Antenna House Formatter V7.4 - MathML Conformance

Antenna House Formatter V7.4 enables to render Mathematical Markup Language (MathML) Version 3.0 2nd Edition (PDF version) defined by W3C utilizing its originally developed engine. For that reason it's possible to render high resolution images in PDF. See also Graphics to learn how to utilize MathML. See also Option Setting File.

Antenna House Formatter V7.4 Lite customers must purchase “Antenna House Formatter MathML Option” to render MathML originally. For more details, see also Antenna House website.

The below table shows the implemented MathML elements and attributes.

[yes] in the list means that the element or property is implemented.
[partial] means that the element or property is partially implemented.
[no] means not implemented.

CAUTION:	We strongly recommend to embed fonts when generating PDF.

Element	Attribute	Condition	Comments
2.1.6	id	yes	Evaluates the following CSS properties: font-family font-weight font-style font-size color background-color As for id and class, external CSS settings will be reflected. The setting takes precedence over the setting by mathvariant, fontfamily, etc. that are specified within the same tag. In CSS, the CSS property specified to <math> is evaluated as a property of the image even if it's not listed above.
	class	yes
	style	yes
	href	yes	A hyperlink does not work.
	xref	no
	other	no	[deprecated attribute]
2.2 <math>		yes	xmlns="http://www.w3.org/1998/Math/MathML"
	display	yes	The default value can be changed in the Option Setting File.
	maxwidth	yes
	overflow	partial	Implements linebreak only. Except for linebreak, the automatic line breaking does not occur but the line overflows. It has been extended to accept the value of none. This does not output an error message.
	altimg	no	Ignored.
	altimg-width	no	Ignored.
	altimg-height	no	Ignored.
	altimg-valign	no	Ignored.
	alttext	yes
	cdgroup	no
	macros	no	[deprecated attribute]
	mode	yes	[deprecated attribute] The setting by display takes precedence.
3.1.10	mathcolor	yes
3.1.10	mathbackground	yes
3.2.1.2 <mglyph>		yes
	src	yes	Supports only to raster images, such as JPEG or PNG.
	width	yes
	height	yes
	valign	yes
	alt	yes
	fontfamily	yes	[deprecated attribute] Invalid when src is specified.
	index	yes	[deprecated attribute] Invalid when src is specified. The value of index is considered GlyphID.
3.2.2	mathvariant	partial	initial, tailed, looped and stretched are not supported.
	mathsize	yes
	dir	yes	See also Restrictions.
	fontfamily	yes	[deprecated attribute] When mathvariant is used together, the effect is not guaranteed.
	fontweight	yes	[deprecated attribute] When mathvariant is used together, the effect is not guaranteed.
	fontstyle	yes	[deprecated attribute] When mathvariant is used together, the effect is not guaranteed.
	fontsize	yes	[deprecated attribute] When mathsize is used together, the effect is not guaranteed.
	color	yes	[deprecated attribute] When mathcolor is used together, the effect is not guaranteed.
	background	yes	[deprecated attribute] When mathbackground is used together, the effect is not guaranteed.
3.2.3 <mi>		yes	Although it is not written in the specification that a number, such as <mi>3</mi> is not made italic, the number does not become italic after the model of lots of implementations. This restriction can be adjusted in the Option Setting File.
3.2.4 <mn>		yes
3.2.5 <mo>		yes
	form	yes
	lspace	yes	The default value can be changed in the Option Setting File when it's not registered to the operator dictionary.
	rspace	yes	The default value can be changed in the Option Setting File when it's not registered to the operator dictionary.
	fence	yes
	separator	no	Ignored.
	stretchy	yes	The extension was made so that the signed length can be specified with a value like stretchy="-0.2em". Note that an unsigned length cannot be specified. Specifying a signed length also means true. Normally a character is stretched by keeping the original width, etc. By specifying a positive length for stretchy, the character is stretched to both left and right (or upwards and downwards) to the specified length. On the other hand, by specifying a negative length for stretchy, the character will be shrunk to the specified length. This length is affected by the restrictions of minsize and maxsize.
	symmetric	yes
	maxsize	yes
	minsize	yes	The default value can be changed in the Option Setting File.
	largeop	yes
	movablelimits	yes
	accent	yes
	linebreak	yes
	lineleading	yes	The default value is 0. The default value can be changed in the Option Setting File.
	linebreakstyle	yes
	linebreakmultchar	yes
	indentalign	yes
	indentshift	yes
	indenttarget	yes	The effect is not guaranteed when the id referenced by the attribute is behind the attribute or is in a position that does not allow for reference.
	indentalignfirst	yes
	indentshiftfirst	yes
	indentalignlast	yes
	indentshiftlast	yes
3.2.6 <mtext>		yes
3.2.7 <mspace>		yes	mathvariant, mathcolor are invalid.
	width	yes
	height	yes
	depth	yes
	linebreak	yes	indentingnewline was abolished. Although it's considered newline, the amount of indents can be specified in the Option Setting File. That value will be added to the value of indentshift.
	indentalign	yes
	indentshift	yes
	indenttarget	yes	The effect is not guaranteed when the id referenced by the attribute is behind the attribute or is in a position that does not allow for reference.
	indentalignfirst	yes
	indentshiftfirst	yes
	indentalignlast	yes
	indentshiftlast	yes
3.2.8 <ms>		yes	An escape character can be changed in the Option Setting File. The escape processing is not performed when lquote and rquote are empty.
	lquote	yes
	rquote	yes
3.3.1 <mrow>		yes
	dir	yes
3.3.2 <mfrac>		yes
	linethickness	yes
	numalign	yes
	denomalign	yes
	bevelled	yes
3.3.3 <msqrt>		yes
3.3.3 <mroot>		yes
3.3.4 <mstyle>		yes
	scriptlevel	yes	Applicable to <math>.
	displaystyle	yes	Applicable to <math>.
	scriptsizemultiplier	yes	Applicable to <math>. The default value can be changed in the Option Setting File.
	scriptminsize	yes	Applicable to <math>. The default value can be changed in the Option Setting File.
	infixlinebreakstyle	yes	Applicable to <math>.
	decimalpoint	yes	Applicable to <math>.
	any attributes	yes	Applicable to <math>. Accepts the following: accent accentunder align alignmentscope bevelled charalign charspacing close columnalign columnlines columnspacing columnspan columnwidth crossout denomalign depth dir edge equalcolumns equalrows fence form frame framespacing groupalign height indentalign indentalignfirst indentalignlast indentshift indentshiftfirst indentshiftlast indenttarget largeop leftoverhang length linebreak linebreakmultchar linebreakstyle lineleading linethickness location longdivstyle lquote lspace mathsize mathvariant maxsize minlabelspacing minsize movablelimits mslinethickness notation numalign open position rightoverhang rowalign rowlines rowspacing rowspan rquote rspace selection separator separators shift side stackalign stretchy subscriptshift superscriptshift symmetric valign width These are default values of the associated attributes that belong to the internal elements.
	veryverythinmathspace	yes	[deprecated attribute]
	verythinmathspace	yes	[deprecated attribute]
	thinmathspace	yes	[deprecated attribute]
	mediummathspace	yes	[deprecated attribute]
	thickmathspace	yes	[deprecated attribute]
	verythickmathspace	yes	[deprecated attribute]
	veryverythickmathspace	yes	[deprecated attribute]
	fontfamily	yes	[deprecated attribute]
	fontweight	yes	[deprecated attribute]
	fontstyle	yes	[deprecated attribute]
	fontsize	yes	[deprecated attribute]
	color	yes	[deprecated attribute]
	background	yes	[deprecated attribute]
3.3.5 <merror>		yes	The display style can be specified in the Option Setting File.
3.3.6 <mpadded>		yes
	width	yes
	height	yes
	depth	yes
	lspace	yes
	voffset	yes
3.3.7 <mphantom>		yes
3.3.8 <mfenced>		yes
	open	yes
	close	yes
	separators	yes
3.3.9 <menclose>		yes
	notation	partial	*arrow and madruwb are not implemented. A circle will be inscribed against the boundary rectangle. This can be changed so circle can be circumscribed with Option Setting File. The extension was made so that a circumscribed circle can be explicitly expressed with circumscribed-circle and an inscribed circle can be explicitly expressed with inscribed-circle.
3.4.1 <msub>		yes
	subscriptshift	yes
3.4.2 <msup>		yes
	superscriptshift	yes
3.4.3 <msubsup>		yes
	subscriptshift	yes
	superscriptshift	yes
3.4.4 <munder>		yes
	accentunder	yes
	align	yes
3.4.5 <mover>		yes
	accent	yes
	align	yes
3.4.6 <munderover>		yes
	accent	yes
	accentunder	yes
	align	yes
3.4.7 <mmultiscripts>		yes
3.4.7 <mprescripts>		yes
3.4.7 <none>		yes
3.5.1 <mtable>		yes
	align	yes
	rowalign	yes
	columnalign	yes
	groupalign	yes
	alignmentscope	no
	columnwidth	yes
	width	yes
	rowspacing	yes	The default value can be changed in the Option Setting File.
	columnspacing	yes	The default value can be changed in the Option Setting File.
	rowlines	yes
	columnlines	yes
	frame	yes
	framespacing	yes	The extension was made so that three lengths of the frame spacing can be specified. The third length can be omitted, and when specified, it shows the spacing of left/right where frame="none" is specified. The default value can be changed in the Option Setting File.
	equalrows	yes
	equalcolumns	yes
	displaystyle	yes
	side	yes
	minlabelspacing	yes
3.5.2 <mtr>		yes
	rowalign	yes
	columnalign	yes
	groupalign	yes
3.5.3 <mlabeledtr>		yes
3.5.4 <mtd>		yes
	rowspan	yes
	columnspan	yes	If a cell has columnspan greater than 1, <maligngroup> will be ignored.
	rowalign	yes
	columnalign	yes
	groupalign	yes
3.5.5 <maligngroup>		yes	If <maligngroup> is not inside <mtd>, <maligngroup> will be ignored.
	groupalign	yes
3.5.5 <malignmark>		yes	If <malignmark> is not inside <mtd>, <malignmark> will be ignored.
	edge	yes
3.6.1 <mstack>		yes
	align	yes
	stackalign	yes
	charalign	yes
	charspacing	yes	The space corresponding to tight, medium, and loose can be specified in the Option Setting File. The automatic adjustment of the space is not performed.
3.6.2 <mlongdiv>		yes	When <msrow> is not contained in the divisor or the result, it is considered an error. It is also possible to apply <mscarries> to the divisor, the dividend, and the result.
	longdivstyle	yes
3.6.3 <msgroup>		yes
	position	yes	position is ignored with the divisor of <mlongdiv>. Also position is ignored with the result of <mlongdiv> when it is not positioned on a dividend.
	shift	yes
3.6.4 <msrow>		yes
	position	yes	position is ignored with the divisor of <mlongdiv>. Also position is ignored with the result of <mlongdiv> when it is not positioned on a dividend.
3.6.5 <mscarries>		yes	When <msrow> does not follow <mscarries>, it is considered an error.
	position	yes
	location	partial	Corresponds to n, ne and nw. Others are considered n.
	crossout	yes
	scriptsizemultiplier	yes
3.6.6 <mscarry>		yes
	location	partial	Corresponds to n, ne and nw. Others are considered n.
	crossout	yes
3.6.7 <msline>		yes
	position	yes
	length	yes
	leftoverhang	yes
	rightoverhang	yes
	mslinethickness	yes
3.7.1 <maction>		yes
	actiontype	yes	When actiontype="toggle" is specified, the element specified to selection is displayed, in other cases, only the first element is displayed.
	selection	yes

It's impossible to change the appearance with reference to the external Content Dictionary dynamically. It is not necessarily displayed similarly as the illustration of MathML3 specifications.

Element	Attribute	Condition	Comments
4.2	encoding	no
4.2	definitionURL	no
4.2.1 <cn>		yes
	type	yes
	base	yes
4.2.1 <sep>		yes
4.2.2 <ci>		yes
	type	no	Ignored.
4.2.3 <csymbol>		partial
	type	no
	cd	no
4.2.4 <cs>		yes
4.2.5 <apply>		yes	As for the shortage and excess of an operand corresponding to an operator, the appearance can be adjusted by enclosing the operand with parentheses and applying <merror>.
4.2.6 <bind>		yes
4.2.6 <bvar>		yes
4.2.7 <share>		yes	Supports to the reference only to itself, href="#id".
	src	no
4.2.9 <cerror>		yes
4.2.10 <cbytes>		yes
4.3.3.1 <domainofapplication>		yes
4.3.3.1 <condition>		yes
4.3.3.1 <lowlimit>		yes
4.3.3.1 <uplimit>		yes
4.3.3.2 <degree>		yes
4.3.3.3 <momentabout>		yes
4.3.3.3 <logbase>		yes
4.4.1.1 <interval>		yes
4.4.1.2 <inverse>		yes
4.4.1.3 <lambda>		yes
4.4.1.4 <compose>		yes
4.4.1.5 <ident>		yes
4.4.1.6 <domain>		yes
4.4.1.7 <codomain>		yes
4.4.1.8 <image>		yes
4.4.1.9 <piecewise>		yes
4.4.1.9 <piece>		yes
4.4.1.9 <otherwise>		yes
4.4.2.1 <quotient>		yes
4.4.2.2 <factorial>		yes
4.4.2.3 <divide>		yes
4.4.2.4 <max>		yes
4.4.2.5 <min>		yes
4.4.2.6 <minus>		yes
4.4.2.7 <plus>		yes	Although there is no unary “+” in the specification, the following way of writing is allowed: `<apply> <plus/> <ci>x</ci> </apply>`
4.4.2.8 <power>		yes
4.4.2.9 <rem>		yes
4.4.2.10 <times>		yes	Usually, U+2062 (⁢) is used, however when a second operand is <cn>, U+00D7 (×) is used as follow: `<apply> <times/> <cn>1</cn> <cn>7</cn> </apply>`
4.4.2.11 <root>		yes
4.4.2.12 <gcd>		yes
4.4.2.13 <and>		yes
4.4.2.14 <or>		yes
4.4.2.15 <xor>		yes
4.4.2.16 <not>		yes
4.4.2.17 <implies>		yes
4.4.2.18 <forall>		yes
4.4.2.19 <exists>		yes
4.4.2.20 <abs>		yes
4.4.2.21 <conjugate>		yes
4.4.2.22 <arg>		yes
4.4.2.23 <real>		yes
4.4.2.24 <imaginary>		yes
4.4.2.25 <lcm>		yes
4.4.2.26 <floor>		yes
4.4.2.27 <ceiling>		yes
4.4.3.1 <eq>		yes
4.4.3.2 <neq>		yes
4.4.3.3 <gt>		yes
4.4.3.4 <lt>		yes
4.4.3.5 <geq>		yes
4.4.3.6 <leq>		yes
4.4.3.7 <equivalent>		yes
4.4.3.8 <approx>		yes	U+2248 (&TildeTilde;) is used as specified in MathML2 specifications or TeX, although U+2243 (&TildeEqual;) is used in MathML3 specifications.
4.4.3.9 <factorof>		yes
4.4.4.1 <int>		yes
4.4.4.2 <diff>		yes
4.4.4.3 <partialdiff>		yes
4.4.4.4 <divergence>		yes
4.4.4.5 <grad>		yes
4.4.4.6 <curl>		yes
4.4.4.7 <laplacian>		yes
4.4.5.1 <set>		yes
	type	no	Ignored.
4.4.5.2 <list>		yes
	order	no	Ignored.
4.4.5.3 <union>		yes
4.4.5.4 <intersect>		yes
4.4.5.5 <in>		yes
4.4.5.6 <notin>		yes
4.4.5.7 <subset>		yes
4.4.5.8 <prsubset>		yes
4.4.5.9 <notsubset>		yes
4.4.5.10 <notprsubset>		yes
4.4.5.11 <setdiff>		yes
4.4.5.12 <card>		yes
4.4.5.13 <cartesianproduct>		yes
4.4.6.1 <sum>		yes
4.4.6.2 <product>		yes
4.4.6.3 <limit>		yes
4.4.6.4 <tendsto>		yes
	type	yes
4.4.7.1 <sin>		yes
4.4.7.1 <cos>		yes
4.4.7.1 <tan>		yes
4.4.7.1 <sec>		yes
4.4.7.1 <csc>		yes
4.4.7.1 <cot>		yes
4.4.7.1 <sinh>		yes
4.4.7.1 <cosh>		yes
4.4.7.1 <tanh>		yes
4.4.7.1 <sech>		yes
4.4.7.1 <csch>		yes
4.4.7.1 <coth>		yes
4.4.7.1 <arcsin>		yes
4.4.7.1 <arccos>		yes
4.4.7.1 <arctan>		yes
4.4.7.1 <arccosh>		yes
4.4.7.1 <arccot>		yes
4.4.7.1 <arccoth>		yes
4.4.7.1 <arccsc>		yes
4.4.7.1 <arccsch>		yes
4.4.7.1 <arcsec>		yes
4.4.7.1 <arcsech>		yes
4.4.7.1 <arcsinh>		yes
4.4.7.1 <arctanh>		yes
4.4.7.2 <exp>		yes
4.4.7.3 <ln>		yes
4.4.7.4 <log>		yes
4.4.8.1 <mean>		yes
4.4.8.2 <sdev>		yes
4.4.8.3 <variance>		yes
4.4.8.4 <median>		yes
4.4.8.5 <mode>		yes
4.4.8.6 <moment>		yes
4.4.9.1 <vector>		yes
4.4.9.2 <matrix>		yes
4.4.9.3 <matrixrow>		yes
4.4.9.4 <determinant>		yes
4.4.9.5 <transpose>		yes
4.4.9.6 <selector>		yes
4.4.9.7 <vectorproduct>		yes
4.4.9.8 <scalarproduct>		yes
4.4.9.9 <outerproduct>		yes
4.4.10.1 <integers>		yes
4.4.10.2 <reals>		yes
4.4.10.3 <rationals>		yes
4.4.10.4 <naturalnumbers>		yes
4.4.10.5 <complexes>		yes
4.4.10.6 <primes>		yes
4.4.10.7 <exponentiale>		yes
4.4.10.8 <imaginaryi>		yes
4.4.10.9 <notanumber>		yes
4.4.10.10 <true>		yes
4.4.10.11 <false>		yes
4.4.10.12 <emptyset>		yes
4.4.10.13 <pi>		yes
4.4.10.14 <eulergamma>		yes
4.4.10.15 <infinity>		yes
4.5.1 <declare>		no	[deprecated element] Ignored.
<reln>		yes	[deprecated element]
<fn>		yes	[deprecated element]

Element	Condition	Comments
5.2.1 <semantics>	partial	The <semantics> tag itself is ignored.
5.2.2 <annotation>	no	Ignored.
5.2.3 <annotation-xml>	no	Ignored.

What is written in the MathML 3.0 2nd Edition is implemented as is in the operator dictionary. However, the following operators are added:

Character	Glyph	Name	form	priority	lspace	rspace	Properties	Remark
U+FE37	︷	presentation form for vertical left curly bracket	postfix	880	0	0	stretchy, accent	recommend to use U+23DE
U+FE38	︸	presentation form for vertical right curly bracket	postfix	880	0	0	stretchy, accent	recommend to use U+23DF

The contents of the operator dictionary can be adjusted with the Option Setting File. There are the following restrictions:

priority is not supported.
separator is ignored.

The default operator dictionary which can be used with the Option Setting File is stored in OperatorDictionary.xml. Antenna House Formatter V7.4 does not refer to this file. It is recommended to extract and use the portion of an operator you want to change.

DTD of the operator dictionary is as follows:

<!ELEMENT operator-dictionary entry*>
<!ELEMENT entry EMPTY>
<!ATTLIST entry operator       CDATA #REQUIRED>
<!ATTLIST entry form           (prefix|infix|postfix) #REQUIRED>
<!ATTLIST entry priority       %integer; "0">
<!ATTLIST entry lspace         (0|1|2|3|4|5|6|7) "5">
<!ATTLIST entry rspace         (0|1|2|3|4|5|6|7) "5">
<!ATTLIST entry minsize        %length; #IMPLIED>
<!ATTLIST entry maxsize        %length: #IMPLIED>
<!ATTLIST entry accent         (false|true) "false">
<!ATTLIST entry fence          (false|true) "false">
<!ATTLIST entry separator      (false|true) "false">
<!ATTLIST entry stretchy       (false|true) "false">
<!ATTLIST entry symmetric      (false|true) "false">
<!ATTLIST entry largeop        (false|true) "false">
<!ATTLIST entry movablelimits  (false|true) "false">
<!ATTLIST entry linebreakstyle (before|after|duplicate) "before">

With MathML, some inputted characters will be substituted for processing. In case of Antenna House Formatter V7.4, characters are substituted as below.

The characters inside <mi>, <mn> and <mo> are substituted. For instance:
1. U+0027 U+0027 U+0027 U+0027 is substituted with U+2057
2. U+0027 U+0027 U+0027 is substituted with U+2034
3. U+0027 U+0027 is substituted with U+2033
4. U+0027 is substituted with U+2032
5. U+002D is substituted with U+2212
each.
For the characters inside the other tags like <mtext>, U+002D is substituted with U+2010.

You can make the substitution invalid with Option Setting File.

You can use the character entity reference defined below:

The line breaking does not occur within the elements below.
- <mfrac>
- <menclose>
- <msub>
- <msup>
- <msubsup>
- <munder>
- <mover>
- <munderover>
- <mmultiscripts>
- <msqrt>
- <mroot>
- <mstack>
- <mlongdiv>
The automatic line breaking does not occur within the elements below.
- <mtable>
Complicated scripts, such as Arabic, and Emoji are not supported.
When dir="rtl" is specified, although horizontal reverse processing of a region is performed, reverse processing in the inline progression direction, a root sign or Σ, etc. will not be mirrored.
Many of <csymbol> are not implemented.
Many of <bvar> includes unknown implementation method.
When displaying MathML in GUI, the display position of symbols such as = and - may shift vertically in some fonts. In such a case, check [Display Glyph on MathML] in Others in Other Settings Dialog in GUI. See also the workaround for GUI drawing in GUI Restrictions. There is no problem with PDF output, etc.

MathML Conformance

Presentation Markup

Content Markup

Mixing Markup

Operator Dictionary

Character Substitutions

Character Entity References

Restrictions