The User’s Manual of LaTeX2HTML 2.0.0

The User’s Manual of LaTeX2HTML 2.0.0 Van Abel 12/03/2016 USTC van141.abel(at)gmail.com

目录
Contents
 1.  How to Write the Basic Information of Your Post
 2.  How to Write Section, Subsection and Subsubsection
 3.  Itemize and Enumerate: How to List Stuffs
 4.  The Footnote and Hyperlinks
 5.  The Color Scheme: How to Colorize You Content
 6.  The Figure Environment
 7.  How to Write a Theorem
   7.1.  Definition, Lemma, Proposition, Theorem, Corollary, Remark, Proof
     7.1.1.  Basic Usage of Environments
     7.1.2.  Assign a Name for Your Theorem
     7.1.3.  The Proof Environment
     7.1.4.  More Examples of Environments
   7.2.  The Problem, Answer Environments
   7.3.  The Exercise Environment
   7.4.  The Quote Environment
 8.  Auto Numbering and Referring Back
   8.1.  Auto Numbering and Referring Back to Equations
     8.1.1.  How to Refer back to Equation Number
     8.1.2.  My Suggestion on “How to Write Equations”
   8.2.  Auto Numbering and Referring Back to Environments
     8.2.1.  Auto Numbering of Environments
     8.2.2.  Referring Back to Environments
   8.3.  Referring Back to Section
 9.  BibTeX Citations
   9.1.  How to Add BibTeX Data
   9.2.  How to Cite
 10.  Last Words and Feed Back
   10.1.  How to Jump Between Links
 11.  How to Get it?
1. How to Write the Basic Information of Your Post Just as in LaTeX, you can use commands such as:\title, \author, \address, \date, \keywords and the environment abstract to produce the basic information of your post. These command has the same meaning as in LaTeX, what’s more,

• you can use |\verbtoday| in \date
• you can use \emph to emphasis some thing
• you can use |\verbtableofcontents| to get the table of contents
• you can use \email or \mailto to set your mail, the first will be centered

Just like in Latex, isn’t it? Replace \section with \subsection and \subsubsection if you want to write subsection and subsubsection, respectively. How about \subsubsubsection? Sorry, there is no such command.

Maybe you are still wandering: how do I get the list of contents by |\verbtableofcontents| command, one key factor is that I added a link just before each section and subsection, by which you can refer to it. See the referring back to Section 8.3 for detail. 3. Itemize and Enumerate: How to List Stuffs As you have already saw, we can list the element with the same syntax as latex. What’s more, it support nested list: What’s more you can nest them, for example

• Firstly
• Secondly
  • The first item of Second
  • The second item of Second
    • The first item of the third item of second item

Enumerate works almost the same as itemize, except the style is different. For example replace enumerate in the above example with enumerate, then we get:

1. Firstly
2. Secondly
   1. The first item of Second
   2. The second item of Second
      1. The first item of the third item of second item

In the new version 2.3.5, the command hyper-link and hyper-link-text are supported, which will create hyper-link to the link and the linked text respectively. 5. The Color Scheme: How to Colorize You Content As we have already showed that you can emphasis you content by \emph, one other way is use \underline. Besides, there is a more powerful scheme, now you emphasis some content with different colors, even for formulae. Firstly, you must decide which class your content belonged to, the text content or the mathematics content, since these two classes are processed by different scheme, text is by latex2html and mathematics by mathjax. Just as in Latex, the you can set a color for your formula by \color{color_name}{color_formula}. For example [ \color{red}{a+b},\quad\color{blue}{a+b},\quad\color{green}{a+b} ] [ \frac{\color{cyan}{a+b}}{c+d}, \quad \frac{a}{\color{magenta}{a+b}},\quad \frac{a}{a+\color{yellow}{b}} ] On the other hand, if you want to give color for your text content, then you should use \textcolor{color_name}{color_contents}, for example red and blue and green and cyan and magenta and yellow. 6. The Figure Environment In LaTeX2HTML version 2.1.0, I have add the ability to proceed figure environment. As an example, you can use

Two important things to be noted:

1. You must use the fullname of the figure, i.e. myfig.png; NOT myfig, since in the later case, we don’t know which figure is to be inserted here;
2. after that you MUST upload the exact figure (named myfig.png in the example) to your WordPress as usual. All the later process is handled by LaTeX2HTML plugin, you can just preview to see the results.

• First group: defn(Definition), lem(Lemma), prop(Proposition), thm(Theorem), cor(Corollary), rem(Remark), excs(Exercise), proof(Proof)
• Second group: prob(Problem), answer(Answer)
• Mixed: examp(Example), quote(Quotation)

A command begin with a | and followed with the \verbname|, at last the content of command. It looks like |\verbemph{text}|; A environment must be wrapped by begin and end.

Definition 1. Suppose that $(X,\mathcal M)$ and $(Y,\mathcal N)$ are measurable spaces, and $f:X\to Y$ is a map. We call $f$ is measurable if for every $B\in\mathcal N$ the set $f^{-1}(B)$ is in $\mathcal M$.

The other is similar, just replace defn with any one of the above environment:

Remark 1. If $Y$ is a topological space, and $\mathcal N$ is the $\sigma$-algebra of Borel sets, then $f$ is measurable if and only if the following condition satisfied:

• For every open set $V$ in $Y$, the inverse image $f^{-1}(V)$ is measurable.

7.1.2. Assign a Name for Your TheoremYou can even assign a name to these environment, just as you did in latex, use [text] just behind the environment, for example:

Lemma 2 (fundamental lemma of integration). Let $\set{f_n}$ be a Cauchy sequence of step mappings. Then there exists a subsequence which converges pointwise almost everywhere, and satisfies the additional property: given $\eps$ there exists a set $Z$ of measure $< \eps$ such that this subsequence converges absolutely and uniformly outside $Z$.

7.1.3. The Proof EnvironmentThe following are the proof environment, and some more examples, if you are impatient to other contents, then just skip this subsection by click Section 7.2.

Proof . For each integer $k$ there exists $N_k$ such that if $m,n\geq N_k$, then [ |f_m-f_n|_1< \frac{1}{2^{2k}}. ] We let our subsequence be $g_k=f_{N_k}$, taking the $N_k$ inductively to be strictly increasing. Then we have for all $m,n$: [ |g_m-g_n|_1 ] We shall show that the series [ g_1(x)+\sum_{k=1}^\infty\left(g_{k+1}(x)-g_k(x)\right) ] converges absolutely for almost all $x$ to an element of $E$, and in fact we shall prove that this convergence is uniform except on a set of arbitrarily small measure. Let $Y_n$ be the set of $x\in X$ such that [ |g_{n+1}(x)-g_n(x)|\geq\frac{1}{2^n}. ] Since $g_n$ and $g_{n+1}$ are step mappings, it follows that $Y_n$ has finite measure. On $Y_n$ we have the inequality [ \frac{1}{2^n}\leq|g_{n+1}-g_n| ] whence [ \frac{1}{2^n}\mu(Y)=\int_{Y_n}\frac{1}{2^n}\leq\int_X|g_{n+1}-g_{n}|\leq\frac{1}{2^{2n}}. ] Hence [ \mu(Y_n)\leq\frac{1}{2^n}. ] Let [ Z_n=Y_n\cup Y_{n+1}\cup\cdots. ] Then [ \mu(Z_n)\leq \frac{1}{2^{n-1}}. ] If $x\not\in Z_n$, then for $k\geq n$ we have [ |g_{k+1}(x)-g_k(x)| ] and from this we conclude that our series [ \sum_{k=n}^\infty\left(g_{k+1}(x)-g_{k}(x)\right) ] is absolutely and uniformly convergent, for $x\not\in Z_n$. This proves the statement concerning the uniform convergence. If we let $Z$ be the intersection of all $Z_n$, then $Z$ has measure $0$, and if $x\not\in Z$, then $x\not\in Z_n$ for some $n$, whence our series converges for this $x$. This proves the lemma.

7.1.4. More Examples of Environments

Theorem 3. Let $f_n$ be a Cauchy sequence in $\mathcal L^1$ which is $L^1$-convergent to an element $f$ in $\mathcal L^1$. Then there exists a subsequence which converges to $f$ almost everywhere, and also such that given $\eps$, there exists a set $Z$ of measure $< \eps$ such that the convergence is uniform on the complement of $Z$.

Corollary 4. An element $f\in\mathcal L^1$ has seminorm $|f|_1=\int_X|f|\rd\mu=0$ if and only if $f$ is equal to $0$ almost everywhere.

Proposition 5 (Monotone Convergence Theorem). Let $\set{f_n}$ be an increasing (resp. decreasing) sequence of real valued functions in $\mathcal L^1$ such that the integrals [ \int_X f_n\rd\mu ] are bounded. Then $\set{f_n}$ is a Cauchy sequence, and is both $\mathcal L^1$ and almost everywhere convergent to some function $f\in\mathcal L^1$.

7.2. The Problem, Answer Environments The second group of environments are provided for discussion, after all, this is a discussion platform. They are: prob for Problem, examp for Example, and answer for Answer. It almost works the same as the first group, for example

Problem 1 (Egoroff’s theorem). Assume that $\mu$ is $\sigma$-finite. Let $f:X\to E$ be a map and assume that $f$ is the pointwise limit of a sequence of simple maps $\set{\varphi_n}$. Given $\eps$, show that there exists a set $Z$ with $\mu(Z)< \eps$ such that the convergence of $\set{\varphi_n}$ is uniform on the complement of $Z$.

But, the differences between them is that, the answer is numbered with prob (the examp, excs, rem will numbered independently), to see this, for example:

Answer 1.1. Assume first that $\mu(X)$ is finite. Let $A_k$ be the set where $|f|\geq k$. The intersection of all $A_k$ is empty so their measures tend to $0$. Excluding a set of small measure, you can assume that $f$ is bounded, in which case $f$ is in $\mathcal L^1(\mu)$ and you can use the fundamental lemma of integration.

Answer 1.2. This is another answer for the problem.

You should note that the number of answer is reset to 1 by prob, of course, more sensible. For example:

Problem 2. Why we should firstly process the positive measurable functions, then the real measurable functions and at last the complex measurable functions for the integral of measurable functions?

Answer 2.1. In fact, you can define the integral of complex function directly.

7.3. The Exercise Environment Maybe, at somewhere, you want the reader consider about something, then you can use excs environment for Exercise. Please keep in mind that it will have independent numbering, just as prob, but will not reset the number of answer. Here is an example:

Exercise 1. Suppose $(X,\mu)$ is a measure space, and that $f$ is measurable, then $\int_X f\rd \mu=0$ if and only if $f\equiv0$ almost everywhere.

7.4. The Quote Environment Sometimes, there are some words or comments on the content, it is like a remark, but it is not so formal. And, if you are write a lecture notes, these words may be the lecturer said before or after an important thing, such as theorems. I have defined a new environment quote to deal with these stuff. For example: Before the theorem

Theorem 6. Let $\Omega\subset\R^n$ and $u:\Omega\to\R$, then

1. If $u\in C^2(\Omega)$ is harmonic in $\Omega$, then $u$ satisfies MVP;
2. If $u\in C(\Omega)$ satisfies MVP, then $u$ is smooth and harmonic.

we want to add a comment on it, then you can use the quote environment

A function satisfying mean-value properties is only required to be continuous. However, a harmonic function is required to be $C^2$. Thus, the equivalence of this two kind of functions will be significant.

8. Auto Numbering and Referring Back The plugin supports two groups of referring back, the first is for section and theorem environment e.g. thm. The second is done by mathjax, which support math formulae auto-numberring . 8.1. Auto Numbering and Referring Back to Equations All the mathematical environments: equation, align, multline, gather will auto-numbering. For example \begin{equation}\begin{cases} 3=2x+y\ 3=y+2x\end{cases} \end{equation} An example of multline, which will make the last line flush right: \begin{multline}\label{eq:2} \int_a^b \biggl{ \int_a^b [ f(x)^2 g(y)^2 + f(y)^2 g(x)^2 ] -2f(x) g(x) f(y) g(y) \,dx \biggr} \,dy \ =\int_a^b \biggl{ g(y)^2 \int_a^b f^2 + f(y)^2 \int_a^b g^2 – 2f(y) g(y) \int_a^b fg \biggr} \,dy \end{multline} The next example will show how to numbered the equation at a given line with \tag{4.a}: \begin{gather} \begin{split} \varphi(x,z) &= z – \gamma_{10} x – \sum_{m+n\ge2} \gamma_{mn} x^m z^n\ &= z – M r^{-1} x – \sum_{m+n\ge2} M r^{-(m+n)} x^m z^n \end{split}\tag{4.a}\label{eq:4a}\ \begin{split} \zeta^0 &= (\xi^0)^2, \ \zeta^1 &= \xi^0 \xi^1 \end{split}\notag \end{gather} 8.1.1. How to Refer back to Equation NumberIf you want to refer the equation, you can add a label \label{eq:4a}, and rerer as \eqref{eq:4a}, it looks as \eqref{eq:4a}. 8.1.2. My Suggestion on “How to Write Equations”

1. if you use > or < for greater and lesser in math, please add a blank-space before > and a blank-space after < . Or you will make the HTML translation program confused, since are standard tags for HTML language(code).
2. use$$ for inline math
3. use[] for oneline unnumbered display math
4. use star version for multiline unnumbered display math, for example, use gather* environment for centered multiline equations
5. use equation environment for oneline numbered display math
6. use align environment for multiline numered display math, if you want make them aligned at some position( use & to set the point of align)

8.2. Auto Numbering and Referring Back to Environments 8.2.1. Auto Numbering of Environments All the environments except proof are auto numbered by latex2html, and the rem, prob, excs, claim are numbered independently, what’s more, answer’s number will be reset by prob. The other environment will numbered continuously in one post (on one page, which means, if you use the <!–nextpage–> to have another page, then the number will all over begin from 1, if you consider this as an bug, sorry, I can’t fix it.) 8.2.2. Referring Back to EnvironmentsYou can refer to the Theorem, Lemma, Corollary, Definition, Proposition, Remark, Problem, Exercise, and Answer environments by:

• first add a \label{thm:labnum}
• and use thm:labnum or thm:labnum to refer back

From Definition 1 we know that… From Proposition 5 we know that… From Answer 2.1 we know that… 8.3. Referring Back to Section You can use \autoref{sec:1} to refer back to Section 1, and \ref{sec:6.1} to refer back to Subsection 1 of Section 6, which will looks like 8.1, and \autoref{sec:621} to refer back to Subsubsection 1 of Subsection 2 of Section 6, which will looks like Section 8.2.1. 9. BibTeX Citations The main new feature of version 2.0.0 is add the BibTeX citation support. By which, you can cite references like in LaTeX. 9.1. How to Add BibTeX Data To add the bibtex data, just turn to the LaTeX2HTML setting page, under the BibTeX table, you can paste you bibtex data into the input box.

I have add an example data. Also try to double click to restore the last content in the input box. 9.2. How to Cite LaTeX2HTML support \nocite, \cite and \citeauthor, all of them require the exactly bibkey (which means |\verbnocite{*} |will not work and it is case sensative).

It also support \citelist of amsrefs. 10. Last Words and Feed Back This document contains the usage of the plugin latex2html, and if you find any errors, or have any suggestions even bugs of the plugin, you can leave a word here, or sent a mail to me: van141.abel(at)gmail.com.

It takes me about one month to write the plugin, I’m too tired to feel glad when I finally finished it. I don’t know whether it will help you a litter to post mathematics with latex language or not, but if it do have any, I will fell much better. 10.1. How to Jump Between Links If you have just click on a link, then you can go back where you were just by Alt+← 11. How to Get it? To get it, visit the plugin in wordpress: https://wordpress.org/plugins-wp/latex2html/.