LaTeX Introducing LaTeX Math Typesetting

[robphy]

robphy,

As I mentioned, the antialiasing done by ghostscript appears to be different now than it used to be. As I said, I prefer the old look, and am going to try to make it look a little better soon. Apparently quite a bit of stuff was changed.

- Warren

What version of Ghostscript? What version and distro of linux?
From googling, these commandline options might worth playing with:

-dTextAlphaBits=4 -dGraphicsAlphaBits=4 -dNOPLATFONTS

...just a thought.

 

[pervect]

<br /> \[<br /> <br /> \unitlength 1mm<br /> \begin{picture}(85.00,95.00)(0,0)<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,0.00){\line(0,1){90.00}}\linethickness{0.15mm}<br /> \put(20.00,90.00){\line(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,90.12){\line(0,1){0.12}}<br /> \put(20.00,90.24){\vector(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(65.12,90.24)(0.12,0.24){1}{\line(0,1){0.24}}<br /> \put(65.24,90.48){\vector(1,2){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(40.12,40.12)(0.12,0.12){1}{\line(1,0){0.12}}<br /> \put(40.24,40.24){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(60.12,80.12)(0.12,0.12){1}{\line(0,1){0.12}}<br /> \put(60.24,80.24){\vector(1,1){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,0.00)(0.12,0.24){375}{\line(0,1){0.24}}<br /> \put(65.00,90.00){\vector(1,2){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,20.00)(0.12,0.12){167}{\line(1,0){0.12}}<br /> \put(40.00,40.00){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(20.00,40.00)(0.12,0.12){333}{\line(1,0){0.12}}<br /> \put(60.00,80.00){\vector(1,1){0.12}}<br /> <br /> \put(20.00,0.00){\makebox(0,0)[cr]{O\,}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[cr]{A\,}}<br /> <br /> \put(40.00,40.00){\makebox(0,0)[cl]{\,B}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[cr]{C\,}}<br /> <br /> \put(60.00,80.00){\makebox(0,0)[cl]{\,D}}<br /> <br /> \put(20.00,92.00){\makebox(0,0)[bc]{T axis}}<br /> <br /> \put(65.00,92.00){\makebox(0,0)[bc]{T&#039; axis}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \end{picture}<br /> <br /> \]<br /> <br />

 

[pervect]

<br /> \[<br /> <br /> \unitlength 1mm<br /> \begin{picture}(85.00,95.00)(0,0)<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,0.00){\line(0,1){90.00}}\linethickness{0.15mm}<br /> \put(20.00,90.00){\line(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,90.12){\line(0,1){0.12}}<br /> \put(20.00,90.24){\vector(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(65.12,90.24)(0.12,0.24){1}{\line(0,1){0.24}}<br /> \put(65.24,90.48){\vector(1,2){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(40.12,40.12)(0.12,0.12){1}{\line(1,0){0.12}}<br /> \put(40.24,40.24){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(60.12,80.12)(0.12,0.12){1}{\line(0,1){0.12}}<br /> \put(60.24,80.24){\vector(1,1){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,0.00)(0.12,0.24){375}{\line(0,1){0.24}}<br /> \put(65.00,90.00){\vector(1,2){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,20.00)(0.12,0.12){167}{\line(1,0){0.12}}<br /> \put(40.00,40.00){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(20.00,40.00)(0.12,0.12){333}{\line(1,0){0.12}}<br /> \put(60.00,80.00){\vector(1,1){0.12}}<br /> <br /> \put(20.00,0.00){\makebox(0,0)[cr]{O\,}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[cr]{A\,}}<br /> <br /> \put(40.00,40.00){\makebox(0,0)[cl]{\,B}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[cr]{C\,}}<br /> <br /> \put(60.00,80.00){\makebox(0,0)[cl]{\,D}}<br /> <br /> \put(20.00,92.00){\makebox(0,0)[bc]{T axis}}<br /> <br /> \put(65.00,92.00){\makebox(0,0)[bc]{T&#039; axis}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \put(20.00,7.00){\makebox(0,0)[bl]{$\alpha$}}<br /> <br /> \end{picture}<br /> <br /> \]<br /> <br />

 

[pervect]

So, I just want to stick an "alpha" in the angle by the point marked O, why is the Latex source for this image invalid?

 

[dav2008]

Is there something I'm doing with wrong trying to get a line break?

<br /> a \\ b<br />

<br /> a \ \ b

a \ \<br /> b<br />

Obviously the following works but it can get annoying

a
b

 

[robphy]

<br /> \[<br /> <br /> \unitlength 1mm<br /> \begin{picture}(85.00,95.00)(0,0)<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,0.00){\line(0,1){90.00}}\linethickness{0.15mm}<br /> \put(20.00,90.00){\line(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,90.12){\line(0,1){0.12}}<br /> \put(20.00,90.24){\vector(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(65.12,90.24)(0.12,0.24){1}{\line(0,1){0.24}}<br /> \put(65.24,90.48){\vector(1,2){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(40.12,40.12)(0.12,0.12){1}{\line(1,0){0.12}}<br /> \put(40.24,40.24){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(60.12,80.12)(0.12,0.12){1}{\line(0,1){0.12}}<br /> \put(60.24,80.24){\vector(1,1){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,0.00)(0.12,0.24){375}{\line(0,1){0.24}}<br /> \put(65.00,90.00){\vector(1,2){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,20.00)(0.12,0.12){167}{\line(1,0){0.12}}<br /> \put(40.00,40.00){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(20.00,40.00)(0.12,0.12){333}{\line(1,0){0.12}}<br /> \put(60.00,80.00){\vector(1,1){0.12}}<br /> <br /> \put(20.00,0.00){\makebox(0,0)[cr]{O\,}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[cr]{A\,}}<br /> <br /> \put(40.00,40.00){\makebox(0,0)[cl]{\,B}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[cr]{C\,}}<br /> <br /> \put(60.00,80.00){\makebox(0,0)[cl]{\,D}}<br /> <br /> \put(20.00,92.00){\makebox(0,0)[bc]{T axis}}<br /> <br /> \put(65.00,92.00){\makebox(0,0)[bc]{T&#039; axis}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[tl]{\beta}}<br /> <br /> \put(0.00,5.00){\makebox(0,0)[bl]{\alpha}}<br /> <br /> \end{picture}<br /> <br /> \]<br /> <br />

<br /> \[<br /> <br /> \unitlength 1mm<br /> \begin{picture}(85.00,95.00)(0,0)<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,0.00){\line(0,1){90.00}}\linethickness{0.15mm}<br /> \put(20.00,90.00){\line(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \put(20.00,90.12){\line(0,1){0.12}}<br /> \put(20.00,90.24){\vector(0,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(65.12,90.24)(0.12,0.24){1}{\line(0,1){0.24}}<br /> \put(65.24,90.48){\vector(1,2){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(40.12,40.12)(0.12,0.12){1}{\line(1,0){0.12}}<br /> \put(40.24,40.24){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(60.12,80.12)(0.12,0.12){1}{\line(0,1){0.12}}<br /> \put(60.24,80.24){\vector(1,1){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,0.00)(0.12,0.24){375}{\line(0,1){0.24}}<br /> \put(65.00,90.00){\vector(1,2){0.12}}\linethickness{0.15mm}<br /> \multiput(20.00,20.00)(0.12,0.12){167}{\line(1,0){0.12}}<br /> \put(40.00,40.00){\vector(1,1){0.12}}<br /> <br /> \linethickness{0.15mm}<br /> \multiput(20.00,40.00)(0.12,0.12){333}{\line(1,0){0.12}}<br /> \put(60.00,80.00){\vector(1,1){0.12}}<br /> <br /> \put(20.00,0.00){\makebox(0,0)[cr]{O\,}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[cr]{A\,}}<br /> <br /> \put(40.00,40.00){\makebox(0,0)[cl]{\,B}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[cr]{C\,}}<br /> <br /> \put(60.00,80.00){\makebox(0,0)[cl]{\,D}}<br /> <br /> \put(20.00,92.00){\makebox(0,0)[bc]{T axis}}<br /> <br /> \put(65.00,92.00){\makebox(0,0)[bc]{T&#039; axis}}<br /> <br /> \put(20.00,20.00){\makebox(0,0)[tl]{$\beta$}}<br /> <br /> \put(20.00,40.00){\makebox(0,0)[tl]{$\beta$}}<br /> <br /> \put(0.00,5.00){\makebox(0,0)[bl]{$\alpha$}}<br /> <br /> \end{picture}<br /> <br /> \]<br /> <br />

The use of \[ and \] I've always used in the \picture environment here
let me use the standard tags $\alpha$ for math symbols. I found this out by trial and error.

 

[robphy]

Is there something I'm doing with wrong trying to get a line break?

<br /> a \\ b<br />

<br /> a \ \ b

a \ \<br /> b<br />

maybe we're in an mbox?
\begin{align*} a \\ b \end{align*}

\] a \\ b \[

\] $ a \\ b $ \[

From these last two posts, it seems one has more familiar control using
[ tex ] \] a \\ b \[ [ /tex ]
instead of the usual
[ tex ] a \\ b [ /tex ]

Did I mention that I really like \LaTeX?
(That's why I'm saddened that the preview mode is broken .)

 

[Hyperreality]

LaTeX

Just an aside, for those who'd like to have LaTeX on their computer http://http://www.artofproblemsolving.com/LaTeX/AoPS_L_Downloads.php" is the place to get it! The whole package is about 400MB.

 

[JonF]

0&lt;|x-x_0| &lt;\delta =&gt; |sin(x) - sin(x_0)|&lt; \epsilon
|sin(x)| - |sin(x_0)|&lt;|sin(x) - sin(x_0)|&lt;\epsilon
|sin(x)| - |x| &lt; |sin(x)| - |sin(x_0)|&lt; \epsilon

 

[dav2008]

Fixed link: http://www.artofproblemsolving.com/LaTeX/AoPS_L_Downloads.php

maybe we're in an mbox?
\begin{align*} a \\ b \end{align*}

\] a \\ b \[

\] $ a \\ b $ \[

From these last two posts, it seems one has more familiar control using
[ tex ] \] a \\ b \[ [ /tex ]
instead of the usual
[ tex ] a \\ b [ /tex ]

Did I mention that I really like \LaTeX?
(That's why I'm saddened that the preview mode is broken .)

hmm ok thanks.

 

[renatzu]

d\vec{B} = \frac{\mu_0}{4\pi}(\frac{Id\vec{s}\times\hat{r}}{r^2})

\int B \cdot ds = \mu_0 I

B = \frac {\mu_0 * 2A}{4 * 2 \pi * .08 m }

F = \frac {2 k_m I_1 I_2 l}{d}

 

[-Job-]

Miktex has all kinds of packages available for download. In order to use these packages must i specifically indicate which to use in the latex code or is there an option to just use all available?

 

[matt grime]

You won't want to use all available. It is unnecessary and there are package conflicts. You cannot use xypic with Paul Taylor's diagrams package for instance. Plus there are some packages that require their own
\usepackage

command and yet others must appear after other packages in the preamble as well.

 

[himanshu121]

T_1 - T_2 = 2k(r\theta -1)

 

[himanshu121]

T_1 - T_2 = m \frac{d^2}{dt^2} y

 

[himanshu121]

T_1-T_2=m \frac{d^2 y}{dt^2}
T_m=\frac{K_mv_2}{R}
T_m=J\frac{d^2\theta}{dt^2}+b\frac{d\theta}{dt}+r(T_1 - T_2)
state variables are
4=\frac{dy}{dt}x_1=\theta , x_2=y , x_3=\frac{d\theta}{dt} , x_

 

[dav2008]

I installed miketex and TeXnicCenter. How do I have to format the new entry in TeXnicCenter to get it to work? On the forums it's just [tex]asadasda[/tex].

Edit: NM found the short tutorial on that webpage.

Is there a way to export to jpg?

 

[-Job-]

Dav, for that you might need some other tool. I know you can convert to PNG and GIF, but neither through TeXnic Center. To convert to png i first convert to dvi and then use the dvipng.exe tool to convert the dvi to a png. To convert to .gif there is a tool called MimeTex. This whole LateX scene is very confusing i think. That's why I'm doing a web based editor that can export/preview as a png, gif, or html.
It's still under construction but it's already usable:
http://www.bloo.us/academic/latex/

I'm actually having some issues implementing the formatting tags in my program. Maybe someone experienced can tell me why the tags:
\tiny
\scriptsize
\footnotesize
\small
\normalsize
\large
\Large
\LARGE
\huge
\Huge
... are not parsed correctly with latex.exe (generate an error). Do i need to use a specific package? Which one?

 

[dav2008]

Dav, for that you might need some other tool. I know you can convert to PNG and GIF, but neither through TeXnic Center. To convert to png i first convert to dvi and then use the dvipng.exe tool to convert the dvi to a png. To convert to .gif there is a tool called MimeTex. This whole LateX scene is very confusing i think. That's why I'm doing a web based editor that can export/preview as a png, gif, or html.
It's still under construction but it's already usable:
http://www.bloo.us/academic/latex/

Thanks I'll check out that link.

I mean what I do now is just preview the file, screen capture, paste into PS, crop and save as jpg. I think that web-utility might be a bit more useful for my purposes, if I just want to make a quick jpg.

 

[matt grime]

There are solutions, depending on your OS, to these problems.

1. If in OS X you have latexit.
2. Use latex2html in any system.
3. Stop using anything but a text editor for latex and buy yourself a copy of Kopka and Daly, you'll be far more productive.

 

[robphy]

plotting example

\]<br /> \unitlength 0.02mm<br /> \begin{picture}(400,3000)(0,0)<br /> <br /> \textcolor{red}{ <br /> \linethickness{3pt}<br /> \qbezier( 6110, 1946 )( 6230, 1948 )( 6230, 1948 )<br /> \qbezier( 5998, 1939 )( 6110, 1946 )( 6110, 1946 )<br /> \qbezier( 5881, 1928 )( 5998, 1939 )( 5998, 1939 )<br /> \qbezier( 5771, 1916 )( 5881, 1928 )( 5881, 1928 )<br /> \qbezier( 5648, 1905 )( 5771, 1916 )( 5771, 1916 )<br /> \qbezier( 5541, 1900 )( 5648, 1905 )( 5648, 1905 )<br /> \qbezier( 5425, 1903 )( 5541, 1900 )( 5541, 1900 )<br /> \qbezier( 5307, 1916 )( 5425, 1903 )( 5425, 1903 )<br /> \qbezier( 5193, 1936 )( 5307, 1916 )( 5307, 1916 )<br /> \qbezier( 5073, 1960 )( 5193, 1936 )( 5193, 1936 )<br /> \qbezier( 4959, 1980 )( 5073, 1960 )( 5073, 1960 )<br /> \qbezier( 4843, 1990 )( 4959, 1980 )( 4959, 1980 )<br /> \qbezier( 4731, 1984 )( 4843, 1990 )( 4843, 1990 )<br /> \qbezier( 4613, 1961 )( 4731, 1984 )( 4731, 1984 )<br /> \qbezier( 4505, 1926 )( 4613, 1961 )( 4613, 1961 )<br /> \qbezier( 4385, 1881 )( 4505, 1926 )( 4505, 1926 )<br /> \qbezier( 4273, 1843 )( 4385, 1881 )( 4385, 1881 )<br /> \qbezier( 4211, 1829 )( 4273, 1843 )( 4273, 1843 )<br /> \qbezier( 4148, 1822 )( 4211, 1829 )( 4211, 1829 )<br /> \qbezier( 4092, 1823 )( 4148, 1822 )( 4148, 1822 )<br /> \qbezier( 4036, 1832 )( 4092, 1823 )( 4092, 1823 )<br /> \qbezier( 3978, 1849 )( 4036, 1832 )( 4036, 1832 )<br /> \qbezier( 3920, 1874 )( 3978, 1849 )( 3978, 1849 )<br /> \qbezier( 3801, 1946 )( 3920, 1874 )( 3920, 1874 )<br /> \qbezier( 3687, 2028 )( 3801, 1946 )( 3801, 1946 )<br /> \qbezier( 3580, 2095 )( 3687, 2028 )( 3687, 2028 )<br /> \qbezier( 3519, 2121 )( 3580, 2095 )( 3580, 2095 )<br /> \qbezier( 3458, 2135 )( 3519, 2121 )( 3519, 2121 )<br /> \qbezier( 3429, 2137 )( 3458, 2135 )( 3458, 2135 )<br /> \qbezier( 3399, 2135 )( 3429, 2137 )( 3429, 2137 )<br /> \qbezier( 3370, 2128 )( 3399, 2135 )( 3399, 2135 )<br /> \qbezier( 3341, 2118 )( 3370, 2128 )( 3370, 2128 )<br /> \qbezier( 3286, 2088 )( 3341, 2118 )( 3341, 2118 )<br /> \qbezier( 3232, 2045 )( 3286, 2088 )( 3286, 2088 )<br /> \qbezier( 3113, 1913 )( 3232, 2045 )( 3232, 2045 )<br /> \qbezier( 2999, 1761 )( 3113, 1913 )( 3113, 1913 )<br /> \qbezier( 2880, 1621 )( 2999, 1761 )( 2999, 1761 )<br /> \qbezier( 2825, 1576 )( 2880, 1621 )( 2880, 1621 )<br /> \qbezier( 2771, 1551 )( 2825, 1576 )( 2825, 1576 )<br /> \qbezier( 2756, 1547 )( 2771, 1551 )( 2771, 1551 )<br /> \qbezier( 2740, 1546 )( 2756, 1547 )( 2756, 1547 )<br /> \qbezier( 2725, 1546 )( 2740, 1546 )( 2740, 1546 )<br /> \qbezier( 2709, 1549 )( 2725, 1546 )( 2725, 1546 )<br /> \qbezier( 2679, 1559 )( 2709, 1549 )( 2709, 1549 )<br /> \qbezier( 2648, 1579 )( 2679, 1559 )( 2679, 1559 )<br /> \qbezier( 2595, 1631 )( 2648, 1579 )( 2648, 1579 )<br /> \qbezier( 2542, 1707 )( 2595, 1631 )( 2595, 1631 )<br /> \qbezier( 2417, 1965 )( 2542, 1707 )( 2542, 1707 )<br /> \qbezier( 2312, 2227 )( 2417, 1965 )( 2417, 1965 )<br /> \qbezier( 2197, 2489 )( 2312, 2227 )( 2312, 2227 )<br /> \qbezier( 2137, 2587 )( 2197, 2489 )( 2197, 2489 )<br /> \qbezier( 2077, 2644 )( 2137, 2587 )( 2137, 2587 )<br /> \qbezier( 2062, 2650 )( 2077, 2644 )( 2077, 2644 )<br /> \qbezier( 2047, 2654 )( 2062, 2650 )( 2062, 2650 )<br /> \qbezier( 2032, 2654 )( 2047, 2654 )( 2047, 2654 )<br /> \qbezier( 2017, 2650 )( 2032, 2654 )( 2032, 2654 )<br /> \qbezier( 1987, 2632 )( 2017, 2650 )( 2017, 2650 )<br /> \qbezier( 1957, 2600 )( 1987, 2632 )( 1987, 2632 )<br /> \qbezier( 1904, 2506 )( 1957, 2600 )( 1957, 2600 )<br /> \qbezier( 1851, 2367 )( 1904, 2506 )( 1904, 2506 )<br /> \qbezier( 1791, 2159 )( 1851, 2367 )( 1851, 2367 )<br /> \qbezier( 1731, 1910 )( 1791, 2159 )( 1791, 2159 )<br /> \qbezier( 1672, 1641 )( 1731, 1910 )( 1731, 1910 )<br /> \qbezier( 1614, 1364 )( 1672, 1641 )( 1672, 1641 )<br /> \qbezier( 1555, 1099 )( 1614, 1364 )( 1614, 1364 )<br /> \qbezier( 1496, 868 )( 1555, 1099 )( 1555, 1099 )<br /> \qbezier( 1439, 698 )( 1496, 868 )( 1496, 868 )<br /> \qbezier( 1383, 597 )( 1439, 698 )( 1439, 698 )<br /> \qbezier( 1369, 585 )( 1383, 597 )( 1383, 597 )<br /> \qbezier( 1355, 578 )( 1369, 585 )( 1369, 585 )<br /> \qbezier( 1342, 576 )( 1355, 578 )( 1355, 578 )<br /> \qbezier( 1328, 580 )( 1342, 576 )( 1342, 576 )<br /> \qbezier( 1300, 604 )( 1328, 580 )( 1328, 580 )<br /> \qbezier( 1273, 651 )( 1300, 604 )( 1300, 604 )<br /> \qbezier( 1214, 832 )( 1273, 651 )( 1273, 651 )<br /> \qbezier( 1155, 1119 )( 1214, 832 )( 1214, 832 )<br /> \qbezier( 1125, 1300 )( 1155, 1119 )( 1155, 1119 )<br /> \qbezier( 1095, 1503 )( 1125, 1300 )( 1125, 1300 )<br /> \qbezier( 1065, 1726 )( 1095, 1503 )( 1095, 1503 )<br /> \qbezier( 1036, 1965 )( 1065, 1726 )( 1065, 1726 )<br /> \qbezier( 1006, 2215 )( 1036, 1965 )( 1036, 1965 )<br /> \qbezier( 977, 2473 )( 1006, 2215 )( 1006, 2215 )<br /> \qbezier( 947, 2735 )( 977, 2473 )( 977, 2473 )<br /> \qbezier( 918, 2996 )( 947, 2735 )( 947, 2735 )<br /> \qbezier( 891, 3223 )( 918, 2996 )( 918, 2996 )<br /> \qbezier( 865, 3442 )( 891, 3223 )( 891, 3223 )<br /> \qbezier( 839, 3649 )( 865, 3442 )( 865, 3442 )<br /> \qbezier( 813, 3841 )( 839, 3649 )( 839, 3649 )<br /> \qbezier( 752, 4202 )( 813, 3841 )( 813, 3841 )<br /> }<br /> \textcolor{yellow}{<br /> \qbezier( 692, 4421 )( 752, 4202 )( 752, 4202 )<br /> \qbezier( 692, 500 )( 692, 4500 )( 692, 4500 )<br /> \qbezier( 670, 537 )( 692, 537 )( 692, 537 )<br /> \qbezier( 670, 637 )( 692, 637 )( 692, 637 )<br /> \qbezier( 670, 736 )( 692, 736 )( 692, 736 )<br /> \qbezier( 670, 836 )( 692, 836 )( 692, 836 )<br /> \qbezier( 648, 935 )( 692, 935 )( 692, 935 )<br /> \qbezier( 670, 1035 )( 692, 1035 )( 692, 1035 )<br /> \qbezier( 670, 1135 )( 692, 1135 )( 692, 1135 )<br /> \qbezier( 670, 1234 )( 692, 1234 )( 692, 1234 )<br /> \qbezier( 670, 1334 )( 692, 1334 )( 692, 1334 )<br /> \qbezier( 648, 1433 )( 692, 1433 )( 692, 1433 )<br /> \qbezier( 670, 1533 )( 692, 1533 )( 692, 1533 )<br /> \qbezier( 670, 1632 )( 692, 1632 )( 692, 1632 )<br /> \qbezier( 670, 1732 )( 692, 1732 )( 692, 1732 )<br /> \qbezier( 670, 1832 )( 692, 1832 )( 692, 1832 )<br /> \qbezier( 648, 1931 )( 692, 1931 )( 692, 1931 )<br /> \qbezier( 670, 2031 )( 692, 2031 )( 692, 2031 )<br /> \qbezier( 670, 2130 )( 692, 2130 )( 692, 2130 )<br /> \qbezier( 670, 2230 )( 692, 2230 )( 692, 2230 )<br /> \qbezier( 670, 2330 )( 692, 2330 )( 692, 2330 )<br /> \qbezier( 648, 2429 )( 692, 2429 )( 692, 2429 )<br /> \qbezier( 670, 2529 )( 692, 2529 )( 692, 2529 )<br /> \qbezier( 670, 2628 )( 692, 2628 )( 692, 2628 )<br /> \qbezier( 670, 2728 )( 692, 2728 )( 692, 2728 )<br /> \qbezier( 670, 2828 )( 692, 2828 )( 692, 2828 )<br /> \qbezier( 648, 2927 )( 692, 2927 )( 692, 2927 )<br /> \qbezier( 670, 3027 )( 692, 3027 )( 692, 3027 )<br /> \qbezier( 670, 3126 )( 692, 3126 )( 692, 3126 )<br /> \qbezier( 670, 3226 )( 692, 3226 )( 692, 3226 )<br /> \qbezier( 670, 3326 )( 692, 3326 )( 692, 3326 )<br /> \qbezier( 648, 3425 )( 692, 3425 )( 692, 3425 )<br /> \qbezier( 670, 3525 )( 692, 3525 )( 692, 3525 )<br /> \qbezier( 670, 3624 )( 692, 3624 )( 692, 3624 )<br /> \qbezier( 670, 3724 )( 692, 3724 )( 692, 3724 )<br /> \qbezier( 670, 3824 )( 692, 3824 )( 692, 3824 )<br /> \qbezier( 648, 3923 )( 692, 3923 )( 692, 3923 )<br /> \qbezier( 670, 4023 )( 692, 4023 )( 692, 4023 )<br /> \qbezier( 670, 4122 )( 692, 4122 )( 692, 4122 )<br /> \qbezier( 670, 4222 )( 692, 4222 )( 692, 4222 )<br /> \qbezier( 670, 4321 )( 692, 4321 )( 692, 4321 )<br /> \qbezier( 648, 4421 )( 692, 4421 )( 692, 4421 )<br /> }<br /> \textcolor{green}{<br /> \qbezier( 692, 1931 )( 6230, 1931 )( 6230, 1931 )<br /> \qbezier( 913, 1915 )( 913, 1931 )( 913, 1931 )<br /> \qbezier( 1135, 1915 )( 1135, 1931 )( 1135, 1931 )<br /> \qbezier( 1356, 1915 )( 1356, 1931 )( 1356, 1931 )<br /> \qbezier( 1578, 1915 )( 1578, 1931 )( 1578, 1931 )<br /> \qbezier( 1799, 1898 )( 1799, 1931 )( 1799, 1931 )<br /> \qbezier( 2021, 1915 )( 2021, 1931 )( 2021, 1931 )<br /> \qbezier( 2243, 1915 )( 2243, 1931 )( 2243, 1931 )<br /> \qbezier( 2464, 1915 )( 2464, 1931 )( 2464, 1931 )<br /> \qbezier( 2686, 1915 )( 2686, 1931 )( 2686, 1931 )<br /> \qbezier( 2907, 1898 )( 2907, 1931 )( 2907, 1931 )<br /> \qbezier( 3129, 1915 )( 3129, 1931 )( 3129, 1931 )<br /> \qbezier( 3350, 1915 )( 3350, 1931 )( 3350, 1931 )<br /> \qbezier( 3572, 1915 )( 3572, 1931 )( 3572, 1931 )<br /> \qbezier( 3793, 1915 )( 3793, 1931 )( 3793, 1931 )<br /> \qbezier( 4015, 1898 )( 4015, 1931 )( 4015, 1931 )<br /> \qbezier( 4236, 1915 )( 4236, 1931 )( 4236, 1931 )<br /> \qbezier( 4458, 1915 )( 4458, 1931 )( 4458, 1931 )<br /> \qbezier( 4679, 1915 )( 4679, 1931 )( 4679, 1931 )<br /> \qbezier( 4901, 1915 )( 4901, 1931 )( 4901, 1931 )<br /> \qbezier( 5123, 1898 )( 5123, 1931 )( 5123, 1931 )<br /> \qbezier( 5344, 1915 )( 5344, 1931 )( 5344, 1931 )<br /> \qbezier( 5566, 1915 )( 5566, 1931 )( 5566, 1931 )<br /> \qbezier( 5787, 1915 )( 5787, 1931 )( 5787, 1931 )<br /> \qbezier( 6009, 1915 )( 6009, 1931 )( 6009, 1931 )<br /> \qbezier( 6230, 1898 )( 6230, 1931 )( 6230, 1931 )<br /> }<br /> <br /> \put(3550,2500){\makebox(0,0)[cc]{e^{-x}\cos(5x)}}<br /> \end{picture}<br /> \[<br />

 

[Leibniz]

\left(\begin{array}{cccc}a&amp;b&amp;c&amp;d\\ 1&amp;0&amp;1&amp;-1\\m&amp;n&amp;p&amp;q\end{array}\right)

 

[Orion1]

test code...

<br /> \unitlength 0.02mm<br /> \begin{picture}(4000,3000)(0,0)<br /> \textcolor{red}{<br /> \linethickness{3pt}<br /> \qbezier( 0, 3000)( 20, 2935)( 40, 2839)<br /> \qbezier( 40, 2839)( 60, 2716)( 80, 2570)<br /> \qbezier( 80, 2570)( 100, 2406)( 120, 2230)<br /> \qbezier( 120, 2230)( 139, 2046)( 159, 1860)<br /> \qbezier( 159, 1860)( 179, 1676)( 199, 1500)<br /> \qbezier( 199, 1500)( 219, 1333)( 239, 1182)<br /> \qbezier( 239, 1182)( 259, 1047)( 279, 932)<br /> \qbezier( 279, 932)( 299, 837)( 319, 765)<br /> \qbezier( 319, 765)( 339, 716)( 360, 689)<br /> \qbezier( 360, 689)( 380, 684)( 400, 699)<br /> \qbezier( 400, 699)( 420, 734)( 440, 785)<br /> \qbezier( 440, 785)( 460, 851)( 480, 929)<br /> \qbezier( 480, 929)( 500, 1016)( 520, 1110)<br /> \qbezier( 520, 1110)( 540, 1208)( 560, 1307)<br /> \qbezier( 560, 1307)( 580, 1405)( 600, 1500)<br /> \qbezier( 600, 1500)( 620, 1588)( 640, 1669)<br /> \qbezier( 640, 1669)( 660, 1741)( 680, 1802)<br /> \qbezier( 680, 1802)( 700, 1853)( 720, 1891)<br /> \qbezier( 720, 1891)( 740, 1917)( 760, 1932)<br /> \qbezier( 760, 1932)( 780, 1935)( 800, 1926)<br /> \qbezier( 800, 1926)( 820, 1908)( 840, 1881)<br /> \qbezier( 840, 1881)( 860, 1846)( 880, 1804)<br /> \qbezier( 880, 1804)( 900, 1757)( 920, 1707)<br /> \qbezier( 920, 1707)( 940, 1655)( 960, 1602)<br /> \qbezier( 960, 1602)( 980, 1550)( 1000, 1499)<br /> \qbezier( 1000, 1499)( 1020, 1452)( 1040, 1409)<br /> \qbezier( 1040, 1409)( 1060, 1371)( 1080, 1338)<br /> \qbezier( 1080, 1338)( 1100, 1311)( 1120, 1291)<br /> \qbezier( 1120, 1291)( 1140, 1277)( 1160, 1269)<br /> \qbezier( 1160, 1269)( 1180, 1267)( 1200, 1272)<br /> \qbezier( 1200, 1272)( 1220, 1282)( 1240, 1296)<br /> \qbezier( 1240, 1296)( 1260, 1315)( 1280, 1337)<br /> \qbezier( 1280, 1337)( 1300, 1362)( 1320, 1389)<br /> \qbezier( 1320, 1389)( 1340, 1417)( 1360, 1445)<br /> \qbezier( 1360, 1445)( 1380, 1473)( 1400, 1500)<br /> \qbezier( 1400, 1500)( 1420, 1525)( 1440, 1548)<br /> \qbezier( 1440, 1548)( 1460, 1568)( 1480, 1586)<br /> \qbezier( 1480, 1586)( 1500, 1600)( 1519, 1611)<br /> \qbezier( 1519, 1611)( 1539, 1618)( 1559, 1623)<br /> \qbezier( 1559, 1623)( 1579, 1623)( 1599, 1621)<br /> \qbezier( 1599, 1621)( 1619, 1616)( 1639, 1608)<br /> \qbezier( 1639, 1608)( 1659, 1598)( 1679, 1586)<br /> \qbezier( 1679, 1586)( 1699, 1573)( 1719, 1559)<br /> \qbezier( 1719, 1559)( 1739, 1544)( 1759, 1529)<br /> \qbezier( 1759, 1529)( 1779, 1514)( 1799, 1500)<br /> \qbezier( 1799, 1500)( 1819, 1486)( 1839, 1474)<br /> \qbezier( 1839, 1474)( 1859, 1463)( 1879, 1453)<br /> \qbezier( 1879, 1453)( 1899, 1446)( 1919, 1440)<br /> \qbezier( 1919, 1440)( 1939, 1436)( 1959, 1434)<br /> \qbezier( 1959, 1434)( 1979, 1433)( 1999, 1435)<br /> \qbezier( 1999, 1435)( 2019, 1437)( 2039, 1442)<br /> \qbezier( 2039, 1442)( 2059, 1447)( 2079, 1453)<br /> \qbezier( 2079, 1453)( 2099, 1460)( 2119, 1468)<br /> \qbezier( 2119, 1468)( 2139, 1476)( 2159, 1484)<br /> \qbezier( 2159, 1484)( 2179, 1492)( 2199, 1499)<br /> \qbezier( 2199, 1499)( 2219, 1507)( 2239, 1513)<br /> \qbezier( 2239, 1513)( 2259, 1519)( 2279, 1524)<br /> \qbezier( 2279, 1524)( 2299, 1528)( 2319, 1531)<br /> \qbezier( 2319, 1531)( 2339, 1533)( 2359, 1535)<br /> \qbezier( 2359, 1535)( 2379, 1535)( 2399, 1534)<br /> \qbezier( 2399, 1534)( 2419, 1533)( 2439, 1530)<br /> \qbezier( 2439, 1530)( 2459, 1528)( 2479, 1524)<br /> \qbezier( 2479, 1524)( 2499, 1520)( 2519, 1516)<br /> \qbezier( 2519, 1516)( 2539, 1512)( 2559, 1508)<br /> \qbezier( 2559, 1508)( 2579, 1504)( 2599, 1500)<br /> \qbezier( 2599, 1500)( 2619, 1496)( 2639, 1492)<br /> \qbezier( 2639, 1492)( 2659, 1489)( 2679, 1486)<br /> \qbezier( 2679, 1486)( 2699, 1484)( 2719, 1483)<br /> \qbezier( 2719, 1483)( 2739, 1481)( 2759, 1481)<br /> \qbezier( 2759, 1481)( 2779, 1481)( 2799, 1481)<br /> \qbezier( 2799, 1481)( 2819, 1482)( 2839, 1483)<br /> \qbezier( 2839, 1483)( 2859, 1485)( 2879, 1486)<br /> \qbezier( 2879, 1486)( 2899, 1488)( 2919, 1491)<br /> \qbezier( 2919, 1491)( 2939, 1493)( 2959, 1495)<br /> \qbezier( 2959, 1495)( 2979, 1497)( 2999, 1499)<br /> \qbezier( 2999, 1499)( 3019, 1502)( 3039, 1503)<br /> \qbezier( 3039, 1503)( 3059, 1505)( 3079, 1506)<br /> \qbezier( 3079, 1506)( 3099, 1508)( 3119, 1509)<br /> \qbezier( 3119, 1509)( 3139, 1509)( 3159, 1509)<br /> \qbezier( 3159, 1509)( 3179, 1510)( 3199, 1509)<br /> \qbezier( 3199, 1509)( 3219, 1509)( 3239, 1508)<br /> \qbezier( 3239, 1508)( 3259, 1507)( 3279, 1507)<br /> \qbezier( 3279, 1507)( 3299, 1505)( 3319, 1504)<br /> \qbezier( 3319, 1504)( 3339, 1503)( 3359, 1502)<br /> \qbezier( 3359, 1502)( 3379, 1501)( 3399, 1500)<br /> \qbezier( 3399, 1500)( 3419, 1498)( 3439, 1497)<br /> \qbezier( 3439, 1497)( 3459, 1497)( 3479, 1496)<br /> \qbezier( 3479, 1496)( 3499, 1495)( 3519, 1495)<br /> \qbezier( 3519, 1495)( 3539, 1494)( 3559, 1494)<br /> \qbezier( 3559, 1494)( 3579, 1494)( 3599, 1494)<br /> \qbezier( 3599, 1494)( 3619, 1494)( 3639, 1495)<br /> \qbezier( 3639, 1495)( 3659, 1495)( 3679, 1496)<br /> \qbezier( 3679, 1496)( 3699, 1496)( 3719, 1497)<br /> \qbezier( 3719, 1497)( 3739, 1498)( 3759, 1498)<br /> \qbezier( 3759, 1498)( 3779, 1499)( 3799, 1499)<br /> \qbezier( 3799, 1499)( 3819, 1500)( 3839, 1501)<br /> \qbezier( 3839, 1501)( 3859, 1501)( 3879, 1501)<br /> \qbezier( 3879, 1501)( 3899, 1502)( 3919, 1502)<br /> \qbezier( 3919, 1502)( 3939, 1502)( 3959, 1502)<br /> \qbezier( 3959, 1502)( 3979, 1502)( 3999, 1502)<br /> }<br /> \linethickness{1pt}<br /> \qbezier(0, 1500)( 2000, 1500)( 4000, 1500)<br /> \linethickness{1pt}<br /> \qbezier(0,0)(0, 1500)(0, 3000)<br /> \put(2000,2250){\makebox(0,0)[cc]{e^{-x}\cos(5x)}}<br /> \end{picture}<br />

 

[robphy]

\] \unitlength 0.02mm \begin{picture}(400,3000)(0,0) \textcolor{red}{ \def\qb#1#2#3#4{\qbezier(#1,#2)(#3,#4)(#3,#4)} \qb{3464}{1145}{3574}{1179} \qb{3353}{1179}{3242}{1221} \qb{3574}{1179}{3685}{1222} \qb{3353}{1179}{3463}{1223} \qb{3574}{1179}{3463}{1223} \qb{3242}{1221}{3131}{1295} \qb{3685}{1222}{3796}{1295} \qb{3242}{1221}{3352}{1300} \qb{3463}{1223}{3352}{1300} \qb{3463}{1223}{3574}{1300} \qb{3685}{1222}{3574}{1300} \qb{3352}{1300}{3463}{1328} \qb{3131}{1295}{3241}{1333} \qb{3352}{1300}{3241}{1333} \qb{3796}{1295}{3685}{1334} \qb{3574}{1300}{3685}{1334} \qb{3131}{1295}{3020}{1345} \qb{3796}{1295}{3907}{1345} \qb{3020}{1345}{2909}{1354} \qb{3907}{1345}{4018}{1355} \qb{2909}{1354}{2798}{1374} \qb{4018}{1355}{4128}{1375} \qb{3117}{1340}{3019}{1388} \qb{2909}{1354}{3019}{1388} \qb{3809}{1340}{3907}{1389} \qb{4018}{1355}{3907}{1389} \qb{3138}{1339}{3241}{1414} \qb{3349}{1331}{3241}{1414} \qb{3788}{1339}{3685}{1414} \qb{3578}{1331}{3685}{1414} \qb{3571}{1331}{3463}{1424} \qb{3355}{1331}{3463}{1424} \qb{2798}{1374}{2687}{1438} \qb{4128}{1375}{4239}{1439} \qb{3019}{1388}{2908}{1499} \qb{2798}{1374}{2908}{1499} \qb{4128}{1375}{4017}{1500} \qb{3907}{1389}{4017}{1500} \qb{2687}{1438}{2576}{1529} \qb{4239}{1439}{4350}{1530} \qb{3019}{1388}{3130}{1539} \qb{3241}{1414}{3130}{1539} \qb{3685}{1414}{3796}{1539} \qb{3907}{1389}{3796}{1539} \qb{3241}{1414}{3352}{1550} \qb{3463}{1424}{3352}{1550} \qb{3685}{1414}{3574}{1550} \qb{3463}{1424}{3574}{1550} \qb{3130}{1539}{3019}{1584} \qb{2908}{1499}{3019}{1584} \qb{4017}{1500}{3906}{1584} \qb{3796}{1539}{3906}{1584} \qb{2908}{1499}{2797}{1594} \qb{2687}{1438}{2797}{1594} \qb{4017}{1500}{4128}{1595} \qb{4239}{1439}{4128}{1595} \qb{2576}{1529}{2465}{1615} \qb{4350}{1530}{4461}{1616} \qb{2797}{1594}{2686}{1635} \qb{2576}{1529}{2686}{1635} \qb{4350}{1530}{4239}{1635} \qb{4128}{1595}{4239}{1635} \qb{2465}{1615}{2575}{1638} \qb{2686}{1635}{2575}{1638} \qb{4461}{1616}{4350}{1639} \qb{4239}{1635}{4350}{1639} \qb{2418}{1643}{2353}{1652} \qb{4507}{1644}{4571}{1653} \qb{3199}{1552}{3130}{1682} \qb{3078}{1573}{3130}{1682} \qb{3847}{1573}{3795}{1683} \qb{3726}{1552}{3795}{1683} \qb{2465}{1615}{2354}{1683} \qb{4461}{1616}{4572}{1684} \qb{2353}{1652}{2242}{1688} \qb{4571}{1653}{4682}{1689} \qb{2746}{1613}{2797}{1710} \qb{2881}{1590}{2797}{1710} \qb{4044}{1591}{4128}{1711} \qb{4179}{1613}{4128}{1711} \qb{2189}{1716}{2131}{1732} \qb{4735}{1717}{4793}{1734} \qb{2353}{1652}{2243}{1737} \qb{2354}{1683}{2243}{1737} \qb{4572}{1684}{4682}{1738} \qb{4571}{1653}{4682}{1738} \qb{2242}{1688}{2131}{1746} \qb{4682}{1689}{4793}{1747} \qb{3439}{1550}{3352}{1762} \qb{3268}{1546}{3352}{1762} \qb{3657}{1546}{3573}{1762} \qb{3486}{1550}{3573}{1762} \qb{2131}{1732}{2081}{1774} \qb{4793}{1734}{4842}{1775} \qb{2131}{1732}{2020}{1780} \qb{4793}{1734}{4904}{1782} \qb{2242}{1688}{2131}{1785} \qb{2243}{1737}{2131}{1785} \qb{4682}{1689}{4793}{1786} \qb{4682}{1738}{4793}{1786} \qb{2131}{1785}{2020}{1831} \qb{2131}{1746}{2020}{1831} \qb{2020}{1780}{1980}{1831} \qb{4904}{1782}{4943}{1832} \qb{4793}{1747}{4904}{1832} \qb{4793}{1786}{4904}{1832} \qb{2020}{1780}{1933}{1853} \qb{4904}{1782}{4990}{1854} \qb{2797}{1710}{2686}{1856} \qb{2608}{1637}{2686}{1856} \qb{4128}{1711}{4239}{1856} \qb{4317}{1638}{4239}{1856} \qb{2020}{1831}{1909}{1870} \qb{4904}{1832}{5015}{1872} \qb{1909}{1870}{1798}{1896} \qb{5015}{1872}{5126}{1898} \qb{2920}{1589}{3019}{1904} \qb{3130}{1682}{3019}{1904} \qb{1798}{1896}{1687}{1904} \qb{4005}{1589}{3906}{1904} \qb{3795}{1683}{3906}{1904} \qb{5126}{1898}{5236}{1906} \qb{1687}{1904}{1576}{1908} \qb{5236}{1906}{5347}{1909} \qb{2008}{1835}{1909}{1919} \qb{1798}{1896}{1909}{1919} \qb{4916}{1836}{5015}{1921} \qb{5126}{1898}{5015}{1921} \qb{1576}{1908}{1465}{1937} \qb{5347}{1909}{5458}{1939} \qb{2480}{1657}{2575}{1961} \qb{2686}{1856}{2575}{1961} \qb{4445}{1658}{4349}{1962} \qb{4239}{1856}{4349}{1962} \qb{3130}{1682}{3241}{1984} \qb{3352}{1762}{3241}{1984} \qb{3795}{1683}{3684}{1984} \qb{3573}{1762}{3684}{1984} \qb{2042}{1822}{2131}{1992} \qb{4882}{1823}{4792}{1993} \qb{3573}{1762}{3462}{1996} \qb{3352}{1762}{3462}{1996} \qb{1687}{1904}{1798}{2010} \qb{1909}{1919}{1798}{2010} \qb{1465}{1937}{1354}{2011} \qb{5236}{1906}{5125}{2011} \qb{5015}{1921}{5125}{2011} \qb{1803}{2006}{1798}{2012} \qb{5458}{1939}{5569}{2013} \qb{5119}{2007}{5125}{2014} \qb{3019}{1904}{3130}{2015} \qb{3241}{1984}{3130}{2015} \qb{3684}{1984}{3795}{2016} \qb{3906}{1904}{3795}{2016} \qb{2575}{1961}{2464}{2027} \qb{2360}{1684}{2464}{2027} \qb{4564}{1685}{4460}{2028} \qb{4349}{1962}{4460}{2028} \qb{1798}{2023}{1909}{2037} \qb{3019}{1904}{2908}{2038} \qb{2797}{1710}{2908}{2038} \qb{5125}{2024}{5014}{2038} \qb{4128}{1711}{4017}{2038} \qb{3906}{1904}{4017}{2038} \qb{2147}{1778}{2242}{2043} \qb{2131}{1992}{2242}{2043} \qb{4792}{1993}{4682}{2044} \qb{4776}{1779}{4682}{2044} \qb{1354}{2011}{1465}{2045} \qb{5569}{2013}{5458}{2047} \qb{2464}{2027}{2353}{2055} \qb{2252}{1733}{2353}{2055} \qb{2242}{2043}{2353}{2055} \qb{4682}{2044}{4571}{2056} \qb{4460}{2028}{4571}{2056} \qb{4672}{1733}{4571}{2056} \qb{1465}{2045}{1576}{2062} \qb{1465}{1937}{1576}{2062} \qb{1576}{1908}{1687}{2064} \qb{1576}{2062}{1687}{2064} \qb{1798}{2010}{1687}{2064} \qb{1798}{2012}{1687}{2064} \qb{5458}{2047}{5347}{2064} \qb{5458}{1939}{5347}{2064} \qb{5347}{1909}{5236}{2065} \qb{5125}{2014}{5236}{2065} \qb{5125}{2011}{5236}{2065} \qb{1465}{2045}{1354}{2084} \qb{5458}{2047}{5568}{2086} \qb{2908}{2038}{2797}{2089} \qb{2686}{1856}{2797}{2089} \qb{4017}{2038}{4128}{2089} \qb{4239}{1856}{4128}{2089} \qb{1354}{2084}{1243}{2096} \qb{1354}{2011}{1243}{2096} \qb{5568}{2086}{5679}{2097} \qb{5569}{2013}{5679}{2097} \qb{3111}{2017}{3129}{2103} \qb{3175}{2002}{3129}{2103} \qb{3748}{2002}{3794}{2103} \qb{3812}{2017}{3794}{2103} \qb{2797}{2089}{2686}{2109} \qb{2575}{1961}{2686}{2109} \qb{4349}{1962}{4238}{2110} \qb{4128}{2089}{4238}{2110} \qb{1243}{2096}{1132}{2139} \qb{5679}{2097}{5790}{2141} \qb{2464}{2027}{2575}{2142} \qb{2686}{2109}{2575}{2142} \qb{4460}{2028}{4349}{2143} \qb{4238}{2110}{4349}{2143} \qb{1798}{2012}{1687}{2147} \qb{1576}{2062}{1687}{2147} \qb{5347}{2064}{5236}{2148} \qb{5125}{2014}{5236}{2148} \qb{1930}{1962}{2020}{2151} \qb{4993}{1963}{4903}{2153} \qb{1132}{2139}{1021}{2160} \qb{5790}{2141}{5901}{2162} \qb{1354}{2084}{1465}{2164} \qb{5568}{2086}{5457}{2166} \qb{1465}{2164}{1354}{2173} \qb{5457}{2166}{5568}{2174} \qb{1132}{2139}{1243}{2178} \qb{1354}{2173}{1243}{2178} \qb{1354}{2084}{1243}{2178} \qb{5790}{2141}{5679}{2180} \qb{5568}{2174}{5679}{2180} \qb{5568}{2086}{5679}{2180} \qb{1465}{2164}{1576}{2196} \qb{1687}{2147}{1576}{2196} \qb{1465}{2045}{1576}{2196} \qb{2817}{2079}{2907}{2197} \qb{2877}{2052}{2907}{2197} \qb{4046}{2052}{4016}{2197} \qb{4106}{2079}{4016}{2197} \qb{5457}{2166}{5347}{2197} \qb{5236}{2148}{5347}{2197} \qb{5458}{2047}{5347}{2197} \qb{1782}{2049}{1687}{2201} \qb{1576}{2196}{1687}{2201} \qb{5140}{2049}{5236}{2202} \qb{5347}{2197}{5236}{2202} \qb{2353}{2055}{2464}{2203} \qb{2575}{2142}{2464}{2203} \qb{4571}{2056}{4460}{2204} \qb{4349}{2143}{4460}{2204} \qb{1021}{2160}{ 910}{2211} \qb{5901}{2162}{6012}{2214} \qb{3129}{2103}{3018}{2218} \qb{2907}{2197}{3018}{2218} \qb{2981}{2030}{3018}{2218} \qb{4016}{2197}{3905}{2218} \qb{3794}{2103}{3905}{2218} \qb{3942}{2031}{3905}{2218} \qb{1021}{2160}{1132}{2238} \qb{1243}{2178}{1132}{2238} \qb{5901}{2162}{5790}{2240} \qb{5679}{2180}{5790}{2240} \qb{ 910}{2211}{1021}{2255} \qb{1132}{2238}{1021}{2255} \qb{5790}{2240}{5901}{2257} \qb{6012}{2214}{5901}{2257} \qb{1354}{2173}{1243}{2267} \qb{1132}{2238}{1243}{2267} \qb{5568}{2174}{5679}{2268} \qb{5790}{2240}{5679}{2268} \qb{1354}{2173}{1465}{2269} \qb{5568}{2174}{5457}{2270} \qb{ 910}{2211}{ 799}{2271} \qb{2751}{2097}{2796}{2271} \qb{4171}{2097}{4126}{2271} \qb{6012}{2214}{6123}{2273} \qb{2464}{2203}{2353}{2276} \qb{2242}{2043}{2353}{2276} \qb{4570}{2277}{4570}{2277} \qb{1762}{2145}{1687}{2277} \qb{4460}{2204}{4571}{2277} \qb{4682}{2044}{4571}{2277} \qb{5160}{2146}{5235}{2278} \qb{2022}{1933}{2131}{2279} \qb{2020}{2151}{2131}{2279} \qb{4901}{1934}{4792}{2280} \qb{4903}{2153}{4792}{2280} \qb{1465}{2269}{1576}{2300} \qb{1687}{2277}{1576}{2300} \qb{1687}{2201}{1576}{2300} \qb{1465}{2164}{1576}{2300} \qb{5235}{2278}{5346}{2302} \qb{5457}{2166}{5346}{2302} \qb{5236}{2202}{5346}{2302} \qb{5457}{2270}{5346}{2302} \qb{1021}{2255}{ 910}{2305} \qb{ 799}{2271}{ 910}{2305} \qb{6123}{2273}{6012}{2307} \qb{5901}{2257}{6012}{2307} \qb{2131}{2279}{2242}{2319} \qb{2353}{2276}{2242}{2319} \qb{2131}{1992}{2242}{2319} \qb{4571}{2277}{4681}{2320} \qb{4792}{2280}{4681}{2320} \qb{4792}{1993}{4681}{2320} \qb{1933}{2101}{2019}{2325} \qb{4989}{2103}{4903}{2326} \qb{1243}{2267}{1132}{2332} \qb{1021}{2255}{1132}{2332} \qb{5679}{2268}{5790}{2334} \qb{5901}{2257}{5790}{2334} \qb{1132}{2332}{1021}{2347} \qb{ 910}{2305}{1021}{2347} \qb{5790}{2334}{5901}{2350} \qb{6012}{2307}{5901}{2350} \qb{1355}{2268}{1465}{2352} \qb{5567}{2269}{5457}{2354} \qb{1132}{2332}{1243}{2366} \qb{1352}{2268}{1243}{2366} \qb{1465}{2352}{1354}{2366} \qb{5790}{2334}{5679}{2368} \qb{5569}{2269}{5679}{2368} \qb{5457}{2354}{5568}{2368} \qb{3460}{1996}{3351}{2382} \qb{3266}{1985}{3351}{2382} \qb{3464}{1996}{3572}{2382} \qb{3657}{1985}{3572}{2382} \qb{1770}{2229}{1686}{2389} \qb{2642}{2122}{2573}{2389} \qb{4279}{2122}{4348}{2390} \qb{5152}{2231}{5235}{2390} \qb{2131}{2279}{2241}{2391} \qb{2293}{2299}{2241}{2391} \qb{4629}{2300}{4681}{2392} \qb{4792}{2280}{4681}{2392} \qb{1686}{2389}{1576}{2394} \qb{1687}{2277}{1576}{2394} \qb{1465}{2352}{1576}{2394} \qb{1465}{2269}{1576}{2394} \qb{5457}{2354}{5346}{2396} \qb{5235}{2390}{5346}{2396} \qb{5457}{2270}{5346}{2396} \qb{5235}{2278}{5346}{2396} \qb{2573}{2389}{2684}{2398} \qb{2750}{2157}{2684}{2398} \qb{4171}{2160}{4237}{2399} \qb{4348}{2390}{4237}{2399} \qb{2264}{2351}{2241}{2414} \qb{2261}{2357}{2241}{2414} \qb{4657}{2350}{4681}{2415} \qb{4661}{2356}{4681}{2415} \qb{1949}{2248}{2019}{2419} \qb{4973}{2250}{4903}{2420} \qb{1243}{2366}{1132}{2421} \qb{1021}{2347}{1132}{2421} \qb{5901}{2350}{5790}{2423} \qb{5679}{2368}{5790}{2423} \qb{2001}{2399}{2019}{2433} \qb{4920}{2401}{4902}{2434} \qb{2241}{2414}{2130}{2453} \qb{2020}{2151}{2130}{2453} \qb{2241}{2391}{2130}{2453} \qb{2019}{2325}{2130}{2453} \qb{2573}{2389}{2462}{2453} \qb{2527}{2168}{2462}{2453} \qb{4681}{2415}{4792}{2454} \qb{4681}{2392}{4792}{2454} \qb{4903}{2326}{4792}{2454} \qb{4903}{2153}{4792}{2454} \qb{4348}{2390}{4459}{2454} \qb{4393}{2167}{4459}{2454} \qb{1354}{2366}{1242}{2471} \qb{1132}{2421}{1242}{2471} \qb{5790}{2423}{5679}{2473} \qb{5568}{2368}{5679}{2473} \qb{1686}{2389}{1575}{2477} \qb{1465}{2352}{1575}{2477} \qb{5235}{2390}{5346}{2479} \qb{5457}{2354}{5346}{2479} \qb{1242}{2471}{1353}{2481} \qb{1463}{2421}{1353}{2481} \qb{1875}{2349}{1797}{2482} \qb{5458}{2423}{5568}{2482} \qb{5679}{2473}{5568}{2482} \qb{2684}{2398}{2795}{2483} \qb{2821}{2382}{2795}{2483} \qb{5047}{2351}{5124}{2483} \qb{4237}{2399}{4126}{2484} \qb{4100}{2385}{4126}{2484} \qb{2299}{2297}{2241}{2508} \qb{2351}{2277}{2241}{2508} \qb{4622}{2297}{4681}{2509} \qb{4570}{2277}{4681}{2509} \qb{1575}{2477}{1686}{2522} \qb{1795}{2308}{1686}{2522} \qb{1797}{2482}{1686}{2522} \qb{5126}{2309}{5235}{2524} \qb{5346}{2479}{5235}{2524} \qb{5124}{2483}{5235}{2524} \qb{1466}{2422}{1575}{2532} \qb{1686}{2522}{1575}{2532} \qb{5235}{2524}{5346}{2533} \qb{5455}{2424}{5346}{2533} \qb{2241}{2508}{2130}{2559} \qb{2019}{2419}{2130}{2559} \qb{2241}{2414}{2130}{2559} \qb{2019}{2325}{2130}{2559} \qb{4681}{2415}{4792}{2560} \qb{4681}{2509}{4792}{2560} \qb{4903}{2420}{4792}{2560} \qb{4903}{2326}{4792}{2560} \qb{1480}{2510}{1575}{2565} \qb{5441}{2512}{5346}{2567} \qb{2796}{2271}{2907}{2570} \qb{2803}{2086}{2907}{2570} \qb{4126}{2271}{4016}{2570} \qb{4119}{2086}{4016}{2570} \qb{2427}{2227}{2352}{2571} \qb{2462}{2453}{2352}{2571} \qb{4494}{2226}{4570}{2572} \qb{4459}{2454}{4570}{2572} \qb{4126}{2484}{4028}{2623} \qb{2795}{2483}{2895}{2627} \qb{1797}{2482}{1686}{2627} \qb{1575}{2532}{1686}{2627} \qb{1575}{2565}{1686}{2627} \qb{5124}{2483}{5235}{2629} \qb{5346}{2567}{5235}{2629} \qb{5346}{2533}{5235}{2629} \qb{3129}{2103}{3240}{2637} \qb{3351}{2382}{3240}{2637} \qb{3572}{2382}{3683}{2637} \qb{3794}{2103}{3683}{2637} \qb{2241}{2508}{2130}{2640} \qb{2019}{2433}{2130}{2640} \qb{2019}{2419}{2130}{2640} \qb{4902}{2434}{4792}{2642} \qb{4681}{2509}{4792}{2642} \qb{4903}{2420}{4792}{2642} \qb{2019}{2433}{2130}{2655} \qb{2097}{2579}{2130}{2655} \qb{1575}{2565}{1686}{2656} \qb{4902}{2434}{4791}{2656} \qb{4822}{2585}{4791}{2656} \qb{5346}{2567}{5235}{2657} \qb{2796}{2271}{2906}{2663} \qb{4126}{2271}{4015}{2664} \qb{1686}{2627}{1797}{2667} \qb{1906}{2440}{1797}{2667} \qb{1686}{2656}{1797}{2667} \qb{5235}{2629}{5124}{2669} \qb{5015}{2441}{5124}{2669} \qb{5235}{2657}{5124}{2669} \qb{2078}{2570}{2018}{2670} \qb{1797}{2667}{1907}{2671} \qb{1997}{2484}{1907}{2671} \qb{2018}{2670}{1907}{2671} \qb{4843}{2572}{4902}{2671} \qb{4924}{2485}{5013}{2672} \qb{5124}{2669}{5013}{2672} \qb{2130}{2655}{2241}{2672} \qb{2130}{2640}{2241}{2672} \qb{2352}{2571}{2241}{2672} \qb{2352}{2277}{2241}{2672} \qb{4570}{2277}{4681}{2673} \qb{4791}{2656}{4681}{2673} \qb{4792}{2642}{4681}{2673} \qb{4570}{2572}{4681}{2673} \qb{2018}{2670}{2129}{2685} \qb{2142}{2669}{2129}{2685} \qb{4902}{2671}{4791}{2686} \qb{4779}{2671}{4791}{2686} \qb{2129}{2685}{2164}{2697} \qb{4791}{2686}{4757}{2697} \qb{2907}{2197}{3018}{2730} \qb{2907}{2570}{3018}{2730} \qb{4016}{2570}{3905}{2731} \qb{4016}{2197}{3905}{2731} \qb{1907}{2671}{1796}{2741} \qb{1686}{2656}{1796}{2741} \qb{5013}{2672}{5124}{2743} \qb{5235}{2657}{5124}{2743} \qb{3018}{2218}{3129}{2749} \qb{3018}{2730}{3129}{2749} \qb{3240}{2637}{3129}{2749} \qb{3905}{2218}{3794}{2750} \qb{3683}{2637}{3794}{2750} \qb{3905}{2731}{3794}{2750} \qb{3351}{2382}{3461}{2766} \qb{3572}{2382}{3461}{2766} \qb{2352}{2571}{2241}{2789} \qb{2130}{2655}{2241}{2789} \qb{4570}{2572}{4680}{2790} \qb{4791}{2656}{4680}{2790} \qb{2018}{2670}{1907}{2810} \qb{1796}{2741}{1907}{2810} \qb{5124}{2743}{5013}{2811} \qb{4902}{2671}{5013}{2811} \qb{2241}{2789}{2351}{2840} \qb{2462}{2453}{2351}{2840} \qb{4459}{2454}{4569}{2841} \qb{4680}{2790}{4569}{2841} \qb{2351}{2840}{2462}{2860} \qb{2573}{2389}{2462}{2860} \qb{4348}{2390}{4458}{2861} \qb{4569}{2841}{4458}{2861} \qb{1907}{2810}{2018}{2864} \qb{2129}{2685}{2018}{2864} \qb{4791}{2686}{4902}{2865} \qb{5013}{2811}{4902}{2865} \qb{2433}{2855}{2462}{2872} \qb{4487}{2856}{4458}{2873} \qb{2684}{2398}{2573}{2893} \qb{2462}{2872}{2573}{2893} \qb{2462}{2860}{2573}{2893} \qb{4237}{2399}{4347}{2894} \qb{4458}{2873}{4347}{2894} \qb{4458}{2861}{4347}{2894} \qb{2217}{2760}{2129}{2912} \qb{2018}{2864}{2129}{2912} \qb{4902}{2865}{4791}{2913} \qb{4703}{2763}{4791}{2913} \qb{2490}{2883}{2572}{2953} \qb{2588}{2919}{2572}{2953} \qb{4428}{2884}{4347}{2953} \qb{4331}{2920}{4347}{2953} \qb{2906}{2663}{3017}{2954} \qb{2907}{2570}{3017}{2954} \qb{4015}{2664}{3905}{2954} \qb{4016}{2570}{3905}{2954} \qb{2795}{2483}{2684}{2954} \qb{2573}{2893}{2684}{2954} \qb{4126}{2484}{4236}{2955} \qb{4347}{2894}{4236}{2955} \qb{2321}{2826}{2240}{2958} \qb{2129}{2912}{2240}{2958} \qb{4791}{2913}{4679}{2959} \qb{4598}{2828}{4679}{2959} \qb{3240}{2637}{3350}{2981} \qb{3461}{2766}{3350}{2981} \qb{3683}{2637}{3572}{2981} \qb{3461}{2766}{3572}{2981} \qb{2240}{2958}{2350}{2998} \qb{2454}{2867}{2350}{2998} \qb{4465}{2869}{4568}{2999} \qb{4679}{2959}{4568}{2999} \qb{2572}{2953}{2461}{3023} \qb{2350}{2998}{2461}{3023} \qb{4568}{2999}{4457}{3024} \qb{4347}{2953}{4457}{3024} \qb{2684}{2954}{2794}{3028} \qb{2903}{2651}{2794}{3028} \qb{4018}{2655}{4125}{3028} \qb{4236}{2955}{4125}{3028} \qb{2713}{2981}{2683}{3044} \qb{2572}{2953}{2683}{3044} \qb{4347}{2953}{4236}{3044} \qb{4206}{2982}{4236}{3044} \qb{2794}{3028}{2905}{3071} \qb{2995}{2895}{2905}{3071} \qb{4125}{3028}{4014}{3071} \qb{3926}{2898}{4014}{3071} \qb{3129}{2749}{3239}{3074} \qb{3350}{2981}{3239}{3074} \qb{3017}{2954}{3128}{3075} \qb{3018}{2730}{3128}{3075} \qb{3572}{2981}{3683}{3075} \qb{3794}{2750}{3683}{3075} \qb{3905}{2731}{3794}{3075} \qb{3683}{3075}{3794}{3075} \qb{3905}{2954}{3794}{3075} \qb{2995}{3062}{3016}{3086} \qb{3030}{3058}{3016}{3086} \qb{3888}{3058}{3903}{3087} \qb{3923}{3062}{3903}{3087} \qb{3016}{3086}{2905}{3096} \qb{3903}{3087}{4014}{3096} \qb{2905}{3096}{2794}{3097} \qb{2835}{3044}{2794}{3097} \qb{2683}{3044}{2794}{3097} \qb{4084}{3044}{4125}{3098} \qb{4236}{3044}{4125}{3098} \qb{4014}{3096}{4125}{3098} \qb{3903}{3087}{3816}{3125} \qb{3016}{3086}{3107}{3127} \qb{2841}{3097}{2904}{3139} \qb{2964}{3106}{2904}{3139} \qb{3954}{3107}{4013}{3139} \qb{4077}{3097}{4013}{3139} \qb{3350}{2981}{3461}{3151} \qb{3572}{2981}{3461}{3151} \qb{3017}{2954}{3128}{3169} \qb{3905}{2954}{3794}{3169} \qb{2904}{3139}{3015}{3223} \qb{3110}{3133}{3015}{3223} \qb{4013}{3139}{3902}{3224} \qb{3810}{3136}{3902}{3224} \qb{3239}{3074}{3350}{3226} \qb{3461}{3151}{3350}{3226} \qb{3683}{3075}{3572}{3227} \qb{3461}{3151}{3572}{3227} \qb{3128}{3169}{3239}{3245} \qb{3128}{3075}{3239}{3245} \qb{3350}{3226}{3239}{3245} \qb{3572}{3227}{3683}{3245} \qb{3794}{3075}{3683}{3245} \qb{3794}{3169}{3683}{3245} \qb{3128}{3169}{3239}{3262} \qb{3794}{3169}{3683}{3263} \qb{3015}{3223}{3126}{3267} \qb{3201}{3230}{3126}{3267} \qb{3719}{3231}{3791}{3267} \qb{3902}{3224}{3791}{3267} \qb{3277}{3282}{3237}{3288} \qb{3126}{3267}{3237}{3288} \qb{3644}{3283}{3680}{3288} \qb{3791}{3267}{3680}{3288} \qb{3572}{3227}{3461}{3295} \qb{3350}{3226}{3461}{3295} \qb{3239}{3245}{3350}{3320} \qb{3239}{3262}{3350}{3320} \qb{3683}{3245}{3572}{3320} \qb{3683}{3263}{3572}{3320} \qb{3461}{3295}{3572}{3320} \qb{3350}{3320}{3461}{3339} \qb{3572}{3320}{3461}{3339} \qb{3379}{3325}{3348}{3339} \qb{3237}{3288}{3348}{3339} \qb{3680}{3288}{3569}{3339} \qb{3539}{3326}{3569}{3339} \qb{3348}{3339}{3458}{3399} } \end{picture} \[

 

[EddieCrash]

Hello, could you tell me how you generated the data used to then 'tex' them into such images ?

 

[Orion1]

If you want to include graphics functions in your tex generated documents, I recommend using 'gnuplot'. It is much easier to use.
[/Color]
Reference:
http://archives.math.utk.edu/software/multi-platform/gnuplot/msdos/

 

[robphy]

Self portrait?

\]<br /> <br /> \unitlength .5mm<br /> \begin{picture}(71,87.5)(0,0)<br /> \linethickness {.03pt}<br /> \qbezier(10,75)(70,15)(70,15)<br /> <br /> \qbezier(10,15)(70,75)(70,75)<br /> <br /> \qbezier(71,77.5)(70.67,81.75)(61.92,84.57)<br /> \qbezier(61.92,84.57)(53.17,87.39)(40,87.5)<br /> <br /> \qbezier(40,87.5)(26.83,87.39)(18.08,84.57)<br /> \qbezier(18.08,84.57)(9.33,81.75)(9,77.5)<br /> <br /> \qbezier(9,77.5)(9.33,73.25)(18.08,70.43)<br /> \qbezier(18.08,70.43)(26.83,67.61)(40,67.5)<br /> <br /> \qbezier(40,67.5)(53.17,67.61)(61.92,70.43)<br /> \qbezier(61.92,70.43)(70.67,73.25)(71,77.5)<br /> \qbezier[20](71,12)(70.67,16.25)(61.92,19.07)<br /> \qbezier[20](61.92,19.07)(53.17,21.89)(40,22)<br /> <br /> \qbezier[20](40,22)(26.83,21.89)(18.08,19.07)<br /> \qbezier[20](18.08,19.07)(9.33,16.25)(9,12)<br /> <br /> \qbezier(9,12)(9.33,7.75)(18.08,4.93)<br /> \qbezier(18.08,4.93)(26.83,2.11)(40,2)<br /> <br /> \qbezier(40,2)(53.17,2.11)(61.92,4.93)<br /> \qbezier(61.92,4.93)(70.67,7.75)(71,12)<br /> <br /> \linethickness {1pt}<br /> \textcolor{yellow}{<br /> \qbezier(35,45)(15,25)(15,25)<br /> \qbezier(35,45)(25,55)(25,55)<br /> }<br /> \textcolor{brown}{<br /> \linethickness {1pt}<br /> \qbezier(15,25)(15,25)(25,55)<br /> \qbezier[15](5,-5)(10,10)(15,25)<br /> \qbezier[15](25,55)(32.5,77.5)(40,100)<br /> }<br /> \end{picture}<br /> <br /> \[

 

[MathematicalPhysicist]

<br /> \circlearrowleft<br />
i am trying to see if it works.

 

[Doc Al]

Latex hosed again?

Test...
\vec{F} = m \vec{a}

 

[Drimar]

\] \unitlength 0.05mm \begin{picture}(4000,3000)(0,0) \textcolor{blue}{ \def\qb#1#2#3#4{\qbezier(#1,#2)(#3,#4)(#3,#4)} \qb{3464}{1145}{3574}{1179} \qb{3353}{1179}{3242}{1221} \qb{3574}{1179}{3685}{1222} \qb{3353}{1179}{3463}{1223} \qb{3574}{1179}{3463}{1223} \qb{3242}{1221}{3131}{1295} \qb{3685}{1222}{3796}{1295} \qb{3242}{1221}{3352}{1300} \qb{3463}{1223}{3352}{1300} \qb{3463}{1223}{3574}{1300} \qb{3685}{1222}{3574}{1300} \qb{3352}{1300}{3463}{1328} \qb{3131}{1295}{3241}{1333} \qb{3352}{1300}{3241}{1333} \qb{3796}{1295}{3685}{1334} \qb{3574}{1300}{3685}{1334} \qb{3131}{1295}{3020}{1345} \qb{3796}{1295}{3907}{1345} \qb{3020}{1345}{2909}{1354} \qb{3907}{1345}{4018}{1355} \qb{2909}{1354}{2798}{1374} \qb{4018}{1355}{4128}{1375} \qb{3117}{1340}{3019}{1388} \qb{2909}{1354}{3019}{1388} \qb{3809}{1340}{3907}{1389} \qb{4018}{1355}{3907}{1389} \qb{3138}{1339}{3241}{1414} \qb{3349}{1331}{3241}{1414} \qb{3788}{1339}{3685}{1414} \qb{3578}{1331}{3685}{1414} \qb{3571}{1331}{3463}{1424} 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\qb{2418}{1643}{2353}{1652} \qb{4507}{1644}{4571}{1653} \qb{3199}{1552}{3130}{1682} \qb{3078}{1573}{3130}{1682} \qb{3847}{1573}{3795}{1683} \qb{3726}{1552}{3795}{1683} \qb{2465}{1615}{2354}{1683} \qb{4461}{1616}{4572}{1684} \qb{2353}{1652}{2242}{1688} \qb{4571}{1653}{4682}{1689} \qb{2746}{1613}{2797}{1710} \qb{2881}{1590}{2797}{1710} \qb{4044}{1591}{4128}{1711} \qb{4179}{1613}{4128}{1711} \qb{2189}{1716}{2131}{1732} \qb{4735}{1717}{4793}{1734} \qb{2353}{1652}{2243}{1737} \qb{2354}{1683}{2243}{1737} \qb{4572}{1684}{4682}{1738} \qb{4571}{1653}{4682}{1738} \qb{2242}{1688}{2131}{1746} \qb{4682}{1689}{4793}{1747} \qb{3439}{1550}{3352}{1762} \qb{3268}{1546}{3352}{1762} \qb{3657}{1546}{3573}{1762} \qb{3486}{1550}{3573}{1762} \qb{2131}{1732}{2081}{1774} \qb{4793}{1734}{4842}{1775} \qb{2131}{1732}{2020}{1780} \qb{4793}{1734}{4904}{1782} \qb{2242}{1688}{2131}{1785} \qb{2243}{1737}{2131}{1785} \qb{4682}{1689}{4793}{1786} \qb{4682}{1738}{4793}{1786} \qb{2131}{1785}{2020}{1831} 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\qb{3795}{1683}{3684}{1984} \qb{3573}{1762}{3684}{1984} \qb{2042}{1822}{2131}{1992} \qb{4882}{1823}{4792}{1993} \qb{3573}{1762}{3462}{1996} \qb{3352}{1762}{3462}{1996} \qb{1687}{1904}{1798}{2010} \qb{1909}{1919}{1798}{2010} \qb{1465}{1937}{1354}{2011} \qb{5236}{1906}{5125}{2011} \qb{5015}{1921}{5125}{2011} \qb{1803}{2006}{1798}{2012} \qb{5458}{1939}{5569}{2013} \qb{5119}{2007}{5125}{2014} \qb{3019}{1904}{3130}{2015} \qb{3241}{1984}{3130}{2015} \qb{3684}{1984}{3795}{2016} \qb{3906}{1904}{3795}{2016} \qb{2575}{1961}{2464}{2027} \qb{2360}{1684}{2464}{2027} \qb{4564}{1685}{4460}{2028} \qb{4349}{1962}{4460}{2028} \qb{1798}{2023}{1909}{2037} \qb{3019}{1904}{2908}{2038} \qb{2797}{1710}{2908}{2038} \qb{5125}{2024}{5014}{2038} \qb{4128}{1711}{4017}{2038} \qb{3906}{1904}{4017}{2038} \qb{2147}{1778}{2242}{2043} \qb{2131}{1992}{2242}{2043} \qb{4792}{1993}{4682}{2044} \qb{4776}{1779}{4682}{2044} \qb{1354}{2011}{1465}{2045} \qb{5569}{2013}{5458}{2047} \qb{2464}{2027}{2353}{2055} \qb{2252}{1733}{2353}{2055} \qb{2242}{2043}{2353}{2055} \qb{4682}{2044}{4571}{2056} \qb{4460}{2028}{4571}{2056} \qb{4672}{1733}{4571}{2056} \qb{1465}{2045}{1576}{2062} \qb{1465}{1937}{1576}{2062} \qb{1576}{1908}{1687}{2064} \qb{1576}{2062}{1687}{2064} \qb{1798}{2010}{1687}{2064} \qb{1798}{2012}{1687}{2064} \qb{5458}{2047}{5347}{2064} \qb{5458}{1939}{5347}{2064} \qb{5347}{1909}{5236}{2065} \qb{5125}{2014}{5236}{2065} \qb{5125}{2011}{5236}{2065} \qb{1465}{2045}{1354}{2084} \qb{5458}{2047}{5568}{2086} \qb{2908}{2038}{2797}{2089} \qb{2686}{1856}{2797}{2089} \qb{4017}{2038}{4128}{2089} \qb{4239}{1856}{4128}{2089} \qb{1354}{2084}{1243}{2096} \qb{1354}{2011}{1243}{2096} \qb{5568}{2086}{5679}{2097} \qb{5569}{2013}{5679}{2097} \qb{3111}{2017}{3129}{2103} \qb{3175}{2002}{3129}{2103} \qb{3748}{2002}{3794}{2103} \qb{3812}{2017}{3794}{2103} \qb{2797}{2089}{2686}{2109} \qb{2575}{1961}{2686}{2109} \qb{4349}{1962}{4238}{2110} \qb{4128}{2089}{4238}{2110} \qb{1243}{2096}{1132}{2139} \qb{5679}{2097}{5790}{2141} \qb{2464}{2027}{2575}{2142} \qb{2686}{2109}{2575}{2142} \qb{4460}{2028}{4349}{2143} \qb{4238}{2110}{4349}{2143} \qb{1798}{2012}{1687}{2147} \qb{1576}{2062}{1687}{2147} \qb{5347}{2064}{5236}{2148} \qb{5125}{2014}{5236}{2148} \qb{1930}{1962}{2020}{2151} \qb{4993}{1963}{4903}{2153} \qb{1132}{2139}{1021}{2160} \qb{5790}{2141}{5901}{2162} \qb{1354}{2084}{1465}{2164} \qb{5568}{2086}{5457}{2166} \qb{1465}{2164}{1354}{2173} \qb{5457}{2166}{5568}{2174} \qb{1132}{2139}{1243}{2178} \qb{1354}{2173}{1243}{2178} \qb{1354}{2084}{1243}{2178} \qb{5790}{2141}{5679}{2180} \qb{5568}{2174}{5679}{2180} \qb{5568}{2086}{5679}{2180} \qb{1465}{2164}{1576}{2196} \qb{1687}{2147}{1576}{2196} \qb{1465}{2045}{1576}{2196} \qb{2817}{2079}{2907}{2197} \qb{2877}{2052}{2907}{2197} \qb{4046}{2052}{4016}{2197} \qb{4106}{2079}{4016}{2197} \qb{5457}{2166}{5347}{2197} \qb{5236}{2148}{5347}{2197} \qb{5458}{2047}{5347}{2197} \qb{1782}{2049}{1687}{2201} \qb{1576}{2196}{1687}{2201} \qb{5140}{2049}{5236}{2202} \qb{5347}{2197}{5236}{2202} \qb{2353}{2055}{2464}{2203} \qb{2575}{2142}{2464}{2203} \qb{4571}{2056}{4460}{2204} \qb{4349}{2143}{4460}{2204} \qb{1021}{2160}{ 910}{2211} \qb{5901}{2162}{6012}{2214} \qb{3129}{2103}{3018}{2218} \qb{2907}{2197}{3018}{2218} \qb{2981}{2030}{3018}{2218} \qb{4016}{2197}{3905}{2218} \qb{3794}{2103}{3905}{2218} \qb{3942}{2031}{3905}{2218} \qb{1021}{2160}{1132}{2238} \qb{1243}{2178}{1132}{2238} \qb{5901}{2162}{5790}{2240} \qb{5679}{2180}{5790}{2240} \qb{ 910}{2211}{1021}{2255} \qb{1132}{2238}{1021}{2255} \qb{5790}{2240}{5901}{2257} \qb{6012}{2214}{5901}{2257} \qb{1354}{2173}{1243}{2267} \qb{1132}{2238}{1243}{2267} \qb{5568}{2174}{5679}{2268} \qb{5790}{2240}{5679}{2268} \qb{1354}{2173}{1465}{2269} \qb{5568}{2174}{5457}{2270} \qb{ 910}{2211}{ 799}{2271} \qb{2751}{2097}{2796}{2271} \qb{4171}{2097}{4126}{2271} \qb{6012}{2214}{6123}{2273} \qb{2464}{2203}{2353}{2276} \qb{2242}{2043}{2353}{2276} \qb{4570}{2277}{4570}{2277} \qb{1762}{2145}{1687}{2277} \qb{4460}{2204}{4571}{2277} \qb{4682}{2044}{4571}{2277} \qb{5160}{2146}{5235}{2278} \qb{2022}{1933}{2131}{2279} \qb{2020}{2151}{2131}{2279} \qb{4901}{1934}{4792}{2280} \qb{4903}{2153}{4792}{2280} \qb{1465}{2269}{1576}{2300} \qb{1687}{2277}{1576}{2300} \qb{1687}{2201}{1576}{2300} \qb{1465}{2164}{1576}{2300} \qb{5235}{2278}{5346}{2302} \qb{5457}{2166}{5346}{2302} \qb{5236}{2202}{5346}{2302} \qb{5457}{2270}{5346}{2302} \qb{1021}{2255}{ 910}{2305} \qb{ 799}{2271}{ 910}{2305} \qb{6123}{2273}{6012}{2307} \qb{5901}{2257}{6012}{2307} \qb{2131}{2279}{2242}{2319} \qb{2353}{2276}{2242}{2319} \qb{2131}{1992}{2242}{2319} \qb{4571}{2277}{4681}{2320} \qb{4792}{2280}{4681}{2320} \qb{4792}{1993}{4681}{2320} \qb{1933}{2101}{2019}{2325} \qb{4989}{2103}{4903}{2326} \qb{1243}{2267}{1132}{2332} \qb{1021}{2255}{1132}{2332} \qb{5679}{2268}{5790}{2334} \qb{5901}{2257}{5790}{2334} \qb{1132}{2332}{1021}{2347} \qb{ 910}{2305}{1021}{2347} \qb{5790}{2334}{5901}{2350} \qb{6012}{2307}{5901}{2350} \qb{1355}{2268}{1465}{2352} \qb{5567}{2269}{5457}{2354} \qb{1132}{2332}{1243}{2366} \qb{1352}{2268}{1243}{2366} \qb{1465}{2352}{1354}{2366} \qb{5790}{2334}{5679}{2368} \qb{5569}{2269}{5679}{2368} \qb{5457}{2354}{5568}{2368} \qb{3460}{1996}{3351}{2382} \qb{3266}{1985}{3351}{2382} \qb{3464}{1996}{3572}{2382} \qb{3657}{1985}{3572}{2382} \qb{1770}{2229}{1686}{2389} \qb{2642}{2122}{2573}{2389} \qb{4279}{2122}{4348}{2390} \qb{5152}{2231}{5235}{2390} \qb{2131}{2279}{2241}{2391} \qb{2293}{2299}{2241}{2391} \qb{4629}{2300}{4681}{2392} \qb{4792}{2280}{4681}{2392} \qb{1686}{2389}{1576}{2394} \qb{1687}{2277}{1576}{2394} \qb{1465}{2352}{1576}{2394} \qb{1465}{2269}{1576}{2394} \qb{5457}{2354}{5346}{2396} \qb{5235}{2390}{5346}{2396} \qb{5457}{2270}{5346}{2396} \qb{5235}{2278}{5346}{2396} \qb{2573}{2389}{2684}{2398} \qb{2750}{2157}{2684}{2398} \qb{4171}{2160}{4237}{2399} \qb{4348}{2390}{4237}{2399} \qb{2264}{2351}{2241}{2414} \qb{2261}{2357}{2241}{2414} \qb{4657}{2350}{4681}{2415} \qb{4661}{2356}{4681}{2415} \qb{1949}{2248}{2019}{2419} \qb{4973}{2250}{4903}{2420} \qb{1243}{2366}{1132}{2421} \qb{1021}{2347}{1132}{2421} \qb{5901}{2350}{5790}{2423} \qb{5679}{2368}{5790}{2423} \qb{2001}{2399}{2019}{2433} \qb{4920}{2401}{4902}{2434} \qb{2241}{2414}{2130}{2453} \qb{2020}{2151}{2130}{2453} \qb{2241}{2391}{2130}{2453} \qb{2019}{2325}{2130}{2453} \qb{2573}{2389}{2462}{2453} \qb{2527}{2168}{2462}{2453} \qb{4681}{2415}{4792}{2454} \qb{4681}{2392}{4792}{2454} \qb{4903}{2326}{4792}{2454} \qb{4903}{2153}{4792}{2454} \qb{4348}{2390}{4459}{2454} \qb{4393}{2167}{4459}{2454} \qb{1354}{2366}{1242}{2471} \qb{1132}{2421}{1242}{2471} \qb{5790}{2423}{5679}{2473} \qb{5568}{2368}{5679}{2473} \qb{1686}{2389}{1575}{2477} \qb{1465}{2352}{1575}{2477} \qb{5235}{2390}{5346}{2479} \qb{5457}{2354}{5346}{2479} \qb{1242}{2471}{1353}{2481} \qb{1463}{2421}{1353}{2481} \qb{1875}{2349}{1797}{2482} \qb{5458}{2423}{5568}{2482} \qb{5679}{2473}{5568}{2482} \qb{2684}{2398}{2795}{2483} \qb{2821}{2382}{2795}{2483} \qb{5047}{2351}{5124}{2483} \qb{4237}{2399}{4126}{2484} \qb{4100}{2385}{4126}{2484} \qb{2299}{2297}{2241}{2508} \qb{2351}{2277}{2241}{2508} \qb{4622}{2297}{4681}{2509} \qb{4570}{2277}{4681}{2509} \qb{1575}{2477}{1686}{2522} \qb{1795}{2308}{1686}{2522} \qb{1797}{2482}{1686}{2522} \qb{5126}{2309}{5235}{2524} \qb{5346}{2479}{5235}{2524} \qb{5124}{2483}{5235}{2524} \qb{1466}{2422}{1575}{2532} \qb{1686}{2522}{1575}{2532} \qb{5235}{2524}{5346}{2533} \qb{5455}{2424}{5346}{2533} \qb{2241}{2508}{2130}{2559} \qb{2019}{2419}{2130}{2559} \qb{2241}{2414}{2130}{2559} \qb{2019}{2325}{2130}{2559} \qb{4681}{2415}{4792}{2560} \qb{4681}{2509}{4792}{2560} \qb{4903}{2420}{4792}{2560} \qb{4903}{2326}{4792}{2560} \qb{1480}{2510}{1575}{2565} \qb{5441}{2512}{5346}{2567} \qb{2796}{2271}{2907}{2570} \qb{2803}{2086}{2907}{2570} \qb{4126}{2271}{4016}{2570} \qb{4119}{2086}{4016}{2570} \qb{2427}{2227}{2352}{2571} \qb{2462}{2453}{2352}{2571} 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