025105, 0×69, 'i'
380×0026109, 0×6D, 'm'
390×0027101, 0×65, 'e'
400×0028115, 0×73, 's'
410×002932, 0×20, ' '
420×002A78, 0×4E, 'N'
430×002B101, 0×65, 'e'
440×002C119, 0×77, 'w'
450×002D32, 0×20, ' '
460×002E82, 0×52, 'R'
470×002F111, 0×6F, 'o'
480×0030109, 0×6D, 'm'
490×003197, 0×61, 'a'
500×0032110, 0×6E, 'n'
510×00330, 0×00
520×003417, 0×11record typeFONT_DEF
font def #2
530×00353, 0×03index of encoding
Symbol
540×003683, 0×53, 'S'font name
"Symbol"
550×0037121, 0×79, 'y'
560×0038109, 0×6D, 'm'
570×003998, 0×62, 'b'
580×003A111, 0×6F, 'o'
590×003B108, 0×6C, 'l'
600×003C0, 0×00
610×003D17, 0×11record typeFONT_DEF
font def #3
620×003E5, 0×05index of encoding
WinAllBasicCodePages
630×003F67, 0×43, 'C'font name
"Courier New"
640×0040111, 0×6F, 'o'
650×0041117, 0×75, 'u'
660×0042114, 0×72, 'r'
670×0043105, 0×69, 'i'
680×0044101, 0×65, 'e'
690×0045114, 0×72, 'r'
700×004632, 0×20, ' '
710×004778, 0×4E, 'N'
720×0048101, 0×65, 'e'
730×0049119, 0×77, 'w'
740×004A0, 0×00
750×004B17, 0×11record typeFONT_DEF
font def #4
760×004C4, 0×04index of encoding
MTExtra
770×004D77, 0×4D, 'M'font name
"MT Extra"
780×004E84, 0×54, 'T'
790×004F32, 0×20, ' '
800×005069, 0×45, 'E'
810×0051120, 0×78, 'x'
820×0052116, 0×74, 't'
830×0053114, 0×72, 'r'
840×005497, 0×61, 'a'
850×00550, 0×00
860×005618, 0×12record typeEQN_PREFS
870×00570, 0×00options
880×00588, 0×08size array count
890×005933, 0×21, '!'nibble array containing:
size #1: "12 points"
size #2: "58 %"
size #3: "42 %"
size #4: "150 %"
size #5: "100 %"
size #6: "75 %"
size #7: "150 %"
size #8: "1 point"
900×005A47, 0×2F, '/'
910×005B69, 0×45, 'E'
920×005C143, 0×8F
930×005D68, 0×44, 'D'
940×005E47, 0×2F, '/'
950×005F65, 0×41, 'A'
960×006080, 0×50, 'P'
970×0061244, 0×F4
980×006216, 0×10
990×006315, 0×0F
1000×006471, 0×47, 'G'
1010×006595, 0×5F, '_'
1020×006665, 0×41, 'A'
1030×006780, 0×50, 'P'
1040×0068242, 0×F2
1050×006931, 0×1F
1060×006A30, 0×1Espacing array count
1070×006B65, 0×41, 'A'nibble array containing
30 values
1080×006C80, 0×50, 'P'
1090×006D244, 0×F4
1100×006E21, 0×15
1110×006F15, 0×0F
1120×007065, 0×41, 'A'
1130×00710, 0×00
1140×0072244, 0×F4
1150×007369, 0×45, 'E'
1160×0074244, 0×F4
1170×007537, 0×25, '%'
1180×0076244, 0×F4
1190×0077143, 0×8F
1200×007866, 0×42, 'B'
1210×007995, 0×5F, '_'
1220×007A65, 0×41, 'A'
1230×007B0, 0×00
1240×007C244, 0×F4
1250×007D16, 0×10
1260×007E15, 0×0F
1270×007F67, 0×43, 'C'
1280×008095, 0×5F, '_'
1290×008165, 0×41, 'A'
1300×00820, 0×00
1310×0083242, 0×F2
1320×008431, 0×1F
1330×008532, 0×20, ' '
1340×0086165, 0×A5
1350×0087242, 0×F2
1360×008810, 0×0A
1370×008937, 0×25
1380×008A244, 0×F4
1390×008B143, 0×8F
1400×008C65, 0×41, '!'
1410×008D244, 0×F4
1420×008E16, 0×10
1430×008F15, 0×0F
1440×009064, 0×41, 'A'
1450×00910, 0×00
1460×0092244, 0×F4
1470×009315, 0×0F
1480×009472, 0×48, 'H'
1490×0095244, 0×F4
1500×009623, 0×17
1510×0097244, 0×F4
1520×0098143, 0×8F
1530×009964, 0×41, 'A'
1540×009A0, 0×00
1550×009B242, 0×F2
1560×009C26, 0×1A
1570×009D95, 0×5F, '_'
1580×009E68, 0×44, 'D'
1590×009F95, 0×5F, '_'
1600×00A069, 0×45, 'E'
1610×00A1244, 0×F4
1620×00A295, 0×5F, '_'
1630×00A369, 0×45, 'E'
1640×00A4244, 0×F4
1650×00A595, 0×5F, '_'
1660×00A665, 0×41, 'A'
1670×00A715, 0×0F
1680×00A812, 0×0Cstyle array count
1690×00A91, 0×01style #1:
font def #1, plain
1700×00AA0, 0×00
1710×00AB1, 0×01style #2:
font def #1, plain
1720×00AC0, 0×00
1730×00AD1, 0×01style #3:
font def #1, italic
1740×00AE2, 0×02
1750×00AF2, 0×02style #4:
font def #2, italic
1760×00B02, 0×02
1770×00B12, 0×02style #5:
font def #2, plain
1780×00B20, 0×00
1790×00B32, 0×02style #6:
font def #2, plain
1800×00B40, 0×00
1810×00B51, 0×01style #7:
font def #1, bold
1820×00B61, 0×01
1830×00B71, 0×01style #8:
font def #1, plain
1840×00B80, 0×00
1850×00B93, 0×03style #9:
font def #3, plain
1860×00BA0, 0×00
1870×00BB1, 0×01style #10:
font def #1, plain
1880×00BC0, 0×00
1890×00BD4, 0×04style #11:
font def #4, plain
1900×00BE0, 0×00
1910×00BF0, 0×00style #12: (not used)
1920×00C010, 0×0Arecord typeSIZE_FULL
1930×00C11, 0×01record typeLINE
1940×00C20, 0×00options
1950×00C33, 0×03record typeTMPL
fraction
1960×00C40, 0×00options
1970×00C511, 0×0Bselector: tmFRACT
1980×00C60, 0×00variation: none
1990×00C70, 0×00template-specific options
2000×00C81, 0×01record typeLINE
numerator
2010×00C90, 0×00options
2020×00CA2, 0×02record typeCHAR
– (minus sign)
2030×00CB4, 0×04options: mtefOPT_CHAR_ENC_CHAR_8
2040×00CC134, 0×86typeface: 134 - 128 = 6 (Symbol style)
2050×00CD18, 0×12MTCode value: 0×2212 (minus sign)
2060×00CE34, 0×22, '""""'
2070×00CF45, 0×2D, '-'font-encoded value: 0×2D (minus sign)
2080×00D02, 0×02record typeCHAR
b
2090×00D10, 0×00options
2100×00D2131, 0×83typeface: 131 - 128 = 3 (Variable style)
2110×00D398, 0×62, 'b'MTCode value: 0×0062 ('b')
2120×00D40, 0×00
2130×00D52, 0×02record typeCHAR
plus-minus sign: ±
2140×00D64, 0×04options: mtefOPT_CHAR_ENC_CHAR_8
2150×00D7134, 0×86typeface: 134 - 128 = 6 (Symbol style)
2160×00D8177, 0×B1MTCode value: 0×00B1 (plus-minus sign)
2170×00D90, 0×00
2180×00DA177, 0×B1font-encoded value: 0×B1 (plus-minus sign)
2190×00DB3, 0×03record typeTMPL
square root
2200×00DC0, 0×00options
2210×00DD10, 0×0Aselector: tmROOT
2220×00DE0, 0×00variations: tvROOT_SQ (square root)
2230×00DF0, 0×00template-specific options
2240×00E01, 0×01record typeLINE
radicand
2250×00E10, 0×00options
2260×00E22, 0×02record typeCHAR
b
2270×00E30, 0×00options
2280×00E4131, 0×83typeface: 131 - 128 = 3 (Variable style)
2290×00E598, 0×62, 'b'MTCode value: 0×0062 ('b')
2300×00E60, 0×00
2310×00E73, 0×03record typeTMPL
superscript
2320×00E80, 0×00options
2330×00E928, 0×1Cselector: tmSUP
2340×00EA0, 0×00variations: none
2350×00EB0, 0×00template-specific options
2360×00EC11, 0×0Brecord typeSIZE_SUB
2370×00ED1, 0×01record typeLINE
missing superscript
2380×00EE1, 0×01options: mtefOPT_LINE_NULL
2390×00EF1, 0×01record typeLINE
subscript
2400×00F00, 0×00options
2410×00F12, 0×02record typeCHAR
2
2420×00F20, 0×00options
2430×00F3136, 0×88typeface: 136 - 128 = 8 (Number style)
2440×00F450, 0×32, '2'MTCode value: 0×0032 ('2')
2450×00F50, 0×00
2460×00F60, 0×00record typeEND of subscript line
2470×00F70, 0×00record typeEND of subscript template
2480×00F810, 0×0Arecord typeSIZE_FULL
2490×00F92, 0×02record typeCHAR
– (minus sign)
2500×00FA4, 0×04options: mtefOPT_CHAR_ENC_CHAR_8
2510×00FB134, 0×86typeface: 134 - 128 = 6 (Symbol style)
2520×00FC18, 0×12MTCode value: 0×2212 (minus sign)
2530×00FD34, 0×22, '""""'
2540×00FE45, 0×2D, '-'font-encoded value: 0×2D (minus sign)
2550×00FF38, 0×26
2560×01002, 0×02record typeCHAR
4
2570×01010, 0×00options
2580×0102136, 0×88typeface: 136 - 128 = 8 (Number style)
2590×010352, 0×34, '4'MTCode value: 0×0034 ('4')
2600×01040, 0×00
2610×01052, 0×02record typeCHAR
a
2620×01060, 0×00options
2630×0107131, 0×83typeface: 131 - 128 = 3 (Variable style)
2640×010897, 0×61, 'a'MTCode value: 0×0061 ('a')
2650×01090, 0×00
2660×010A2, 0×02record typeCHAR
c
2670×010B0, 0×00options
2680×010C131, 0×83typeface: 131 - 128 = 3 (Variable style)
2690×010D99, 0×63, 'c'MTCode value: 0×0063 ('c')
2700×010E 0, 0×00
2710×010F0, 0×00record typeEND of radicand line
2720×011011, 0×0Brecord typeSIZE_SUB
2730×01111, 0×01record typeLINE
missing radicand
2740×01121, 0×01options: mtefOPT_LINE_NULL
2750×01130, 0×00record typeEND of radical template
2760×01140, 0×00record typeEND of numerator line
2770×011510, 0×0Arecord typeSIZE_FULL
2780×01161, 0×01record typeLINE
denominator
2790×01170, 0×00options
2800×01182, 0×02record typeCHAR
2
2810×01190, 0×00options
2820×011A136, 0×88typeface: 136 - 128 = 8 (Number style)
2830×011B50, 0×32, '2'MTCode value: 0×0032 ('2')
2840×011C0, 0×00
2850×011D2, 0×02record typeCHAR
a
2860×011E0, 0×00options
2870×011F131, 0×83typeface: 131 - 128 = 3 (Variable style)
2880×012097, 0×61, 'a'MTCode value: 0×0061 ('a')
2890×01210, 0×00
2900×01220, 0×00record typeEND of denominator line
2910×01230, 0×00record typeEND of fraction template
2920×01240, 0×00record typeEND of equation line
2930×01250, 0×00record typeEND of equation