## LaTeX and other markup!

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

bosecondensate
Posts: 1
Joined: Tue Apr 13, 2010 12:35 am UTC

### Re: LaTeX and other markup!

Testing support for xypic
$\xymatrix{T\times V\ar[r]^p\ar[dr]_i&T\otimes V\ar[d]^h\\&W$

dotproduct
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Joined: Mon Feb 22, 2010 3:39 am UTC

### Re: LaTeX and other markup!

It's not showing up right in preview, so I'll check if that's just the preview or if it's really not working.

<imath>\Delta^1_2</imath>

Ended
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Location: The Tower of Flints. (Also known as: England.)

### Re: LaTeX and other markup!

dotproduct wrote:It's not showing up right in preview, so I'll check if that's just the preview or if it's really not working.

<imath>\Delta^1_2</imath>

You need square brackets:

Code: Select all

[imath]\Delta^1_2[/imath]
[imath]\Delta^1_2[/imath]
Generally I try to make myself do things I instinctively avoid, in case they are awesome.
-dubsola

__Jonny
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Location: England

### Re: LaTeX and other markup!

[imath]1+1=2[/imath]

...

Dason
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### Re: LaTeX and other markup!

__Jonny wrote:[imath]1+1=2[/imath]

...

Note: Please don't use imath for something like this in any other thread. That is all. Carry on.
double epsilon = -.0000001;

Eastwinn
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Location: Maryland

### Re: LaTeX and other markup!

This site is a huge time saver: http://www.codecogs.com/latex/eqneditor.php .
http://aselliedraws.tumblr.com/ - surreal sketches and characters.

IllvilJa
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Joined: Wed Mar 11, 2009 8:39 pm UTC
Location: Stockholm

### Re: LaTeX and other markup!

Aah... mathematics typeset by LaTeX is pure poetry... Wonderful thread, wonderful feature.

$\left\langle p,l,s,v \mid (pl)^{5},(ps)^{2},(pv)^{2},(ls)^{3},(lv)^{2},(sv)^{3}\right\rangle$

A cookie to anyone who can tell what the above formula describes . Hope I got all the exponents right though.

(Yes, the formula actually means something and odd enough, something I'm particularly interested in. Yes, I'm a nerd beyond any help...)

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: LaTeX and other markup!

Is it the monster?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

IllvilJa
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Joined: Wed Mar 11, 2009 8:39 pm UTC
Location: Stockholm

### Re: LaTeX and other markup!

Actually it is! To be more specific, it is the Coxeter group describing this monster.

(As said, I might have gotten some of the exponents in the formula wrong, I did not find the specific formula for that polytope anywhere)

jestingrabbit
Factoids are just Datas that haven't grown up yet
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Location: Sydney

### Re: LaTeX and other markup!

So its not the monster.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

PM 2Ring
Posts: 3715
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: LaTeX and other markup!

IllvilJa wrote:Actually it is! To be more specific, it is the Coxeter group describing this monster.

Coxeter was one of the greatest geometers of all time.
John Baez wrote:The University of Toronto is an urban campus, rather grey and chilly at this time of year. Nestled amid other buildings at the southern edge of campus, the Fields Institute doesn't stand out.

But inside, you'll find a spacious and peaceful atrium, with a fireplace to keep you cozy. A spiral staircase winds up three or four stories. Hanging from the ceiling far above is a 3d model of the "120-cell": a beautiful 4-dimensional solid with 120 regular dodecahedra as faces.

This is a tribute to the great geometer H. S. M. Coxeter, master of polyhedra, who worked for 60 years at the University of Toronto after studying philosophy at Cambridge under Wittgenstein. You'll also find Coxeter's piano sitting at the base of the spiral staircase.

To get back on topic, I like LaTeX, but the way it's implemented here really slows down page loading, so I try to avoid using it when it's possible to make do with high ascii codes and sub & sup.

joshz
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Location: Pittsburgh, PA

### Re: LaTeX and other markup!

antonfire wrote:
Random832 wrote:Blackboard bold (i.e. ℤ for the integers) isn't supported (\mathbb just gives ordinary bold) is there any way to add support for that?
This is genuinely broken now. At the time of this writing, "\mathbb{Z}", [imath]\mathbb{Z}[/imath], gives the error "Unknown control sequence '\msbm'".

I can probably install fonts locally to make this go away (can I?), but that would hardly fix the problem of people being unable to read what I write.
This is still broken. Are there any plans to fix it? It's a bit of a kludge to go to wikipedia and copy it in (or look up the unicode) each time I want to use blackboard bold Z, R, etc.
You, sir, name? wrote:If you have over 26 levels of nesting, you've got bigger problems ... than variable naming.
suffer-cait wrote:it might also be interesting to note here that i don't like 5 fingers. they feel too bulky.

Slonimsky
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### Re: LaTeX and other markup!

-Snip-

nevermind, I got it (kinda) fixed

the tree
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### Re: LaTeX and other markup!

Not sure if this the right thread to ask general LaTeX question but if anyone could help me with this, it'd be cool.

In a document I'm writing I have:
Some writing

 god awful equation that is a million billion characters long and makes you want to cry 

some more writing
And within the double-dolars, TeX isn't automatically inserting any line breaks at all and the equation is going off of the edge the page. Is there something I can do to encourage TeX to put a line break in an appropriate place? Or should I try to do that manually (how I do that?)?

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: LaTeX and other markup!

the tree wrote:Not sure if this the right thread to ask general LaTeX question but if anyone could help me with this, it'd be cool.

In a document I'm writing I have:
Some writing

 god awful equation that is a million billion characters long and makes you want to cry 

some more writing
And within the double-dolars, TeX isn't automatically inserting any line breaks at all and the equation is going off of the edge the page. Is there something I can do to encourage TeX to put a line break in an appropriate place? Or should I try to do that manually (how I do that?)?

You'll need to do it manually. There are a few ways around it. I like to use the align environment, though its kinda deprecated these days. You can do it all with array, or eqnarray, and they're both described pretty well in lshort.pdf.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

the tree
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### Re: LaTeX and other markup!

Thanks, eqn array managed to do it. (I had to spend a good bit of time staring at it to realise how to make that not ennumerate every line).

gmedina
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Location: Colombia

### Re: LaTeX and other markup!

jestingrabbit wrote:...I like to use the align environment, though its kinda deprecated these days. You can do it all with array, or eqnarray, and they're both described pretty well in lshort.pdf.

It's the other way around. In a LaTeX document it is advisable not to use eqnarray anymore and to use align (or any other of the environments provided by the amsmath package, for example). The reasons can be found in this article by Lars Madsen: Avoid eqnarray!.

As a side note, in a LaTeX document, the construct $$...$$ shouldn't be used anymore (refer to l2tabu for the reasons); one should use $...$ instead.
In Memoriam

Rippy
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### Re: LaTeX and other markup!

Just started learning LaTeX today! (eventually I plan to transcribe all my math notes into searchable, pretty digital format).

...Aaaand 3/4 of a page into said notes, I have a question. If I have a matrix with entries involving addition, and I want the plus signs aligned, how would I do so? Using an &, as you would for column alignment, adds some space in addition to aligning.

For example, with no alignment (and a bit of garbage added to make things easier to see):
$\begin{bmatrix} a_{11}x_{1}o_{1}m_{3}f_{3}g_{7} + a_{12}x_{2} + \ldots + a_{1n}x_{n} \\ \vdots \\ a_{m1}x_{1} + a_{m2}x_{2} + \ldots + a_{mn}x{n} \end{bmatrix}$

With ampersands:
$\begin{bmatrix} a_{11}x_{1}o_{1}m_{3}f_{3}g_{7}& + a_{12}x_{2}& + \ldots + a_{1n}x_{n} \\ &\vdots \\ a_{m1}x_{1}& + a_{m2}x_{2}& + \ldots + a_{mn}x{n} \end{bmatrix}$

Also, is there a better way to center-align (or something close) those vdots in the 2nd row than by putting an ampersand in front to align them with one of the + signs?

Talith
Proved the Goldbach Conjecture
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### Re: LaTeX and other markup!

$\left [ \begin{array}{rcccccl} a_{11}x_{1}o_{1}m_{3}f_{3}g_{7}& + & a_{12}x_{2} & + & \ldots & + & a_{1n}x_{n} \\ &&&\vdots&&& \\ a_{m1}x_{1}& + & a_{m2}x_{2} & + & \ldots & + & a_{mn}x{n} \end{array}\right ]$
(double click the LaTeX to see the code)

gmedina
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Location: Colombia

### Re: LaTeX and other markup!

Change \ldots to \cdots in Talith's code.
In Memoriam

gmedina
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Location: Colombia

### Re: LaTeX and other markup!

To reduce the space between the plus signs, I would change the code to

Code: Select all

\left[\begin{array}{r@{\,+\,}c@{\,+\,}c@{\,+\,}l}   a_{11}x_{1}o_{1}m_{3}f_{3}g_{7} & a_{12}x_{2} & \cdots & a_{1n}x_{n} \\   \multicolumn{4}{c}{\vdots}    \\ a_{m1}x_{1}&  a_{m2}x_{2} & \cdots &  a_{mn}x{n} \end{array}\right]
In Memoriam

Rippy
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Location: Ontario, Can o' Duh

### Re: LaTeX and other markup!

Well, I can't say I quite understand all that yet, but it seems to work much more nicely .

I've written out a few more pages (in between all these exams...), and I'm wondering if someone could have a quick look at the whole .tex file and maybe give some pointers. Stylistically I find the result just looks like everything is mashed together; none of the proofs or theorems get indented so if you, say, try to place a remark inside a theorem, it looks like the theorem ends and a remark begins because there's no indentation. The section/subsection headings are also really small and easy to miss.

I'm using the amsart document class, and I'm assuming I just haven't got the right style template for my needs. (My statistics course notes, which I assume are done in LaTeX, are lousy the same way, except they do have nice substantial headers for each chapter)

Also, is there any particular style to use when writing the LaTeX for long documents? I've gotten into the habit of indenting stuff as a visual aid, but I have no idea if this is common.

Anyway, here's my document; I was going to just upload the file but there are filetype restriction (no .tex, .txt, or my creative .lol apparently), so hopefully this is readable:

Spoiler:

Code: Select all

1 \documentclass{amsart}  2   3 \numberwithin{equation}{section}  4   5 \newtheorem{theorem}{Theorem}[subsection]  6 \newtheorem{lemma}[theorem]{Lemma}  7 \newtheorem{proposition}[theorem]{Proposition}  8 \newtheorem{corollary}[theorem]{Corollary}  9 \newenvironment{definition}[1][Definition]{\begin{trivlist} 10 \item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}} 11 \newenvironment{example}[1][Example]{\begin{trivlist} 12 \item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}} 13 \newenvironment{remark}[1][Remark]{\begin{trivlist} 14 \item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}} 15 \addtolength{\parskip}{\baselineskip} %more space between paragraphs 16 \setlength{\parindent}{0pt}           %no identing of first line of paragraphs 17  18 \begin{document} 19  20 \title{MATH 235 Course Notes} 21 \author{John G.} 22 \date{Fall 2010} 23  24 \maketitle 25 \newpage 26 \tableofcontents 27 \newpage 28  29 \section{Linear Mappings and Bases} 30         \subsection{Rank and Columnspace} 31                 \begin{theorem} 32                 \label{cspace} 33                 Let $B$ be the RREF matrix of $A$. Certain columns of $A$ form a basis of $Col(A)$ iff the c    orresponding 34                 column of $B$ form a basis for $Col(B)$. 35                 \end{theorem} 36                 \begin{proof} 37                         We know that $\vec{x}$ is a solution for $A\vec{x} = \vec{0}$ iff it is a solution f    or $B\vec{x}=\vec{0}.$ 38                         \begin{equation*} \begin{split} 39                                 A\vec{x} & = 40                                 \begin{bmatrix} 41                                         a_{11} & \dotsm & a_{1n} \\ 42                                         \vdots & \ddots & \vdots \\ 43                                         a_{m1} & \dotsm & a_{mn} 44                                 \end{bmatrix} \\ 45                                 & = 46                                 \begin{bmatrix} 47                                         a_{11}x_{1}&+&a_{12}x_{2} + & \ldots + & a_{1n}x{n} \\ 48                                         &&\vdots \\ 49                                         a_{m1}x_{1}&+&a_{m2}x_{2} + & \ldots + & a_{mn}x{n} 50                                 \end{bmatrix} \\ 51                                 & = 52                                 \begin{bmatrix} a_{\downarrow1} \end{bmatrix}x_{1} + 53                                 \begin{bmatrix} a_{\downarrow2} \end{bmatrix}x_{2} + \ldots + 54                                 \begin{bmatrix} a_{\downarrow{}n} \end{bmatrix}x_{n} \\ 55                                 & = \vec{0} 56                         \end{split} \end{equation*} 57                         Similarly, 58                         \begin{equation*} \begin{split} 59                                 B\vec{x} =  60                                 \begin{bmatrix} b_{\downarrow1} \end{bmatrix}x_{1} + 61                                 \begin{bmatrix} b_{\downarrow2} \end{bmatrix}x_{2} + \ldots + 62                                 \begin{bmatrix} b_{\downarrow{}n} \end{bmatrix}x_{n} 63                                 = \vec{0} 64                         \end{split} \end{equation*} 65                         Certain columns of $A$ are linearly dependent iff there is a solution $\vec{x} \neq \vec{0}$. 66                         The same holds true for $B$. 67                         Therefore, certain columns of A are linearly (in)dependent iff the corresponding col    umns of B are 68                         linearly (in)dependent. \\ 69                         We construct a basis using any largest possible linearly independent set. 70                 \end{proof} 71  72                 \begin{remark} 73                         Way to create/check a basis: 74                         \begin{enumerate} 75                                 \item Linearly independent and a spanning set 76                                 \item Linearly independent and ensure it is a maximal set 77                         \end{enumerate} 78                 \end{remark} 79  80                 \begin{example} 81                         \begin{equation*} 82                                 A =  83                                 \begin{bmatrix} 84                                         1 & 2 & 2 & -1 \\ 85                                         3 & 6 & 5 & 0 \\ 86                                         1 & 2 & 1 & 2 87                                 \end{bmatrix} 88                                 \rightarrow \ldots \rightarrow 89                                 \begin{bmatrix} 90                                         1 & 2 & 0 & 5 \\ 91                                         0 & 0 & 1 & -3 \\ 92                                         0 & 0 & 0 & 0 93                                 \end{bmatrix} 94                                 = B 95                         \end{equation*} 96                         In matrix $B$, columns 1,3 form a basis for $Col(B)$. \\ 97                         In matrix $A$, columns 1,3 form a basis for $Col(A)$. 98  99                         \emph{NOTE:} Columns 1 and 3 of matrix $B$ do NOT form a basis for $Col(A)$.100                         Row operations do NOT preserve columspace. $Col(A) \neq Col(B)$.101 102                 \end{example}103 104                 \begin{corollary}105                         \label{cor1}106                         if $B$ is the RREF matrix of $A$ and given the columns of $B$ with leading107                         1's, the corresponding columns of A form a basis of $Col(A)$.108                 \end{corollary}109 110                 \begin{corollary}111                         \label{cor2}112                         $dim(Col(A)) = rank(A)$113                 \end{corollary}114 115                 \begin{proof}[Proof of \ref{cor1}]116                         The columns with leading 1's are linearly independent (standard basis vectors)117                         and all entries below the leading 1's are zero. Thus, the linearly independent118                         set is maximal $\Rightarrow$ it forms a basis of $Col(B)$. Use the corresponding119                         columns in $A$ for $Col(A)$.120                 \end{proof}121 122                 \begin{proof}[Proof of \ref{cor2}]123                         \# of leading 1's $=$ maximum \# of linearly independent columns.124                 \end{proof}125 126                 \emph{NOTE:} if $A \in M(m,n)$ then $Col(A) = \{ A\vec{x} | \vec{x} \in \mathbb{R}^n\}$.127 128                 For a linear mapping $L : \mathbb{R}^n \rightarrow \mathbb{R}^m$, the output is given by129                 $[L]\vec{x}, x \in \mathbb{R}^n$.130 131                 \begin{theorem}132                         For a linear mapping $L : \mathbb{R}^n \rightarrow \mathbb{R}^m$,133                         \begin{equation*}134                                 dim(Range(L)) = dim(Col(L)) = rank(L)135                         \end{equation*}136                 \end{theorem}137 138                 The rank of a linear mapping has nothing to do with its matrix representation. This gives139                 a non-matrix meaning for rank.140 141                 \begin{definition}142                         The \emph{rank} of a linear mapping $L : \mathbb{R}^n \rightarrow \mathbb{R}^m$143                         is the dimension of its range.144                 \end{definition}145 146                 Rank also has a relationship with the nullspace.147 148                 \begin{example}149                         \begin{equation*}150                         A = 151                                 \begin{bmatrix}152                                         1 & 2 & 2 & -1 \\153                                         3 & 6 & 5 & 0 \\154                                         1 & 2 & 1 & 2155                                 \end{bmatrix}156                                 \rightarrow \ldots \rightarrow157                                 \begin{bmatrix}158                                         1 & 2 & 0 & 5 \\159                                         0 & 0 & 1 & -3 \\160                                         0 & 0 & 0 & 0161                                 \end{bmatrix}162                                 = B163                         \end{equation*}164                         To find the nullspace of $A$, find the solution of $A\vec{x} = \vec{0} = B\vec{x}$.165                         The solutions to $A\vec{x} = \vec{0}$ are166                         \begin{equation*}167                                 Null(A) = span\{(-5,0,3,1),(-2,1,0,0)\} \\168                                 dim(Null(A)) = 2169                         \end{equation*}170                 \end{example}171 172         \subsection{Nullity and Rank/Dimension Theorem}173                 \begin{definition}174                         The dimension of the nullspace of a linear mapping $L$ is also called the175                         \emph{nullity} of $L$.176                 \end{definition}177 178                 $rank([L])$ measures the dimension of the range of $L$. The nullspace focuses on all179                 vectors where $[L]\vec{x} = \vec{0}$. If $\vec{x}\in\mathbb{R}^n$ and the dimension of180                 the range is less than n, some vectors became $\vec{0}$.181 182                 \begin{theorem}[Rank/Dimension Theorem]183                         Let $V$ be an n-dimensional vector space.184 185                         If $L : V \rightarrow W$, then186                         187                                 rank(L) + dim(Null(L)) = n188                         189                 \end{theorem}190                 \begin{proof}191                         Recall: For $L : V \rightarrow V$, the nullspace of L is a subspace of $V$ made up192                         of vectors $\vec{x} \in V$ where $L(\vec{x}) = \vec{0}$.193 194                         Let $\{\vec{v_1}, \ldots, \vec{v_n}\}$ be a basis for $Null(L)$.195                         We can extend this to a basis of $V$ by adding vectors196                         $\vec{u_{k+1}}, \vec{u_{k+2}}, \ldots, \vec{u_n}$.197 198                         For a vector $\vec{w}$ in the range of $L$, there must be a corresponding vector199                         $\vec{x} \in V$ where200                         \begin{equation*} \vec{w} = L(\vec{x}) \end{equation*}201 202                         There are constants $c_1, \ldots, c_n$ such that203                         \begin{equation*} \begin{split}204                                 \vec{x} = c_1\vec{v_1} + c_2\vec{v_2} + \ldots + c_n\vec{v_n} \\205                                 + c_{k+1}\vec{u_{k+1}} + \ldots + c_n\vec{u_n}206                         \end{split} \end{equation*}207                 \end{proof}208 209 \section{End}210 211 \end{document}

Random832
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### Re: LaTeX and other markup!

$\left [ \begin{array}{rcccccl} a_{11}x_{1}o_{1}m_{3}f_{3}g_{7}& + & a_{12}x_{2} & + & \ldots & + & a_{1n}x_{n} \\ &&&\vdots&&& \\ a_{m1}x_{1}& + & a_{m2}x_{2} & + & \ldots & + & a_{mn}x{n} \end{array}\right ]$
(double click the LaTeX to see the code)

I actually think it'd look better with the vdots lined up with the other dots [I'd include sample code, but don't want to insult anyone's intelligence]

Talith
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### Re: LaTeX and other markup!

Random832 wrote:I actually think it'd look better with the vdots lined up with the other dots [I'd include sample code, but don't want to insult anyone's intelligence]

Actually I think I agree, I just tried to stick to what the Rippy asked for. Hopefully the way it's layed it makes it pretty obvious how to move the vdots to another column.

Jyrki
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### Re: LaTeX and other markup!

Sometimes we may feel the need to insert eps-graphics (like those produced by Mathematica). Is that possible?

Heck. I guess all I need is a way to convert eps to jpg. Any suggestions? While I'm at it, does anyone know, if it is possible to insert jpg-images into a document typeset by LaTeX? At the moment I can handle eps, which suffices for most of the things, but occasionally I get the urge to insert other types of images into e.g. sets of slides or lecture notes.

gmalivuk
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### Re: LaTeX and other markup!

At least in the Windows version, you can just copy Mathematica output as a bitmap, and then paste it into MS Paint or GIMP or whatever your image editor of choice is. From there, save it in whatever format you like.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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antonfire
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### Re: LaTeX and other markup!

Jyrki wrote:I guess all I need is a way to convert eps to jpg. Any suggestions?
ImageMagick can do it.

Jyrki wrote:While I'm at it, does anyone know, if it is possible to insert jpg-images into a document typeset by LaTeX? At the moment I can handle eps, which suffices for most of the things, but occasionally I get the urge to insert other types of images into e.g. sets of slides or lecture notes.
I believe I got this to work once, but only if by going directly through pdflatex instead of the usual latex, ps, dvi, pdf thing. This unfortunately means that I couldn't get both jpegs and eps's into the same document.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Jyrki
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### Re: LaTeX and other markup!

Thanks for the suggestions, gmalivuk and antonfire.

@antonfire: Somebody else told about a similar end result (can't have both eps and jpg). Too bad BTW, love the quote in your sig. A long time ago I decided to simply believe in naïve set theory, Russell's paradox, Zorn's lemma and not to worry about the rest. Seems to work - in a way.

Ephphatha
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### Re: LaTeX and other markup!

I just noticed this today:

With $, Code: Select all $s^2_i=\frac{1}{n_i-1}\left(\displaystyle\sum^{n_i}_{j=1}x^2_{ij}-\frac{\left(\displaystyle\sum^{n_i}_{j=1}x_{ij}\right)^2}{n_i}\right)\$

With $, Code: Select all \[s^2_i=\frac{1}{n_i-1}\left(\displaystyle\sum^{n_i}_{j=1}x^2_{ij}-\frac{\left(\displaystyle\sum^{n_i}_{j=1}x_{ij}\right)^2}{n_i}\right)$

$s^2_i=\frac{1}{n_i-1}\left(\displaystyle\sum^{n_i}_{j=1}x^2_{ij}-\frac{\left(\displaystyle\sum^{n_i}_{j=1}x_{ij}\right)^2}{n_i}\right)$

It seems to me like this shouldn't happen. Is it desired behaviour? Why?
I'm not lazy, I'm just getting in early for Christmas is all...

phlip
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### Re: LaTeX and other markup!

Well, it is jsMath's default behavior... I don't think there's anything you can do about it inside code tags, unfortunately.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
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mdyrud
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### Re: LaTeX and other markup!

Is there any way to reduce the font size within math tags? I'm having trouble with an equation extending beyond the margin, but it isn't long enough to create a manual break without looking strange.

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### Re: LaTeX and other markup!

You know when you're doing a definite integral, and you've gotten rid of the integral symbol but you still have that bar thing that shows the limits of integration? What is that called and how do I make it in LaTeX?

skeptical scientist
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### Re: LaTeX and other markup!

alreadytaken4536 wrote:You know when you're doing a definite integral, and you've gotten rid of the integral symbol but you still have that bar thing that shows the limits of integration? What is that called and how do I make it in LaTeX?

I just use the vertical bar | like for absolute value signs. You can make it bigger using \big, \Big, \bigg, or \Bigg, e.g.

Code: Select all

\int_0^1 3x^2 \, dx = x^3 \bigg|_0^1 = 1.
which makes $\int_0^1 3x^2 \, dx = x^3 \bigg|_0^1 = 1.$ You can also use it with \left and \right to have it adapt in size to an interior expression, as you would when writing $\left( \frac{1}{\sin x} \right)^2.$ You can use \left and \right with many different types of delimiters, including parentheses, brackets, and braces. They need not match, and you can use \left. or \right. with a period after it as a placeholder if you only want a delimiter to show on one side of the delimited expression.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson