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MathToWeb User's Guide Version 2.0.2 - 2008/09/17

Contents

Using MathToWeb

MathToWeb will convert any text file containing mathematical expressions written in AMS-Latex to MathML. In this respect, the file extension is of no importance, it could be: *.txt, *.xml, *.htm, etc., MathToWeb will convert them all in the same way. The file extension does become important when it comes to displaying your documents in a browser however, and the *.xml extension, along with the mandatory declarations found in the template below are recommended for this purpose.

MathToWeb can be downloaded as a graphics-based program (a picture of which can be seen on the home page) or a command-line program. The former is very simple to use: simply select a file (one that contains AMS-Latex math expressions that you would like converted to MathML) and press the 'Convert' button. For information on the using the command-line version, click here.

Regardless of which version you use (graphics or command-line), MathToWeb will create a separate file into which it will place your converted text. It will put this file in the same directory as the source file and name it by tacking '_MathToWeb_###' to the original file name.

MathToWeb can be used in one of two general ways:

There are a few things to be aware of before writing documents containing MathML.

MathML is an XML application and web pages that use it must comply with strict XML syntax rules.
This can be achieved by writing your web pages in a form of HTML called XHTML (see the Wiki page on XHTML).

It is not difficult to conform to the XHTML standard. Four essential rules follow:

Below is a template that contains all the necessary XHTML declarations etc. that are required to have MathML display properly in a browser. It should be copied and saved to a text file with an .xml extension (for example, my_web_page_template.xml).

Within the body of this template you'll find a couple of example equations written in Latex. These can be deleted and replaced with your own work; however, before doing this, it is instructive to convert the template, as is, to MathML. This simple procedure is explained below.

  Testing the template

  To convert the template using the command-line version, click here.

Template for web pages that will contain MathML

A single click inside the text-area will 'Select All'.

Math environments

Environment Properties Example Rendering
$...$  or  \(...\)
  • inline
  • unnumbered
 this equation, $(a+b)$ is inline... this equation, ( a + b ) is inline...
\[...\]
  • displayed
  • unnumbered
 
\[ a^3+b^2+c \]
a 3 + b 2 + c ()
\begin{equation*}
...
\end{equation*}
  • displayed
  • unnumbered
 
\begin{equation*}
a_1 + b_2 + c
\end{equation*}
a 1 + b 2 + c ()
\begin{equation}
...
\end{equation}
  • displayed
  • numbered
  • single equation /
    single number
 
\begin{equation}
\tag{1.1}\label{equation-eg}
x_1 + x_2 + x_3
\end{equation}
x 1 + x 2 + x 3 (1.1)
\begin{multline}
...
\end{multline}
  • displayed
  • numbered
  • single equation \
    single number
 
\begin{multline}
\tag{1.2}\label{multline-eg}
a+b+c+d+e+f+g\\
+h+i+j+k\\
+l+m+n
\end{multline}
a + b + c + d + e + f + g + h + i + j + k + l + m + n (1.2)
  • multline left-aligns the first row, centre-aligns the middle row (or rows), and right-aligns the last row, as can be seen in the above example. This behaviour can be modified by applying the commands \shoveleft and \shoveright, which take as their argument the entire row in question, excluding the row separator \\. These commands are used only on the middle rows and have the effect of forcing them left or right. An example using \shoveright is below.

    \begin{multline}
\tag{1.2}\label{multline-shoveright-eg}
	a+b+c+d+e+f+g\\
	\shoveright{+h+i+j+k}\\
	+l+m+n
\end{multline}
    		⟶   which is rendered as  
    a + b + c + d + e + f + g + h + i + j + k + l + m + n (1.2)
\begin{gather}
...
\end{gather}
  • displayed
  • numbered
  • multi-equation /
    multi-numbered
 
\begin{gather}
a_1=b+c+d              \tag{1.3}\label{gather-eq1}\\
a_2=e+f+g+h+i+j+k+l+m  \tag{1.4}\label{gather-eq2}\\
a_3=n+o+p+q            \tag{1.5}\label{gather-eq3}
\end{gather}
⟶                   
a 1 = b + c + d a 2 = e + f + g + h + i + j + k + l + m a 3 = n + o + p + q (1.3)
(1.4)
(1.5)
  • gather centre-aligns all of its rows as can be seen from the above example.
  • The subordinate environment split can be used within the gather environment (see the section on split below).
\begin{align}
...
\end{align}
  • displayed
  • numbered
  • multi-equation /
    multi-numbered
 
\begin{align}
a&=b     & A&=B     & x&=y+z  \tag{1.6}\label{align-eq1}\\
cd&=ef   & CD&=EF   & k&=m    \tag{1.7}\label{align-eq2}\\
g+h&=i+j & G+H&=I+J & nq&=rs  \tag{1.8}\label{align-eq3}
\end{align}
⟶                   
a = b A = B x = y + z c d = e f C D = E F k = m g + h = i + j G + H = I + J n q = r s (1.6)
(1.7)
(1.8)
  • align permits alignment points to be specified using & and rows by \\, and is commonly used to vertically align two or more equations, usually on binary operators such as equal signs (the example above illustrates this).
  • Alignment for this environment is actually as follows:  right & left & right & left & right & left ... .
  • To have numbering suspended on a particular row, place a \notag command instead of  \tag{...}\label{...}.
  • The subordinate environment split can be used within the align environment (see the section on split below).
  • The spacing around the equal sign in the above example is not optimal. This problem is being addressed and it is hoped that a solution will be at hand in the near future.
  • \text{...} can be used inside any of the math environments, but in case of align, it is often used to annotate a multi-line equation line-by-line
    (the example below illustrates this).
  • There a couple of things to note regarding this example:
    • \notag is used to suspend numbering on the second line (the first row is numbered 1.9, the second has no tag, the last is 2.0).
    • References to other equations using the command \ref{...} (or \eqref{...}) are made from inside \text{...} calls.
    • MathToWeb treats references (which are, in fact, just links) that are inside MathML differently that those that are outside. Looking at the MathML for the example below, we see that the hyperlinks representing cross-references (which are inside MathML code) are actually XML xlink calls made from <mrow> tags, for example,
      <mrow xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="#align-eq1">1.6</mrow>, rather than normal HTML hyperlinks <a href="#align-eq1">1.6</a>. The former is necessary for links inside MathML, which is an XML application. Although not illustrated here, MathToWeb does use the latter mentioned HTML links for cross-references outside of MathML code (see Cross-referencing your equations for more on this topic). 
\begin{align}
y& = x_0+x_1-x_2+x_3-\dotsb  && \text{by \ref{align-eq1}}    \tag{1.9}\label{align-eq4}\\
 & = y_0+y_1                 && \text{by \eqref{align-eq2}}  \notag \\
 & = q_0-q_1+q_2             && \text {by Axiom 4.}          \tag{2.0}\label{align-eq5}
\end{align}
⟶                   
y = x 0 + x 1 - x 2 + x 3 - ⋯ by 1.6 = y 0 + y 1 by (1.7) = q 0 - q 1 + q 2 by Axiom 4. (1.9)
()
(2.0)
\begin{split}
...
\end{split}
  • subordinate
  • numbered by parent environment as a single equation
  • split must be used inside: equation, gather or align (or their * forms).
    Do not use it inside multline or multline*.
  • The subordinate environment split allows a single equation to be broken into multiple lines in such a way that rows are marked by \\ and alignment points by &. Each split has associated with it just one equation number (see 2.1 in example below, and 1.4 in the example below that).
  • split  inside  equation
    • In this instance, split must constitute the entire body of the equation.
    • Take a look at this more realistic example.
\begin{equation}
\tag{2.1}\label{equation-split-eg}
\begin{split}
a_2+a_3+a_4&=e+f+g+h\\
           &\quad +i+j+k\\
           &=l+m+n
\end{split}
\end{equation}
⟶   which is rendered as  
a 2 + a 3 + a 4 = e + f + g + h + i + j + k = l + m + n (2.1)
  • split  inside  gather or align
\begin{gather}
a_1=b+c+d \tag{1.3}\label{gather-eq1}\\
\begin{split}
a_2+a_3+a_4&=e+f+g+h\\
           &\quad +i+j+k\\
           &=l+m+n
\end{split} \tag{1.4}\label{gather-eq2} \\
a_5=o+p+q+r+s+t+u+v+w \tag{1.5}\label{gather-eq3}
\end{gather}
⟶   which is rendered as  
a 1 = b + c + d a 2 + a 3 + a 4 = e + f + g + h + i + j + k = l + m + n a 5 = o + p + q + r + s + t + u + v + w (1.3)
(1.4)
(1.5)
\begin{gathered}
...
\end{gathered} 		\begin{aligned}
...
\end{aligned}
  • subordinate
  • numbered by parent environment as a single equation
  • gathered and aligned must be used inside: equation or equation*.
  • These environments exist primarily to allow delimiters to be placed around multi-lined equation structures, as a whole, something that can not done using gather or align because these expand to the full width of the line, allowing nothing else.

    For example, one might try the following in order to place curly braces around an align structure; however, such a construct will produce an error, both in Latex and MathToWeb. 
    \begin{equation}
\left\{
\begin{align}
...
\end{align}
\right\}
\end{equation}
         		Error:  align can not be nested inside equation.
    Similar code below using aligned rather than align, however, works as expected. 
    \begin{equation}\tag*{- ii -}\label{eq:aligned-eg1}
\left\{
\begin{aligned}
a&=b\\
 &=c
\end{aligned}
\right\}
\end{equation}
         		⟶   which is rendered as  
    { a = b = c } - ii -
      * Recall that \tag*{...} typesets whatever text is supplied literally, with no parenthesis being added. 
\begin{equation}
\tag{2.5}\label{equation-aligned-eg}
\left.\begin{aligned}
 y_0&=n_0+n_1\\
 z_0&=r_0+r_1
\end{aligned}\right\}
\qquad \text{$Y_0$ equations}
\end{equation}
⟶   which is rendered as  
( y 0 = n 0 + n 1 z 0 = r 0 + r 1 } Y 0  equations (2.5)
  There are a couple of points to note regarding the above example:
  • \left. is used in place of \left\{, to insert a 'phantom delimiter' that does not appear, but which makes the necessary match with the automatically sized right pairing delimiter \right\}. Recall that the \left and \right commands cause the pairing delimiters \{ and \} to be automatically sized.  (MathToWeb also supports \right.).
    Looking at the MathML for this example, we see that <mphantom>...</mphantom> tags are used to accomplish this effect.
  • On the second-last line we have \text{$Y_0$ equations}. A \text{...} call, in which there exists a nested inline math environment, $Y_0$. This is allowed in Latex and MathToWeb.
\begin{cases}
...
\end{cases}
  • subordinate
  • numbered by parent environment as a single equation
  • cases must be used inside: equation or equation*.
 
\begin{equation}
\tag{2.6}\label{eq:cases-eg}
\delta_{mn} = 
 \begin{cases}
  1& \text{if $n=m$}\\
  0& \text{if $n\nem$}
 \end{cases}
\end{equation}
⟶   which is rendered as  
δ mn = { 1 if  n = m 0 if  n ≠ m } (2.6)
Another example
\begin{subequations}
...
\end{subequations}
  • displayed
  • numbered subordinately using lower-case Latin letters (a, b, c,...) relative to the parent number.
  • With subequations you get a reference to the entire equation group (see  "\label{eq:group}"  below which is numbered 2.7).
  • The multi-equation display environments that can be used within subequations are:  gather, align and flalign.
    (The * forms of these are permissible also, however, there is not much point in this.)
 
\begin{subequations}\tag{2.7}\label{eq:group}
 \begin{align}
  a&=b+c+d\tag{2.7a}\label{eq:first}\\
  e&=f+g\tag{2.7b}\label{eq:second}\\
  h&=i+j+k+l\tag{2.7c}\label{eq:third}
 \end{align}
\end{subequations}
⟶   which is rendered as  
a = b + c + d e = f + g h = i + j + k + l (2.7a)
(2.7b)
(2.7c)

Using the \intertext{...} command

MathToWeb supports the command \intertext{...} which is used to insert short interjectional remarks in the middle of multi-line display environments, while at the same time preserving alignment.

The following example was borrowed from section 3.10 of AMS User's Guide for the amsmath Package (Version 2.0)
(\tag{...} and \label{...} commands have been added).
The position of the word "and" is significant here. Notice that it is aligned on the page margin, rather than the equation margin. 

\begin{align}
A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'), \tag{2.8}\label{eq:align1}\\
A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega), \tag{2.9}\label{eq:align2}\\
\intertext{and}
A_3&=\mathcal{N}(\lambda;\omega).                \tag{3.0}\label{eq:align3}
\end{align}
⟶                   
A 1 = N 0 ( λ ; Ω ' ) - φ ( λ ; Ω ' ) , A 2 = φ ( λ ; Ω ' ) - φ ( λ ; Ω ) , and A 3 = 𝒩 ( λ ; ω ) . (2.8)
(2.9)
()
(3.0)

Punctuation

General

. .  (period)
/ /   (forward slash)
| |
, ,  (comma)
; ;  (semi-colon)
: :  (colon)
: \colon
! !
? ?

Dots

⋯ \dotsb "dots with binary operators/relations"
… \dotsc "dots with commas"
⋯ \dotsi "dots with integrals"
⋯ \dotsm "multiplication dots"
… \dotso "other dots"
⋱ \ddots
⋮ \vdots

The commands  \cdots  and  \ldots  are also supported by MathToWeb, although the AMS literature encourages the use of the more
semantically oriented commands:   \dotsb, \dotsc, \dotsi, \dotsm and \dotso .

Examples:

a 1 + a 2 + ⋯ + a n = ∑ i = 1 n a i $a_1 + a_2 + \dotsb + a_n = \sum_{i=1}^n a_i$("dots with binary operators/relations") MathML

L 1 ( x ) ≤ ⋯ ≤ f ( x ) ⋯ ≤ U 2 ( x ) ≤ U 1 ( x ) $L_1(x) \le \dotsb \le f(x) \dotsb \le U_2(x) \le U_1(x)$ MathML

P k = { x 0 , x 1 , … , x n } $P_k = \{x_0,x_1, \dotsc, x_n\}$("dots with commas") MathML

∫ K 1 ∫ K 2 ⋯ ∫ K n $\int_{K_1} \int_{K_2} \dotsi \int_{K_n}$("dots with integrals") MathML

x ( x + 1 ) ⋯ ( x + n ) $x(x+1) \dotsm (x+n)$("multiplication dots") MathML Other examples

Special 'escaped' characters

Care must be taken when using the following characters which are used internally by Latex and MathToWeb.
Each must be preceded by a \ character (a backslash) in order to have it interpreted properly, as the list below illustrates.
Note particularly, that curly braces are in this list.

\# \$ \% \& \~ \_ \^ \\ \{ \}

Note:  MathToWeb processes only the contents of Latex math environments, one of which is delimited by dollar symbols, $...$   (see AMS math environments).
If a dollar symbol is present anywhere else in a given document, either inside or outside of a math environment, it must be escaped using \$.

Example:

{ P # } $\{ P_{\#} \}$ MathML

Spaces

Example Syntax Command Synonym Description
uv u v - - - - - - - - normal spacing
uv u \, v \, \thinspace thin space
uv u \: v \: \medspace medium space
uv u \; v \; \thickspace thick space
uv u \quad v \quad - - - - quad space
uv u \qquad v \qquad - - - - double quad space

Example:

∫ ∫ f ( x , y ) d x d y $\iint f(x,y) \;\, dx \, dy$ MathML

Accents

x˙ \dot{x} x⇀ \vec{x}
x¨ \ddot{x} x´ \acute{x}
x¯ \bar{x} x` \grave{x}
x^ \hat{x} x˘ \breve{x}
x˜ \tilde{x}

Primes

x′ x' or x^\prime
x′′ x'' or x^{\prime\prime}
(Note: The  '  used above for both single and double primes is the single quotation mark from the keyboard.)

• Single or multiple characters can be underlined using code such as \underline{A} which is rendered as A ‾ .    A practical example is below.

• Any symbol can be typeset below or above a particular base character using the commands \underset and \overset.
  \underset{*}{A} → A * \overset{*}{Z} → Z *

f ' ( a ) = lim h → 0 f ( a + h ) - f ( a ) h $f'(a) = \lim_{h \to 0} \frac{f(a+h)-f(a)}{h}$ MathML

a = a a ^ $\mathbf{a} = a \mathbf{ \hat{a} }$ MathML

r ¨ = ( x ¨ , y ¨ , z ¨ ) $\mathbf{ \ddot{r} } = (\ddot{x}, \ddot{y}, \ddot{z})$ MathML

e ‾ i = ∂ x k ∂ y i E ‾ k ${\underline{e}}_{\, i} = \frac{\partial x^k}{\partial y^i} {\underline{E}}_{\, k}$ MathML

Roots

The \sqrt command produces a square root. A different radix can be specified by making use of the optional argument (see the middle example below).

2 $\sqrt{2}$ 2 3 $\sqrt[3]{2}$ 1 - δ n N $\sqrt{\frac{1-\delta_n}{N}}$ MathML

Fractions

The \frac command takes two arguments, the numerator being the first and the denominator the second.

(At present, MathToWeb has limited support \dfrac and \tfrac (d=display-style, t=text-style), in that it will display them in the same way it does \frac.)

a b $\frac{a}{b}$

Example:

The example below was borrowed from the Short Math Guide for Latex, version 1.09,  p 12.

ℜ z = n π θ + ψ 2 ( θ + ψ 2 ) 2 + ( 1 2 log | B A | ) 2 . () 
\begin{equation}
\Re{z} = \frac{n\pi \dfrac{\theta +\psi}{2}}{
         \left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2}
         \log \left\lvert\dfrac{B}{A}\right\rvert\right)^2}.
\end{equation}

Binomials

The \binom command takes two arguments.

(At present, MathToWeb has limited support \dbinom and \tbinom (d=display-style, t=text-style), in that it will display them in the same way it does \binom.)

( a b ) $\binom{a}{b}

Top and bottom embellishments

abcde ˜ \widetilde{abcde}
abcde ^ \widehat{abcde}
abcde ‾ \overline{abcde}
abcde ‾ \underline{abcde}
abcde ⏞ \overbrace{abcde}
abcde ⏟ \underbrace{abcde}
abcde ⟵ \overleftarrow{abcde}
abcde ⟵ \underleftarrow{abcde}
abcde ⟶ \overrightarrow{abcde}
abcde ⟶ \underrightarrow{abcde}
abcde ⟷ \overleftrightarrow{abcde}
abcde ⟷ \underleftrightarrow{abcde}

In addition, \overbrace can take a superscript and \underbrace a subscript:

\overbrace{abcde}^{123} abcde ⏞ 123
\underbrace{abcde}_{123} abcde ⏟ 123 Other examples

Examples:

AB ⟶ + BC ⟶ = AC ⟶ $\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}$ MathML

( Δ n ) 2 ‾ ≡ ( n - n ¯ ) 2 ‾ $\overline{ { (\Delta n) }^2 } \equiv \overline{ { (n - \bar{n}) }^2 }$ MathML

Extensible horizontal arrows

\xleftarrow and \xrightarrow will widen automatically to accommodate the width of their superscripts and subscripts. These commands allow one optional argument (in square brackets) that represent the subscript, and have one mandatory argument (in curly braces) that represent the superscript.

⟵   a     A   \xleftarrow[a]{A} ⟶   b     B   \xrightarrow[b]{B}

Examples:

A ⟵   α ± 2 - 1   B ⟶   H +     130 ∘ C   C $A \; \xleftarrow{\alpha \pm 2 - 1} \; B \; \xrightarrow[H^+]{{130}^\circ C} \; C$ MathML

⟶   this converts to   $\xrightarrow{ \text{this converts to} }$ MathML

Extensible vertical arrows

↑ \uparrow ⇑ \uparrow ↓ \uparrow ⇓ \uparrow ↕ \uparrow ⇕ \uparrow

Example:

A 2 B 3 ↑ $\frac{A^2}{B^3} \uparrow$ MathML

Delimiter sizes

Pairing delimiters (see the next section) will not adjust their height to enclose their contents unless you specifically request it. This can be achieved using a pair of \big... prefixes (see the list below), which set the delimiters to a particular fixed size, or by using \left and \right, which causes auto-sizing.

The second example illustrates the use of the commands \left \right which auto-size the parentheses on which they act (these are absent in the first example, for comparison).

( A 2 b n ) $( \frac{A^2}{b_n} )$ MathML

( A 2 b n ) $\left( \frac{A^2}{b_n} \right)$ MathML


( ) \left \right \bigl \bigr \Bigl \Bigr \biggl \biggr \Biggl \Biggr
( ab) (ab) (ab) (ab) (ab) (ab)

Delimiters (extensible, pairing delimiters)

() ( )
[] [ ]
{} \{ \}or\lbrace \rbrace
|| \lvert \rvert
∥∥ \lVert \rVert
⟨⟩ \langle \rangle
⌈⌉ \lceil \rceil
⌊⌋ \lfloor \rfloor
⎰⎱ \lmoustache \rmoustache

Examples:

( a b ) $\left( \frac{a}{b} \right)$ MathML

| f ( x + δ m ) - f