| blob | 0423c10d7b1ae305e83c62a5124fca3cf0e583c7 |
1 <TeXmacs|1.0.1.20>
3 <style|<tuple|tmdoc|maxima>>
5 <\body>
6 <\expand|tmdoc-title>
7 Using Octave sessions inside <TeXmacs>
8 </expand>
10 GNU <name|Octave> is a free clone of <name|Matlab>, which can be downloaded
11 from
13 <\verbatim>
14 \ \ \ \ http://octave.sf.net
15 </verbatim>
17 An <name|Octave> session is started using <apply|menu|Text|Session|Octave>.
18 Below, it is shown how to do linear algebra operations with <name|Octave>,
19 such as matrix multiplication, inversion and diagonalization. Notice that
20 you need to use the <verbatim|tmdisp> command (at the moment) in order to
21 display the output in mathematical form.
23 <\session|octave|default>
24 <\output>
25 GNU Octave, version 2.1.40 (i386-redhat-linux-gnu).
27 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 John W. Eaton.
29 This is free software; see the source code for copying conditions.
31 There is ABSOLUTELY NO WARRANTY; not even for MERCHANTIBILITY or
33 FITNESS FOR A PARTICULAR PURPOSE.
35 \;
37 Report bugs to \<less\>bug-octave@bevo.che.wisc.edu\<gtr\>.
39 \;
40 </output>
42 <\input|octave\<gtr\> >
43 A=[1 0 0 0;2 2 0 0;-1 0 2 0;0 -1 2 2]
44 </input>
46 <\output>
47 A =
49 \;
51 \ \ \ 1 \ \ 0 \ \ 0 \ \ 0
53 \ \ \ 2 \ \ 2 \ \ 0 \ \ 0
55 \ \ -1 \ \ 0 \ \ 2 \ \ 0
57 \ \ \ 0 \ -1 \ \ 2 \ \ 2
59 \;
61 \;
62 </output>
64 <\input|octave\<gtr\> >
65 tmdisp(A^2)
66 </input>
68 <\output>
69 <with|mode|math|formula style|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|6>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|-3>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|-4>>|<cell|<with|mode|math|-4>>|<cell|<with|mode|math|8>>|<cell|<with|mode|math|4>>>>>>>
71 \;
72 </output>
74 <\input|octave\<gtr\> >
75 tmdisp(A.^2)
76 </input>
78 <\output>
79 <with|mode|math|formula style|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|4>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0>>>|<row|<cell|<with|mode|math|0>>|<cell|<with|mode|math|1>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|4>>>>>>>
81 \;
82 </output>
84 <\input|octave\<gtr\> >
85 [u,v]=eig(A)
86 </input>
88 <\output>
89 u =
91 \;
93 \ \ \ 0.00000 \ \ 0.00000 \ \ 0.00000 \ \ 0.21320
95 \ \ \ 0.00000 \ \ 0.00000 \ \ 0.00000 \ -0.42640
97 \ \ \ 0.00000 \ \ 0.00000 \ \ 0.00000 \ \ 0.21320
99 \ \ \ 1.00000 \ \ 1.00000 \ -1.00000 \ -0.85280
101 \;
103 v =
105 \;
107 \ \ 2 \ 0 \ 0 \ 0
109 \ \ 0 \ 2 \ 0 \ 0
111 \ \ 0 \ 0 \ 2 \ 0
113 \ \ 0 \ 0 \ 0 \ 1
115 \;
117 \;
118 </output>
120 <\input|octave\<gtr\> >
121 Q=[1 0 0 0;-2 2 1 0;1 1 0 0;-4 0 0 -1]
122 </input>
124 <\output>
125 Q =
127 \;
129 \ \ \ 1 \ \ 0 \ \ 0 \ \ 0
131 \ \ -2 \ \ 2 \ \ 1 \ \ 0
133 \ \ \ 1 \ \ 1 \ \ 0 \ \ 0
135 \ \ -4 \ \ 0 \ \ 0 \ -1
137 \;
139 \;
140 </output>
142 <\input|octave\<gtr\> >
143 P=inv(Q)
144 </input>
146 <\output>
147 P =
149 \;
151 \ \ \ 1 \ -0 \ \ 0 \ \ 0
153 \ \ -1 \ \ 0 \ \ 1 \ \ 0
155 \ \ \ 4 \ \ 1 \ -2 \ \ 0
157 \ \ -4 \ \ 0 \ \ 0 \ -1
159 \;
161 \;
162 </output>
164 <\input|octave\<gtr\> >
165 P*A*Q
166 </input>
168 <\output>
169 ans =
171 \;
173 \ \ 1 \ 0 \ 0 \ 0
175 \ \ 0 \ 2 \ 0 \ 0
177 \ \ 0 \ 0 \ 2 \ 0
179 \ \ 0 \ 0 \ 1 \ 2
181 \;
183 \;
184 </output>
186 <\input|octave\<gtr\> >
187 \;
188 </input>
189 </session>
191 The second part shows the graph capacity of Octave, 2D and 3D graphs. 2D
192 graphs can be automatically embedded into the worksheet but 3D graphs are
193 not yet.
195 <\session|octave|default>
196 <\input|octave\<gtr\> >
197 x=linspace(-10,10,1000);
198 </input>
200 <\input|octave\<gtr\> >
201 y=x+sin(x);
202 </input>
204 <\input|octave\<gtr\> >
205 plot(x,y,";Function y=x+sin(x);");
206 </input>
208 <\output>
209 \;
211 \;
213 <postscript|<tuple|<raw_data|%!PS-Adobe-2.0 EPSF-2.0\n%%Title:
214 /tmp/tmplot.eps\n%%Creator: gnuplot 3.7 patchlevel 2\n%%CreationDate:
215 Wed Jul 23 17:35:03 2003\n%%DocumentFonts: (atend)\n%%BoundingBox: 50
216 50 230 176\n%%Orientation: Portrait\n%%EndComments\n/gnudict 256 dict
217 def\ngnudict begin\n/Color true def\n/Solid false def\n/gnulinewidth
218 5.000 def\n/userlinewidth gnulinewidth def\n/vshift -46 def\n/dl {10
219 mul} def\n/hpt_ 31.5 def\n/vpt_ 31.5 def\n/hpt hpt_ def\n/vpt vpt_
220 def\n/M {moveto} bind def\n/L {lineto} bind def\n/R {rmoveto} bind
221 def\n/V {rlineto} bind def\n/vpt2 vpt 2 mul def\n/hpt2 hpt 2 mul
222 def\n/Lshow { currentpoint stroke M\n \ 0 vshift R show } def\n/Rshow {
223 currentpoint stroke M\n \ dup stringwidth pop neg vshift R show }
224 def\n/Cshow { currentpoint stroke M\n \ dup stringwidth pop -2 div
225 vshift R show } def\n/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt
226 exch def\n \ /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def\n/DL { Color
227 {setrgbcolor Solid {pop []} if 0 setdash }\n {pop pop pop Solid {pop
228 []} if 0 setdash} ifelse } def\n/BL { stroke userlinewidth 2 mul
229 setlinewidth } def\n/AL { stroke userlinewidth 2 div setlinewidth }
230 def\n/UL { dup gnulinewidth mul /userlinewidth exch def\n \ \ \ \ \ dup
231 1 lt {pop 1} if 10 mul /udl exch def } def\n/PL { stroke userlinewidth
232 setlinewidth } def\n/LTb { BL [] 0 0 0 DL } def\n/LTa { AL [1 udl mul 2
233 udl mul] 0 setdash 0 0 0 setrgbcolor } def\n/LT0 { PL [] 1 0 0 DL }
234 def\n/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def\n/LT2 { PL [2 dl 3 dl] 0 0 1
235 DL } def\n/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def\n/LT4 { PL [5 dl 2 dl
236 1 dl 2 dl] 0 1 1 DL } def\n/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL }
237 def\n/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def\n/LT7 { PL [2 dl 2
238 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def\n/LT8 { PL [2 dl 2 dl 2 dl 2
239 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def\n/Pnt { stroke [] 0
240 setdash\n \ \ gsave 1 setlinecap M 0 0 V stroke grestore } def\n/Dia {
241 stroke [] 0 setdash 2 copy vpt add M\n \ hpt neg vpt neg V hpt vpt neg
242 V\n \ hpt vpt V hpt neg vpt V closepath stroke\n \ Pnt } def\n/Pls {
243 stroke [] 0 setdash vpt sub M 0 vpt2 V\n \ currentpoint stroke M\n
244 \ hpt neg vpt neg R hpt2 0 V stroke\n \ } def\n/Box { stroke [] 0
245 setdash 2 copy exch hpt sub exch vpt add M\n \ 0 vpt2 neg V hpt2 0 V 0
246 vpt2 V\n \ hpt2 neg 0 V closepath stroke\n \ Pnt } def\n/Crs { stroke
247 [] 0 setdash exch hpt sub exch vpt add M\n \ hpt2 vpt2 neg V
248 currentpoint stroke M\n \ hpt2 neg 0 R hpt2 vpt2 V stroke } def\n/TriU
249 { stroke [] 0 setdash 2 copy vpt 1.12 mul add M\n \ hpt neg vpt -1.62
250 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V closepath stroke\n
251 \ Pnt \ } def\n/Star { 2 copy Pls Crs } def\n/BoxF { stroke [] 0
252 setdash exch hpt sub exch vpt add M\n \ 0 vpt2 neg V \ hpt2 0 V \ 0
253 vpt2 V\n \ hpt2 neg 0 V \ closepath fill } def\n/TriUF { stroke [] 0
254 setdash vpt 1.12 mul add M\n \ hpt neg vpt -1.62 mul V\n \ hpt 2 mul 0
255 V\n \ hpt neg vpt 1.62 mul V closepath fill } def\n/TriD { stroke [] 0
256 setdash 2 copy vpt 1.12 mul sub M\n \ hpt neg vpt 1.62 mul V\n \ hpt 2
257 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath stroke\n \ Pnt \ }
258 def\n/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg vpt
259 1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath
260 fill} def\n/DiaF { stroke [] 0 setdash vpt add M\n \ hpt neg vpt neg V
261 hpt vpt neg V\n \ hpt vpt V hpt neg vpt V closepath fill } def\n/Pent {
262 stroke [] 0 setdash 2 copy gsave\n \ translate 0 hpt M 4 {72 rotate 0
263 hpt L} repeat\n \ closepath stroke grestore Pnt } def\n/PentF { stroke
264 [] 0 setdash gsave\n \ translate 0 hpt M 4 {72 rotate 0 hpt L} repeat\n
265 \ closepath fill grestore } def\n/Circle { stroke [] 0 setdash 2 copy\n
266 \ hpt 0 360 arc stroke Pnt } def\n/CircleF { stroke [] 0 setdash hpt 0
267 360 arc fill } def\n/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450
268 \ arc } bind def\n/C1 { BL [] 0 setdash 2 copy \ \ \ \ \ \ \ moveto\n
269 \ \ \ \ \ \ 2 copy \ vpt 0 90 arc closepath fill\n
270 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C2 {
271 BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 90 180 arc
272 closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath }
273 bind def\n/C3 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy
274 \ vpt 0 180 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360
275 arc closepath } bind def\n/C4 { BL [] 0 setdash 2 copy moveto\n
276 \ \ \ \ \ \ 2 copy \ vpt 180 270 arc closepath fill\n
277 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C5 {
278 BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 0 90 arc\n
279 \ \ \ \ \ \ 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 180 270 arc
280 closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc } bind
281 def\n/C6 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ 2 copy \ vpt 90
282 270 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc
283 closepath } bind def\n/C7 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ 2
284 copy \ vpt 0 270 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0
285 360 arc closepath } bind def\n/C8 { BL [] 0 setdash 2 copy moveto\n
286 \ \ \ \ \ 2 copy vpt 270 360 arc closepath fill\n
287 \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C9 { BL
288 [] 0 setdash 2 copy moveto\n \ \ \ \ \ 2 copy \ vpt 270 450 arc
289 closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath }
290 bind def\n/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc
291 closepath fill\n \ \ \ \ \ \ 2 copy moveto\n \ \ \ \ \ \ 2 copy vpt 90
292 180 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc
293 closepath } bind def\n/C11 { BL [] 0 setdash 2 copy moveto\n
294 \ \ \ \ \ \ 2 copy \ vpt 0 180 arc closepath fill\n \ \ \ \ \ \ 2 copy
295 moveto\n \ \ \ \ \ \ 2 copy \ vpt 270 360 arc closepath fill\n
296 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C12 {
297 BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 180 360 arc
298 closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath }
299 bind def\n/C13 { BL [] 0 setdash \ 2 copy moveto\n \ \ \ \ \ \ 2 copy
300 \ vpt 0 90 arc closepath fill\n \ \ \ \ \ \ 2 copy moveto\n
301 \ \ \ \ \ \ 2 copy \ vpt 180 360 arc closepath fill\n
302 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C14 {
303 BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 90 360 arc
304 closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc } bind
305 def\n/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill\n
306 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/Rec
307 \ \ { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto\n
308 \ \ \ \ \ \ neg 0 rlineto closepath } bind def\n/Square { dup Rec }
309 bind def\n/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind
310 def\n/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare }
311 bind def\n/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind
312 def\n/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill
313 Bsquare } bind def\n/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2
314 vpt Rec fill Bsquare } bind def\n/S4 { BL [] 0 setdash 2 copy exch vpt
315 sub exch vpt sub vpt Square fill Bsquare } bind def\n/S5 { BL [] 0
316 setdash 2 copy 2 copy vpt Square fill\n \ \ \ \ \ \ exch vpt sub exch
317 vpt sub vpt Square fill Bsquare } bind def\n/S6 { BL [] 0 setdash 2
318 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind
319 def\n/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2
320 Rec fill\n \ \ \ \ \ \ 2 copy vpt Square fill\n \ \ \ \ \ \ Bsquare }
321 bind def\n/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare
322 } bind def\n/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill
323 Bsquare } bind def\n/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square
324 fill 2 copy exch vpt sub exch vpt Square fill\n \ \ \ \ \ \ Bsquare }
325 bind def\n/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy
326 exch vpt sub exch vpt2 vpt Rec fill\n \ \ \ \ \ \ Bsquare } bind
327 def\n/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt
328 Rec fill Bsquare } bind def\n/S13 { BL [] 0 setdash 2 copy exch vpt sub
329 exch vpt sub vpt2 vpt Rec fill\n \ \ \ \ \ \ 2 copy vpt Square fill
330 Bsquare } bind def\n/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt
331 sub vpt2 vpt Rec fill\n \ \ \ \ \ \ 2 copy exch vpt sub exch vpt Square
332 fill Bsquare } bind def\n/S15 { BL [] 0 setdash 2 copy Bsquare fill
333 Bsquare } bind def\n/D0 { gsave translate 45 rotate 0 0 S0 stroke
334 grestore } bind def\n/D1 { gsave translate 45 rotate 0 0 S1 stroke
335 grestore } bind def\n/D2 { gsave translate 45 rotate 0 0 S2 stroke
336 grestore } bind def\n/D3 { gsave translate 45 rotate 0 0 S3 stroke
337 grestore } bind def\n/D4 { gsave translate 45 rotate 0 0 S4 stroke
338 grestore } bind def\n/D5 { gsave translate 45 rotate 0 0 S5 stroke
339 grestore } bind def\n/D6 { gsave translate 45 rotate 0 0 S6 stroke
340 grestore } bind def\n/D7 { gsave translate 45 rotate 0 0 S7 stroke
341 grestore } bind def\n/D8 { gsave translate 45 rotate 0 0 S8 stroke
342 grestore } bind def\n/D9 { gsave translate 45 rotate 0 0 S9 stroke
343 grestore } bind def\n/D10 { gsave translate 45 rotate 0 0 S10 stroke
344 grestore } bind def\n/D11 { gsave translate 45 rotate 0 0 S11 stroke
345 grestore } bind def\n/D12 { gsave translate 45 rotate 0 0 S12 stroke
346 grestore } bind def\n/D13 { gsave translate 45 rotate 0 0 S13 stroke
347 grestore } bind def\n/D14 { gsave translate 45 rotate 0 0 S14 stroke
348 grestore } bind def\n/D15 { gsave translate 45 rotate 0 0 S15 stroke
349 grestore } bind def\n/DiaE { stroke [] 0 setdash vpt add M\n \ hpt neg
350 vpt neg V hpt vpt neg V\n \ hpt vpt V hpt neg vpt V closepath stroke }
351 def\n/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M\n \ 0 vpt2
352 neg V hpt2 0 V 0 vpt2 V\n \ hpt2 neg 0 V closepath stroke } def\n/TriUE
353 { stroke [] 0 setdash vpt 1.12 mul add M\n \ hpt neg vpt -1.62 mul V\n
354 \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V closepath stroke }
355 def\n/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg vpt
356 1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath
357 stroke } def\n/PentE { stroke [] 0 setdash gsave\n \ translate 0 hpt M
358 4 {72 rotate 0 hpt L} repeat\n \ closepath stroke grestore }
359 def\n/CircE { stroke [] 0 setdash \n \ hpt 0 360 arc stroke }
360 def\n/Opaque { gsave closepath 1 setgray fill grestore 0 setgray
361 closepath } def\n/DiaW { stroke [] 0 setdash vpt add M\n \ hpt neg vpt
362 neg V hpt vpt neg V\n \ hpt vpt V hpt neg vpt V Opaque stroke }
363 def\n/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M\n \ 0 vpt2
364 neg V hpt2 0 V 0 vpt2 V\n \ hpt2 neg 0 V Opaque stroke } def\n/TriUW {
365 stroke [] 0 setdash vpt 1.12 mul add M\n \ hpt neg vpt -1.62 mul V\n
366 \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V Opaque stroke } def\n/TriDW
367 { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg vpt 1.62 mul V\n
368 \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V Opaque stroke } def\n/PentW
369 { stroke [] 0 setdash gsave\n \ translate 0 hpt M 4 {72 rotate 0 hpt L}
370 repeat\n \ Opaque stroke grestore } def\n/CircW { stroke [] 0 setdash
371 \n \ hpt 0 360 arc Opaque stroke } def\n/BoxFill { gsave Rec 1 setgray
372 fill grestore } def\n/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0]
373 makefont\ndup length dict begin {1 index /FID eq {pop pop} {def}
374 ifelse} forall\ncurrentdict end definefont\n/MFshow {{dup dup 0 get
375 findfont exch 1 get scalefont setfont\n \ \ \ \ [ currentpoint ] exch
376 dup 2 get 0 exch rmoveto dup dup 5 get exch 4 get\n \ \ \ \ {show}
377 {stringwidth pop 0 rmoveto}ifelse dup 3 get\n \ \ \ \ {2 get neg 0 exch
378 rmoveto pop} {pop aload pop moveto}ifelse} forall} bind def\n/MFwidth
379 {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont
380 setfont\n \ \ \ \ \ 5 get stringwidth pop add}\n \ \ \ {pop} ifelse}
381 forall} bind def\n/MLshow { currentpoint stroke M\n \ 0 exch R MFshow }
382 bind def\n/MRshow { currentpoint stroke M\n \ exch dup MFwidth neg 3 -1
383 roll R MFshow } def\n/MCshow { currentpoint stroke M\n \ exch dup
384 MFwidth -2 div 3 -1 roll R MFshow } def\nend\n%%EndProlog\ngnudict
385 begin\ngsave\n50 50 translate\n0.050 0.050 scale\n0
386 setgray\nnewpath\n(Helvetica) findfont 140 scalefont setfont\n1.000
387 UL\nLTb\n490 280 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 280 M\n[
388 [(Helvetica) 140.0 0.0 true true (-10)]\n] -46.7 MRshow\n490 487 M\n63
389 0 V\n2809 0 R\n-63 0 V\n stroke\n406 487 M\n[ [(Helvetica) 140.0 0.0
390 true true (-8)]\n] -46.7 MRshow\n490 694 M\n63 0 V\n2809 0 R\n-63 0 V\n
391 stroke\n406 694 M\n[ [(Helvetica) 140.0 0.0 true true (-6)]\n] -46.7
392 MRshow\n490 902 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 902 M\n[
393 [(Helvetica) 140.0 0.0 true true (-4)]\n] -46.7 MRshow\n490 1109 M\n63
394 0 V\n2809 0 R\n-63 0 V\n stroke\n406 1109 M\n[ [(Helvetica) 140.0 0.0
395 true true (-2)]\n] -46.7 MRshow\n490 1316 M\n63 0 V\n2809 0 R\n-63 0
396 V\n stroke\n406 1316 M\n[ [(Helvetica) 140.0 0.0 true true ( 0)]\n]
397 -46.7 MRshow\n490 1523 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 1523
398 M\n[ [(Helvetica) 140.0 0.0 true true ( 2)]\n] -46.7 MRshow\n490 1730
399 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 1730 M\n[ [(Helvetica) 140.0
400 0.0 true true ( 4)]\n] -46.7 MRshow\n490 1938 M\n63 0 V\n2809 0 R\n-63
401 0 V\n stroke\n406 1938 M\n[ [(Helvetica) 140.0 0.0 true true ( 6)]\n]
402 -46.7 MRshow\n490 2145 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 2145
403 M\n[ [(Helvetica) 140.0 0.0 true true ( 8)]\n] -46.7 MRshow\n490 2352
404 M\n63 0 V\n2809 0 R\n-63 0 V\n stroke\n406 2352 M\n[ [(Helvetica) 140.0
405 0.0 true true ( 10)]\n] -46.7 MRshow\n490 280 M\n0 63 V\n0 2009 R\n0
406 -63 V\n stroke\n490 140 M\n[ [(Helvetica) 140.0 0.0 true true (-10)]\n]
407 -46.7 MCshow\n1208 280 M\n0 63 V\n0 2009 R\n0 -63 V\n stroke\n1208 140
408 M\n[ [(Helvetica) 140.0 0.0 true true (-5)]\n] -46.7 MCshow\n1926 280
409 M\n0 63 V\n0 2009 R\n0 -63 V\n stroke\n1926 140 M\n[ [(Helvetica) 140.0
410 0.0 true true ( 0)]\n] -46.7 MCshow\n2644 280 M\n0 63 V\n0 2009 R\n0
411 -63 V\n stroke\n2644 140 M\n[ [(Helvetica) 140.0 0.0 true true ( 5)]\n]
412 -46.7 MCshow\n3362 280 M\n0 63 V\n0 2009 R\n0 -63 V\n stroke\n3362 140
413 M\n[ [(Helvetica) 140.0 0.0 true true ( 10)]\n] -46.7 MCshow\n1.000
414 UL\nLTb\n490 280 M\n2872 0 V\n0 2072 V\n-2872 0 V\n490 280 L\n1.000
415 UL\nLT0\n2711 2219 M\n[ [(Helvetica) 140.0 0.0 true true (Function
416 y=x+sin\\(x\\))]\n] -46.7 MRshow\n2795 2219 M\n399 0 V\n490 336 M\n3 1
417 V\n3 0 V\n3 0 V\n2 1 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0
418 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 1 V\n3 0
419 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0
420 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0
421 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n3 0
422 V\n2 0 V\n3 1 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n2 1 V\n3 0
423 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n2 1 V\n3 0 V\n3 1 V\n3 1
424 V\n3 0 V\n3 1 V\n3 1 V\n3 1 V\n2 1 V\n3 0 V\n3 1 V\n3 1 V\n3 1 V\n3 1
425 V\n3 1 V\n3 1 V\n2 2 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 2 V\n3 1 V\n3 2
426 V\n2 1 V\n3 1 V\n3 2 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 2 V\n2 2 V\n3 2
427 V\n3 2 V\n3 1 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n2 2 V\n3 3 V\n3 2 V\n3 2
428 V\n3 2 V\n3 2 V\n3 3 V\n3 2 V\n2 3 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2
429 V\n3 3 V\n3 3 V\n2 2 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3
430 V\n2 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 4 V\n3 3 V\n2 3 V\n3 4
431 V\n3 3 V\n3 3 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n2 4 V\n3 4 V\n3 3 V\n3 4
432 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n2 4 V\n3 3 V\n3 4 V\n3 4 V\n3 4 V\n3 4
433 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4
434 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 5 V\n3 4
435 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 5 V\n2 4 V\n3 4 V\n3 4 V\n3 4
436 V\n3 4 V\n3 4 V\n3 5 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4
437 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4
438 V\n2 4 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n3 4 V\n3 3 V\n2 4 V\n3 4
439 V\n3 3 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n2 4 V\n3 3 V\n3 3 V\n3 4
440 V\n3 3 V\n3 3 V\n3 4 V\n3 3 V\n2 3 V\n3 3 V\n3 3 V\n3 3 V\n3 4 V\n3 3
441 V\n3 3 V\n3 2 V\n2 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 2 V\n3 3 V\n3 3
442 V\n2 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n3 2 V\n2 3 V\n3 2
443 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n2 2 V\n3 2 V\n3 2 V\n3 2
444 V\n3 1 V\n3 2 V\n3 2 V\n3 2 V\n2 1 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 2
445 V\n3 1 V\n3 1 V\n2 2 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 2
446 V\n2 1 V\n3 0 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 0 V\n2 1 V\n3 1
447 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n2 1 V\n3 0 V\n3 1 V\n3 0
448 V\n3 1 V\n3 0 V\n3 0 V\n3 1 V\n2 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0
449 V\n3 0 V\n3 0 V\n2 1 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0
450 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n2 0 V\n3 0
451 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0
452 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0
453 V\n3 1 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n3 0 V\n3 1
454 V\n2 0 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n2 1 V\n3 0
455 V\n3 1 V\n3 0 V\n3 1 V\n3 1 V\n3 0 V\n3 1 V\n2 1 V\n3 1 V\n3 1 V\n3 1
456 V\n3 0 V\n3 1 V\n3 1 V\n3 1 V\n2 1 V\n3 2 V\ncurrentpoint stroke M\n3 1
457 V\n3 1 V\n3 1 V\n3 1 V\n3 2 V\n3 1 V\n2 1 V\n3 2 V\n3 1 V\n3 2 V\n3 1
458 V\n3 2 V\n3 1 V\n3 2 V\n2 2 V\n3 1 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2
459 V\n3 2 V\n2 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 3 V\n2 2
460 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 3 V\n2 2 V\n3 3 V\n3 3
461 V\n3 3 V\n3 2 V\n3 3 V\n3 3 V\n3 3 V\n2 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3
462 V\n3 3 V\n3 4 V\n3 3 V\n2 3 V\n3 3 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n3 3
463 V\n3 4 V\n2 3 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n2 4
464 V\n3 3 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n2 4 V\n3 4 V\n3 4
465 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 5
466 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 5 V\n3 4
467 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 5 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4
468 V\n3 4 V\n3 4 V\n3 4 V\n3 5 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4
469 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 3 V\n3 4 V\n3 4
470 V\n3 4 V\n3 4 V\n3 3 V\n2 4 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n3 4
471 V\n3 4 V\n2 3 V\n3 4 V\n3 3 V\n3 3 V\n3 4 V\n3 3 V\n3 4 V\n3 3 V\n2 3
472 V\n3 3 V\n3 4 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n2 3 V\n3 3 V\n3 3
473 V\n3 3 V\n3 2 V\n3 3 V\n3 3 V\n3 3 V\n2 2 V\n3 3 V\n3 3 V\n3 2 V\n3 3
474 V\n3 2 V\n3 3 V\n3 2 V\n2 2 V\n3 3 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2
475 V\n3 2 V\n2 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 1 V\n2 2
476 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 2 V\n2 1 V\n3 1 V\n3 2
477 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 2 V\n2 1 V\n3 1 V\n3 1 V\n3 1 V\n3 0
478 V\n3 1 V\n3 1 V\n3 1 V\n2 1 V\n3 1 V\n3 0 V\n3 1 V\n3 1 V\n3 0 V\n3 1
479 V\n3 0 V\n2 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n2 0
480 V\n3 1 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 1
481 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0
482 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0
483 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0
484 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 1 V\n3 0 V\n3 0
485 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n2 0 V\n3 1 V\n3 0 V\n3 0 V\n3 1
486 V\n3 0 V\n3 1 V\n3 0 V\n2 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n3 1
487 V\n3 1 V\n2 1 V\n3 0 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 0 V\n2 1
488 V\n3 2 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n2 2 V\n3 1 V\n3 1
489 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 2 V\n2 1 V\n3 2 V\n3 2 V\n3 2 V\n3 1
490 V\n3 2 V\n3 2 V\n3 2 V\n2 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 2
491 V\n3 2 V\n2 3 V\n3 2 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n2 2
492 V\n3 3 V\n3 3 V\n3 2 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n2 3 V\n3 2 V\n3 3
493 V\n3 3 V\n3 4 V\n3 3 V\n3 3 V\n3 3 V\n2 3 V\n3 3 V\n3 4 V\n3 3 V\n3 3
494 V\n3 4 V\n3 3 V\n3 3 V\n2 4 V\n3 3 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n3 3
495 V\n3 4 V\n2 4 V\n3 3 V\n3 4 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n2 4
496 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4
497 V\ncurrentpoint stroke M\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4
498 V\n3 4 V\n3 5 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 5 V\n3 4
499 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n2 5 V\n3 4 V\n3 4 V\n3 4 V\n3 4
500 V\n3 4 V\n3 4 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4
501 V\n3 4 V\n2 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 4 V\n3 3 V\n2 4
502 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n3 4 V\n3 3 V\n3 4 V\n2 4 V\n3 3 V\n3 4
503 V\n3 3 V\n3 4 V\n3 3 V\n3 3 V\n3 4 V\n2 3 V\n3 3 V\n3 4 V\n3 3 V\n3 3
504 V\n3 3 V\n3 3 V\n3 3 V\n2 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3 V\n3 3
505 V\n3 3 V\n2 2 V\n3 3 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n3 3 V\n3 2 V\n2 3
506 V\n3 2 V\n3 3 V\n3 2 V\n3 2 V\n3 2 V\n3 2 V\n3 3 V\n2 2 V\n3 2 V\n3 2
507 V\n3 2 V\n3 2 V\n3 1 V\n3 2 V\n3 2 V\n2 2 V\n3 2 V\n3 1 V\n3 2 V\n3 1
508 V\n3 2 V\n3 2 V\n3 1 V\n2 1 V\n3 2 V\n3 1 V\n3 2 V\n3 1 V\n3 1 V\n3 1
509 V\n3 1 V\n2 2 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 1 V\n3 0 V\n2 1
510 V\n3 1 V\n3 1 V\n3 1 V\n3 0 V\n3 1 V\n3 1 V\n3 0 V\n2 1 V\n3 0 V\n3 1
511 V\n3 0 V\n3 1 V\n3 0 V\n3 1 V\n3 0 V\n2 1 V\n3 0 V\n3 0 V\n3 1 V\n3 0
512 V\n3 0 V\n3 0 V\n3 1 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0
513 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0
514 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0
515 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n3 0 V\n2 1 V\n3 0 V\n3 0 V\n3 0 V\n3 0
516 V\n3 0 V\n3 0 V\n3 0 V\n2 0 V\n3 0 V\n3 0 V\n3 1 V\n3 0 V\n3 0 V\n3 0
517 V\n3 0 V\n2 1 V\n3 0 V\n3 0 V\n3 1 V\nstroke\ngrestore\nend\nshowpage\n>|ps>||||||>
519 \;
520 </output>
522 <\input|octave\<gtr\> >
523 x0=[2;5;10];
524 </input>
526 <\input|octave\<gtr\> >
527 t = linspace (0,10,800);
528 </input>
530 <\input|octave\<gtr\> >
531 function dx = butter (x ,t) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dx(1)
532 = -10.0*(x(1)-x(2)); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dx(2)
533 = 28.0*x(1)-x(2)-x(1)*x(3); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dx(3)
534 = 8.0/3.0*( x(1)*x(2) -x(3) ); \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ end;
535 </input>
537 <\input|octave\<gtr\> >
538 y=lsode("butter",x0,t);
539 </input>
541 <\input|octave\<gtr\> >
542 gset parametric;
543 </input>
545 <\input|octave\<gtr\> >
546 gset set term postscript enhanced color eps;
547 </input>
549 <\input|octave\<gtr\> >
550 gset xtics 10;gset ytics 10; gset ztics 10;
551 </input>
553 <\input|octave\<gtr\> >
554 gset out "/tmp/butterfly.eps";
555 </input>
557 <\input|octave\<gtr\> >
558 gsplot y title "Butterfly Effect"
559 </input>
561 <\input|octave\<gtr\> >
562 \;
563 </input>
564 </session>
566 In order to embed the 3D graph, we first save it as butterfly.eps in /tmp
567 directory. Then we can embed this EPS file into the worksheet using
568 <apply|menu|Insert|Image>.
570 <expand|big-figure|<postscript|<tuple|<raw_data|%!PS-Adobe-2.0
571 EPSF-2.0\n%%Title: /tmp/butterfly.eps\n%%Creator: gnuplot 3.7 patchlevel
572 3\n%%CreationDate: Wed Jul \ 9 21:26:06 2003\n%%DocumentFonts:
573 (atend)\n%%BoundingBox: 50 50 230 176\n%%Orientation:
574 Portrait\n%%EndComments\n/gnudict 256 dict def\ngnudict begin\n/Color true
575 def\n/Solid false def\n/gnulinewidth 5.000 def\n/userlinewidth gnulinewidth
576 def\n/vshift -46 def\n/dl {10 mul} def\n/hpt_ 31.5 def\n/vpt_ 31.5
577 def\n/hpt hpt_ def\n/vpt vpt_ def\n/M {moveto} bind def\n/L {lineto} bind
578 def\n/R {rmoveto} bind def\n/V {rlineto} bind def\n/vpt2 vpt 2 mul
579 def\n/hpt2 hpt 2 mul def\n/Lshow { currentpoint stroke M\n \ 0 vshift R
580 show } def\n/Rshow { currentpoint stroke M\n \ dup stringwidth pop neg
581 vshift R show } def\n/Cshow { currentpoint stroke M\n \ dup stringwidth pop
582 -2 div vshift R show } def\n/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt
583 exch def\n \ /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def\n/DL { Color
584 {setrgbcolor Solid {pop []} if 0 setdash }\n {pop pop pop Solid {pop []} if
585 0 setdash} ifelse } def\n/BL { stroke userlinewidth 2 mul setlinewidth }
586 def\n/AL { stroke userlinewidth 2 div setlinewidth } def\n/UL { dup
587 gnulinewidth mul /userlinewidth exch def\n \ \ \ \ \ dup 1 lt {pop 1} if 10
588 mul /udl exch def } def\n/PL { stroke userlinewidth setlinewidth }
589 def\n/LTb { BL [] 0 0 0 DL } def\n/LTa { AL [1 udl mul 2 udl mul] 0 setdash
590 0 0 0 setrgbcolor } def\n/LT0 { PL [] 1 0 0 DL } def\n/LT1 { PL [4 dl 2 dl]
591 0 1 0 DL } def\n/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def\n/LT3 { PL [1 dl 1.5
592 dl] 1 0 1 DL } def\n/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def\n/LT5 {
593 PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def\n/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0
594 0 0 DL } def\n/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL }
595 def\n/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL }
596 def\n/Pnt { stroke [] 0 setdash\n \ \ gsave 1 setlinecap M 0 0 V stroke
597 grestore } def\n/Dia { stroke [] 0 setdash 2 copy vpt add M\n \ hpt neg vpt
598 neg V hpt vpt neg V\n \ hpt vpt V hpt neg vpt V closepath stroke\n \ Pnt }
599 def\n/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V\n \ currentpoint stroke
600 M\n \ hpt neg vpt neg R hpt2 0 V stroke\n \ } def\n/Box { stroke [] 0
601 setdash 2 copy exch hpt sub exch vpt add M\n \ 0 vpt2 neg V hpt2 0 V 0 vpt2
602 V\n \ hpt2 neg 0 V closepath stroke\n \ Pnt } def\n/Crs { stroke [] 0
603 setdash exch hpt sub exch vpt add M\n \ hpt2 vpt2 neg V currentpoint stroke
604 M\n \ hpt2 neg 0 R hpt2 vpt2 V stroke } def\n/TriU { stroke [] 0 setdash 2
605 copy vpt 1.12 mul add M\n \ hpt neg vpt -1.62 mul V\n \ hpt 2 mul 0 V\n
606 \ hpt neg vpt 1.62 mul V closepath stroke\n \ Pnt \ } def\n/Star { 2 copy
607 Pls Crs } def\n/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M\n
608 \ 0 vpt2 neg V \ hpt2 0 V \ 0 vpt2 V\n \ hpt2 neg 0 V \ closepath fill }
609 def\n/TriUF { stroke [] 0 setdash vpt 1.12 mul add M\n \ hpt neg vpt -1.62
610 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V closepath fill }
611 def\n/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M\n \ hpt neg vpt
612 1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath stroke\n
613 \ Pnt \ } def\n/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg
614 vpt 1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath
615 fill} def\n/DiaF { stroke [] 0 setdash vpt add M\n \ hpt neg vpt neg V hpt
616 vpt neg V\n \ hpt vpt V hpt neg vpt V closepath fill } def\n/Pent { stroke
617 [] 0 setdash 2 copy gsave\n \ translate 0 hpt M 4 {72 rotate 0 hpt L}
618 repeat\n \ closepath stroke grestore Pnt } def\n/PentF { stroke [] 0
619 setdash gsave\n \ translate 0 hpt M 4 {72 rotate 0 hpt L} repeat\n
620 \ closepath fill grestore } def\n/Circle { stroke [] 0 setdash 2 copy\n
621 \ hpt 0 360 arc stroke Pnt } def\n/CircleF { stroke [] 0 setdash hpt 0 360
622 arc fill } def\n/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 \ arc } bind
623 def\n/C1 { BL [] 0 setdash 2 copy \ \ \ \ \ \ \ moveto\n \ \ \ \ \ \ 2 copy
624 \ vpt 0 90 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc
625 closepath } bind def\n/C2 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2
626 copy \ vpt 90 180 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0
627 360 arc closepath } bind def\n/C3 { BL [] 0 setdash 2 copy moveto\n
628 \ \ \ \ \ \ 2 copy \ vpt 0 180 arc closepath fill\n
629 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C4 { BL []
630 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 180 270 arc closepath
631 fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C5
632 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 0 90 arc\n
633 \ \ \ \ \ \ 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 180 270 arc closepath
634 fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc } bind def\n/C6 { BL [] 0
635 setdash 2 copy moveto\n \ \ \ \ \ 2 copy \ vpt 90 270 arc closepath fill\n
636 \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C7 { BL [] 0
637 setdash 2 copy moveto\n \ \ \ \ \ 2 copy \ vpt 0 270 arc closepath fill\n
638 \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C8 { BL [] 0
639 setdash 2 copy moveto\n \ \ \ \ \ 2 copy vpt 270 360 arc closepath fill\n
640 \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C9 { BL [] 0
641 setdash 2 copy moveto\n \ \ \ \ \ 2 copy \ vpt 270 450 arc closepath fill\n
642 \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C10 { BL []
643 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill\n
644 \ \ \ \ \ \ 2 copy moveto\n \ \ \ \ \ \ 2 copy vpt 90 180 arc closepath
645 fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C11
646 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 0 180 arc
647 closepath fill\n \ \ \ \ \ \ 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 270
648 360 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc
649 closepath } bind def\n/C12 { BL [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2
650 copy \ vpt 180 360 arc closepath fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0
651 360 arc closepath } bind def\n/C13 { BL [] 0 setdash \ 2 copy moveto\n
652 \ \ \ \ \ \ 2 copy \ vpt 0 90 arc closepath fill\n \ \ \ \ \ \ 2 copy
653 moveto\n \ \ \ \ \ \ 2 copy \ vpt 180 360 arc closepath fill\n
654 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/C14 { BL
655 [] 0 setdash 2 copy moveto\n \ \ \ \ \ \ 2 copy \ vpt 90 360 arc closepath
656 fill\n \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc } bind def\n/C15 { BL [] 0
657 setdash 2 copy vpt 0 360 arc closepath fill\n
658 \ \ \ \ \ \ \ \ \ \ \ \ \ \ vpt 0 360 arc closepath } bind def\n/Rec \ \ {
659 newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto\n \ \ \ \ \ \ neg
660 0 rlineto closepath } bind def\n/Square { dup Rec } bind def\n/Bsquare {
661 vpt sub exch vpt sub exch vpt2 Square } bind def\n/S0 { BL [] 0 setdash 2
662 copy moveto 0 vpt rlineto BL Bsquare } bind def\n/S1 { BL [] 0 setdash 2
663 copy vpt Square fill Bsquare } bind def\n/S2 { BL [] 0 setdash 2 copy exch
664 vpt sub exch vpt Square fill Bsquare } bind def\n/S3 { BL [] 0 setdash 2
665 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def\n/S4 { BL [] 0
666 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind
667 def\n/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill\n \ \ \ \ \ \ exch
668 vpt sub exch vpt sub vpt Square fill Bsquare } bind def\n/S6 { BL [] 0
669 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind
670 def\n/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec
671 fill\n \ \ \ \ \ \ 2 copy vpt Square fill\n \ \ \ \ \ \ Bsquare } bind
672 def\n/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind
673 def\n/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind
674 def\n/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt
675 sub exch vpt Square fill\n \ \ \ \ \ \ Bsquare } bind def\n/S11 { BL [] 0
676 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt
677 Rec fill\n \ \ \ \ \ \ Bsquare } bind def\n/S12 { BL [] 0 setdash 2 copy
678 exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def\n/S13 { BL
679 [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill\n
680 \ \ \ \ \ \ 2 copy vpt Square fill Bsquare } bind def\n/S14 { BL [] 0
681 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill\n \ \ \ \ \ \ 2
682 copy exch vpt sub exch vpt Square fill Bsquare } bind def\n/S15 { BL [] 0
683 setdash 2 copy Bsquare fill Bsquare } bind def\n/D0 { gsave translate 45
684 rotate 0 0 S0 stroke grestore } bind def\n/D1 { gsave translate 45 rotate 0
685 0 S1 stroke grestore } bind def\n/D2 { gsave translate 45 rotate 0 0 S2
686 stroke grestore } bind def\n/D3 { gsave translate 45 rotate 0 0 S3 stroke
687 grestore } bind def\n/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore
688 } bind def\n/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind
689 def\n/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def\n/D7
690 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def\n/D8 { gsave
691 translate 45 rotate 0 0 S8 stroke grestore } bind def\n/D9 { gsave
692 translate 45 rotate 0 0 S9 stroke grestore } bind def\n/D10 { gsave
693 translate 45 rotate 0 0 S10 stroke grestore } bind def\n/D11 { gsave
694 translate 45 rotate 0 0 S11 stroke grestore } bind def\n/D12 { gsave
695 translate 45 rotate 0 0 S12 stroke grestore } bind def\n/D13 { gsave
696 translate 45 rotate 0 0 S13 stroke grestore } bind def\n/D14 { gsave
697 translate 45 rotate 0 0 S14 stroke grestore } bind def\n/D15 { gsave
698 translate 45 rotate 0 0 S15 stroke grestore } bind def\n/DiaE { stroke [] 0
699 setdash vpt add M\n \ hpt neg vpt neg V hpt vpt neg V\n \ hpt vpt V hpt neg
700 vpt V closepath stroke } def\n/BoxE { stroke [] 0 setdash exch hpt sub exch
701 vpt add M\n \ 0 vpt2 neg V hpt2 0 V 0 vpt2 V\n \ hpt2 neg 0 V closepath
702 stroke } def\n/TriUE { stroke [] 0 setdash vpt 1.12 mul add M\n \ hpt neg
703 vpt -1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V closepath
704 stroke } def\n/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg
705 vpt 1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V closepath
706 stroke } def\n/PentE { stroke [] 0 setdash gsave\n \ translate 0 hpt M 4
707 {72 rotate 0 hpt L} repeat\n \ closepath stroke grestore } def\n/CircE {
708 stroke [] 0 setdash \n \ hpt 0 360 arc stroke } def\n/Opaque { gsave
709 closepath 1 setgray fill grestore 0 setgray closepath } def\n/DiaW { stroke
710 [] 0 setdash vpt add M\n \ hpt neg vpt neg V hpt vpt neg V\n \ hpt vpt V
711 hpt neg vpt V Opaque stroke } def\n/BoxW { stroke [] 0 setdash exch hpt sub
712 exch vpt add M\n \ 0 vpt2 neg V hpt2 0 V 0 vpt2 V\n \ hpt2 neg 0 V Opaque
713 stroke } def\n/TriUW { stroke [] 0 setdash vpt 1.12 mul add M\n \ hpt neg
714 vpt -1.62 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt 1.62 mul V Opaque stroke
715 } def\n/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M\n \ hpt neg vpt 1.62
716 mul V\n \ hpt 2 mul 0 V\n \ hpt neg vpt -1.62 mul V Opaque stroke }
717 def\n/PentW { stroke [] 0 setdash gsave\n \ translate 0 hpt M 4 {72 rotate
718 0 hpt L} repeat\n \ Opaque stroke grestore } def\n/CircW { stroke [] 0
719 setdash \n \ hpt 0 360 arc Opaque stroke } def\n/BoxFill { gsave Rec 1
720 setgray fill grestore } def\n/Symbol-Oblique /Symbol findfont [1 0 .167 1 0
721 0] makefont\ndup length dict begin {1 index /FID eq {pop pop} {def} ifelse}
722 forall\ncurrentdict end definefont pop\n/MFshow {{dup dup 0 get findfont
723 exch 1 get scalefont setfont\n \ \ \ \ [ currentpoint ] exch dup 2 get 0
724 exch rmoveto dup dup 5 get exch 4 get\n \ \ \ \ {show} {stringwidth pop 0
725 rmoveto}ifelse dup 3 get\n \ \ \ \ {2 get neg 0 exch rmoveto pop} {pop
726 aload pop moveto}ifelse} forall} bind def\n/MFwidth {0 exch {dup 3 get{dup
727 dup 0 get findfont exch 1 get scalefont setfont\n \ \ \ \ \ 5 get
728 stringwidth pop add}\n \ \ \ {pop} ifelse} forall} bind def\n/MLshow {
729 currentpoint stroke M\n \ 0 exch R MFshow } bind def\n/MRshow {
730 currentpoint stroke M\n \ exch dup MFwidth neg 3 -1 roll R MFshow }
731 def\n/MCshow { currentpoint stroke M\n \ exch dup MFwidth -2 div 3 -1 roll
732 R MFshow } def\nend\n%%EndProlog\ngnudict begin\ngsave\n50 50
733 translate\n0.050 0.050 scale\n0 setgray\nnewpath\n(Helvetica) findfont 140
734 scalefont setfont\n1.000 UL\nLTb\n1.000 UL\nLT0\n2802 2036 M\n[
735 [(Helvetica) 140.0 0.0 true true (Butterfly Effect)]\n] -46.7 MRshow\n2886
736 2036 M\n399 0 V\n1989 1344 M\n24 3 V\n27 5 V\n29 8 V\n31 10 V\n34 13 V\n36
737 16 V\n39 20 V\n40 22 V\n41 27 V\n40 29 V\n39 33 V\n34 34 V\n27 35 V\n19 35
738 V\n6 30 V\n-6 26 V\n-19 18 V\n-33 9 V\n-44 1 V\n-52 -8 V\n-58 -14 V\n-59
739 -19 V\n-59 -21 V\n-55 -22 V\n-51 -22 V\n-46 -21 V\n-41 -18 V\n-35 -17
740 V\n-30 -15 V\n-26 -13 V\n-23 -12 V\n-19 -11 V\n-16 -10 V\n-13 -10 V\n-12 -9
741 V\n-11 -8 V\n-9 -9 V\n-8 -8 V\n-8 -9 V\n-7 -8 V\n-7 -8 V\n-7 -7 V\n-8 -8
742 V\n-7 -8 V\n-8 -7 V\n-9 -7 V\n-9 -7 V\n-10 -7 V\n-11 -6 V\n-12 -6 V\n-13 -6
743 V\n-14 -5 V\n-16 -4 V\n-17 -4 V\n-18 -3 V\n-20 -3 V\n-21 0 V\n-23 0 V\n-23
744 2 V\n-25 4 V\n-25 5 V\n-26 9 V\n-25 11 V\n-24 13 V\n-22 17 V\n-19 20 V\n-15
745 22 V\n-10 25 V\n-5 26 V\n2 27 V\n8 26 V\n15 25 V\n21 22 V\n26 19 V\n30 14
746 V\n32 10 V\n34 6 V\n34 1 V\n33 -3 V\n31 -6 V\n29 -9 V\n27 -11 V\n23 -12
747 V\n21 -13 V\n18 -13 V\n16 -14 V\n14 -14 V\n11 -13 V\n9 -13 V\n7 -13 V\n6
748 -13 V\n4 -12 V\n4 -11 V\n2 -12 V\n0 -10 V\n0 -11 V\n0 -10 V\n-2 -9 V\n-3
749 -10 V\n-3 -8 V\n-4 -9 V\n-5 -8 V\n-6 -8 V\n-7 -8 V\n-7 -8 V\n-9 -7 V\n-9 -7
750 V\n-11 -6 V\n-12 -6 V\n-13 -6 V\n-15 -5 V\n-17 -5 V\n-18 -4 V\n-19 -4
751 V\n-22 -2 V\n-23 -2 V\n-26 0 V\n-27 2 V\n-28 3 V\n-30 6 V\n-31 9 V\n-30 12
752 V\n-30 16 V\n-28 19 V\n-24 24 V\n-20 27 V\n-14 30 V\n-6 33 V\n2 34 V\n10 33
753 V\n19 32 V\n27 28 V\n34 23 V\n38 17 V\n41 11 V\n42 5 V\n42 0 V\n40 -5 V\n37
754 -9 V\n34 -12 V\n31 -13 V\n27 -15 V\n23 -16 V\n21 -16 V\n17 -15 V\n15 -16
755 V\n12 -14 V\n11 -15 V\n8 -14 V\n7 -13 V\n6 -12 V\n5 -12 V\n4 -12 V\n2 -10
756 V\n3 -11 V\n2 -10 V\n1 -9 V\n1 -9 V\n0 -9 V\n1 -8 V\n0 -8 V\n-1 -8 V\n0 -7
757 V\n-1 -7 V\n-1 -7 V\n-1 -7 V\n-1 -6 V\n-1 -7 V\n-2 -6 V\n-2 -6 V\n-2 -6
758 V\n-2 -5 V\n-3 -6 V\n-3 -5 V\n-4 -5 V\n-4 -6 V\n-4 -5 V\n-5 -5 V\n-6 -5
759 V\n-7 -4 V\n-7 -5 V\n-8 -5 V\n-10 -5 V\n-10 -5 V\n-12 -4 V\n-14 -5 V\n-15
760 -4 V\n-17 -4 V\n-20 -4 V\n-21 -4 V\n-25 -3 V\n-27 -2 V\n-31 -1 V\n-33 1
761 V\n-37 2 V\n-40 5 V\n-42 9 V\n-45 13 V\n-45 18 V\n-44 24 V\n-42 31 V\n-36
762 38 V\n-27 45 V\n-16 51 V\n-2 55 V\n15 56 V\n29 53 V\n45 47 V\n55 37 V\n64
763 26 V\n66 14 V\n67 4 V\n63 -6 V\n59 -12 V\n53 -17 V\n46 -20 V\n41 -21 V\n35
764 -22 V\n29 -21 V\n26 -19 V\n21 -19 V\n18 -17 V\n16 -17 V\n14 -14 V\n11 -14
765 V\n11 -12 V\n10 -11 V\n9 -11 V\n8 -9 V\n9 -8 V\n8 -7 V\n9 -7 V\n9 -6 V\n10
766 -4 V\n10 -4 V\n11 -3 V\n12 -2 V\n12 -2 V\n14 0 V\n15 1 V\n16 2 V\n16 3
767 V\n18 5 V\n19 5 V\n19 7 V\n20 9 V\n21 10 V\n20 11 V\n20 12 V\n19 14 V\n18
768 14 V\n15 15 V\n13 14 V\n9 14 V\n5 14 V\n1 11 V\n-5 10 V\n-8 7 V\n-14 5
769 V\n-17 2 V\n-21 -1 V\n-23 -4 V\n-25 -5 V\n-26 -8 V\n-26 -8 V\n-26 -10
770 V\n-24 -9 V\n-23 -11 V\n-20 -10 V\n-19 -10 V\n-17 -9 V\n-15 -10 V\n-12 -9
771 V\n-11 -8 V\n-8 -9 V\n-7 -8 V\n-6 -7 V\n-4 -8 V\n-2 -7 V\n-1 -6 V\n0 -6
772 V\n1 -6 V\n2 -6 V\n3 -5 V\n5 -5 V\n5 -4 V\n7 -4 V\n7 -4 V\n9 -2 V\n10 -2
773 V\n11 -2 V\n12 0 V\n14 0 V\n15 2 V\n16 2 V\n17 4 V\n19 5 V\n20 6 V\n21 7
774 V\n22 10 V\n22 10 V\n23 13 V\n23 13 V\n22 16 V\n21 16 V\n18 17 V\n16 17
775 V\n12 17 V\n7 15 V\n2 14 V\n-4 12 V\n-9 9 V\n-15 6 V\n-19 3 V\n-24 -1
776 V\n-26 -4 V\n-29 -6 V\n-30 -9 V\n-30 -10 V\n-29 -11 V\n-28 -11 V\n-25 -12
777 V\n-24 -11 V\n-21 -11 V\n-19 -11 V\n-16 -10 V\n-14 -10 V\n-12 -9 V\n-10 -9
778 V\n-8 -8 V\n-6 -8 V\n-5 -8 V\n-3 -8 V\n-2 -7 V\n-1 -7 V\n0 -7 V\n1 -6 V\n3
779 -6 V\n3 -6 V\n4 -5 V\n5 -5 V\n6 -4 V\n7 -4 V\n8 -4 V\n10 -3 V\n10 -2 V\n12
780 -1 V\n13 -1 V\n14 1 V\n15 1 V\n18 2 V\n18 4 V\n20 5 V\n22 7 V\n23 8 V\n25
781 10 V\n25 12 V\n27 13 V\n26 16 V\n26 17 V\n25 19 V\n23 20 V\n20 20 V\n16 20
782 V\n10 20 V\n4 18 V\n-3 15 V\n-9 11 V\n-17 8 V\n-23 3 V\n-28 -1 V\n-32 -4
783 V\n-34 -8 V\n-35 -11 V\n-36 -12 V\n-34 -13 V\n-32 -13 V\n-30 -14 V\n-27 -13
784 V\n-24 -12 V\n-21 -12 V\n-19 -11 V\n-16 -11 V\n-13 -10 V\n-11 -9 V\n-9 -9
785 V\n-8 -9 V\n-6 -8 V\n-4 -9 V\n-4 -8 V\n-2 -7 V\n-1 -8 V\n0 -7 V\n0 -7 V\n1
786 -7 V\n2 -6 V\n3 -6 V\ncurrentpoint stroke M\n3 -6 V\n5 -6 V\n4 -5 V\n6 -5
787 V\n6 -4 V\n8 -4 V\n8 -3 V\n9 -3 V\n11 -2 V\n11 -2 V\n13 -1 V\n14 1 V\n16 1
788 V\n18 2 V\n19 3 V\n22 5 V\n23 7 V\n25 8 V\n28 10 V\n29 13 V\n30 14 V\n32 18
789 V\n33 19 V\n32 22 V\n31 24 V\n29 26 V\n24 27 V\n18 26 V\n11 25 V\n3 22
790 V\n-7 18 V\n-16 13 V\n-26 7 V\n-33 0 V\n-39 -4 V\n-43 -10 V\n-46 -13 V\n-45
791 -15 V\n-44 -17 V\n-41 -17 V\n-37 -16 V\n-34 -16 V\n-30 -15 V\n-26 -14
792 V\n-23 -12 V\n-19 -12 V\n-17 -11 V\n-14 -10 V\n-11 -10 V\n-10 -9 V\n-9 -9
793 V\n-6 -9 V\n-6 -9 V\n-5 -8 V\n-4 -9 V\n-4 -8 V\n-3 -8 V\n-2 -8 V\n-3 -7
794 V\n-2 -8 V\n-2 -7 V\n-2 -8 V\n-2 -7 V\n-2 -7 V\n-3 -7 V\n-2 -7 V\n-3 -6
795 V\n-3 -7 V\n-3 -6 V\n-3 -6 V\n-4 -6 V\n-4 -6 V\n-5 -6 V\n-6 -6 V\n-6 -6
796 V\n-7 -5 V\n-7 -6 V\n-9 -5 V\n-9 -5 V\n-11 -6 V\n-13 -5 V\n-13 -5 V\n-16 -4
797 V\n-17 -5 V\n-20 -4 V\n-21 -3 V\n-25 -3 V\n-27 -2 V\n-29 -1 V\n-33 1 V\n-35
798 3 V\n-38 5 V\n-40 9 V\n-42 13 V\n-41 18 V\n-41 24 V\n-37 30 V\n-32 36
799 V\n-23 42 V\n-13 47 V\n1 51 V\n14 50 V\n28 47 V\n41 42 V\n51 33 V\n57 23
800 V\n61 14 V\n60 3 V\n59 -4 V\n54 -11 V\n49 -15 V\n44 -19 V\n38 -19 V\n33 -20
801 V\n28 -20 V\n24 -19 V\n20 -18 V\n18 -18 V\n15 -16 V\n13 -14 V\n11 -14 V\n10
802 -13 V\n8 -12 V\n9 -11 V\n7 -10 V\n8 -9 V\n7 -8 V\n8 -7 V\n8 -7 V\n8 -6 V\n9
803 -5 V\n9 -5 V\n11 -3 V\n11 -3 V\n12 -2 V\n13 -1 V\n15 0 V\n16 1 V\n17 2
804 V\n18 4 V\n20 4 V\n20 7 V\n23 8 V\n23 9 V\n24 12 V\n24 12 V\n24 15 V\n24 16
805 V\n22 17 V\n20 18 V\n17 19 V\n12 18 V\n8 17 V\n2 15 V\n-4 13 V\n-10 9
806 V\n-16 6 V\n-21 3 V\n-26 -2 V\n-29 -4 V\n-31 -7 V\n-32 -10 V\n-32 -10
807 V\n-31 -12 V\n-29 -12 V\n-27 -13 V\n-24 -12 V\n-22 -11 V\n-20 -11 V\n-17
808 -11 V\n-14 -10 V\n-12 -9 V\n-10 -9 V\n-9 -9 V\n-6 -8 V\n-5 -9 V\n-4 -7
809 V\n-2 -8 V\n-2 -7 V\n0 -7 V\n1 -7 V\n2 -6 V\n2 -6 V\n4 -6 V\n4 -5 V\n6 -5
810 V\n6 -5 V\n7 -4 V\n8 -3 V\n9 -3 V\n10 -3 V\n12 -1 V\n13 -1 V\n14 0 V\n16 1
811 V\n17 2 V\n19 4 V\n20 5 V\n22 6 V\n24 8 V\n26 10 V\n27 12 V\n27 14 V\n29 16
812 V\n29 18 V\n27 19 V\n26 22 V\n24 22 V\n19 23 V\n13 22 V\n7 20 V\n0 18 V\n-8
813 14 V\n-15 10 V\n-24 5 V\n-29 0 V\n-34 -5 V\n-37 -8 V\n-39 -11 V\n-39 -13
814 V\n-37 -14 V\n-36 -14 V\n-33 -15 V\n-30 -14 V\n-26 -13 V\n-23 -13 V\n-21
815 -12 V\n-17 -11 V\n-15 -10 V\n-12 -10 V\n-11 -10 V\n-8 -9 V\n-7 -8 V\n-6 -9
816 V\n-4 -8 V\n-3 -8 V\n-2 -8 V\n-2 -8 V\n-1 -7 V\n0 -8 V\n0 -7 V\n1 -7 V\n2
817 -6 V\n2 -6 V\n2 -7 V\n3 -5 V\n3 -6 V\n4 -5 V\n5 -5 V\n5 -5 V\n6 -4 V\n7 -4
818 V\n7 -3 V\n8 -3 V\n10 -2 V\n10 -2 V\n12 -1 V\n13 0 V\n15 1 V\n16 1 V\n18 3
819 V\n21 4 V\n22 5 V\n25 7 V\n27 9 V\n30 12 V\n32 13 V\n34 17 V\n36 19 V\n37
820 22 V\n37 25 V\n37 28 V\n33 30 V\n29 31 V\n23 32 V\n14 30 V\n4 26 V\n-8 22
821 V\n-20 15 V\n-31 8 V\n-40 0 V\n-47 -7 V\n-52 -13 V\n-54 -17 V\n-52 -19
822 V\n-50 -20 V\n-47 -19 V\n-42 -19 V\n-37 -18 V\n-33 -15 V\n-28 -15 V\n-24
823 -13 V\n-21 -11 V\n-18 -11 V\n-15 -11 V\n-13 -9 V\n-11 -10 V\n-9 -9 V\n-8 -8
824 V\n-7 -9 V\n-7 -9 V\n-6 -8 V\n-5 -8 V\n-6 -8 V\n-6 -8 V\n-5 -8 V\n-6 -8
825 V\n-6 -7 V\n-7 -8 V\n-7 -7 V\n-8 -7 V\n-9 -7 V\n-9 -7 V\n-11 -6 V\n-11 -7
826 V\n-13 -6 V\n-15 -5 V\n-15 -5 V\n-17 -5 V\n-19 -3 V\n-21 -3 V\n-22 -2
827 V\n-24 -1 V\n-26 0 V\n-28 3 V\n-29 5 V\n-30 7 V\n-31 10 V\n-30 14 V\n-29 17
828 V\n-26 21 V\n-22 25 V\n-18 28 V\n-10 31 V\n-3 34 V\n5 33 V\n15 33 V\n22 30
829 V\n30 26 V\n35 20 V\n40 15 V\n41 8 V\n42 3 V\n41 -3 V\n39 -6 V\n35 -11
830 V\n33 -12 V\n29 -14 V\n25 -15 V\n22 -16 V\n19 -16 V\n17 -15 V\n13 -15 V\n12
831 -15 V\n9 -14 V\n8 -13 V\n7 -13 V\n5 -13 V\n4 -11 V\n3 -11 V\n3 -11 V\n2 -10
832 V\n1 -10 V\n1 -9 V\n1 -9 V\n0 -9 V\n0 -8 V\n0 -8 V\n-1 -7 V\n0 -8 V\n-1 -7
833 V\n-1 -7 V\n-2 -6 V\n-2 -7 V\n-1 -6 V\n-3 -6 V\n-2 -6 V\n-3 -6 V\n-3 -5
834 V\n-4 -6 V\n-4 -5 V\n-4 -6 V\n-5 -5 V\n-6 -5 V\n-7 -5 V\n-7 -5 V\n-9 -5
835 V\n-9 -5 V\n-11 -5 V\n-12 -5 V\n-14 -5 V\n-15 -4 V\n-17 -4 V\n-20 -4 V\n-22
836 -4 V\n-24 -3 V\n-28 -2 V\n-30 -1 V\n-33 1 V\n-37 3 V\ncurrentpoint stroke
837 M\n-39 5 V\n-42 9 V\n1.000 UL\nLTb\n3024 948 M\n2128 464 L\n575 743 M\n2128
838 464 L\n575 743 M\n896 484 V\n3024 948 M\n1471 1227 L\n575 743 M\n0 968 V\n0
839 -968 R\n55 29 V\n stroke\n501 676 M\n[ [(Helvetica) 140.0 0.0 true true
840 (-20)]\n] -46.7 MCshow\n1471 1227 M\n-56 -30 V\n963 673 M\n55 29 V\n
841 stroke\n889 606 M\n[ [(Helvetica) 140.0 0.0 true true (-10)]\n] -46.7
842 MCshow\n1860 1157 M\n-56 -30 V\n1351 603 M\n55 29 V\n stroke\n1277 536 M\n[
843 [(Helvetica) 140.0 0.0 true true ( 0)]\n] -46.7 MCshow\n2248 1087 M\n-56
844 -30 V\n1739 533 M\n55 29 V\n stroke\n1665 466 M\n[ [(Helvetica) 140.0 0.0
845 true true ( 10)]\n] -46.7 MCshow\n2636 1018 M\n-56 -30 V\n2128 464 M\n55 29
846 V\n stroke\n2054 397 M\n[ [(Helvetica) 140.0 0.0 true true ( 20)]\n] -46.7
847 MCshow\n3024 948 M\n-56 -30 V\n2128 464 M\n-63 11 V\n stroke\n2210 439 M\n[
848 [(Helvetica) 140.0 0.0 true true (-20)]\n] -46.7 MLshow\n575 743 M\n62 -12
849 V\n2352 585 M\n-63 11 V\n stroke\n2434 560 M\n[ [(Helvetica) 140.0 0.0 true
850 true (-10)]\n] -46.7 MLshow\n799 864 M\n62 -12 V\n2576 706 M\n-63 11 V\n
851 stroke\n2658 681 M\n[ [(Helvetica) 140.0 0.0 true true ( 0)]\n] -46.7
852 MLshow\n1023 985 M\n62 -12 V\n2800 827 M\n-63 11 V\n stroke\n2882 802 M\n[
853 [(Helvetica) 140.0 0.0 true true ( 10)]\n] -46.7 MLshow\n1247 1106 M\n62
854 -12 V\n3024 948 M\n-63 11 V\n stroke\n3106 923 M\n[ [(Helvetica) 140.0 0.0
855 true true ( 20)]\n] -46.7 MLshow\n1471 1227 M\n62 -12 V\n575 1066 M\n63 0
856 V\n stroke\n449 1066 M\n[ [(Helvetica) 140.0 0.0 true true ( 0)]\n] -46.7
857 MRshow\n575 1195 M\n63 0 V\n stroke\n449 1195 M\n[ [(Helvetica) 140.0 0.0
858 true true ( 10)]\n] -46.7 MRshow\n575 1324 M\n63 0 V\n stroke\n449 1324
859 M\n[ [(Helvetica) 140.0 0.0 true true ( 20)]\n] -46.7 MRshow\n575 1453
860 M\n63 0 V\n stroke\n449 1453 M\n[ [(Helvetica) 140.0 0.0 true true (
861 30)]\n] -46.7 MRshow\n575 1582 M\n63 0 V\n stroke\n449 1582 M\n[
862 [(Helvetica) 140.0 0.0 true true ( 40)]\n] -46.7 MRshow\n575 1711 M\n63 0
863 V\n stroke\n449 1711 M\n[ [(Helvetica) 140.0 0.0 true true ( 50)]\n] -46.7
864 MRshow\nstroke\ngrestore\nend\nshowpage\n>|eps>||||||>|Embedded 3D graph
865 from Octave.>
867 <apply|tmdoc-copyright|2003|Chu-Ching Huang|Joris van der Hoeven>
869 <expand|tmdoc-license|Permission is granted to copy, distribute and/or
870 modify this document under the terms of the GNU Free Documentation License,
871 Version 1.1 or any later version published by the Free Software Foundation;
872 with no Invariant Sections, with no Front-Cover Texts, and with no
873 Back-Cover Texts. A copy of the license is included in the section entitled
874 "GNU Free Documentation License".>
875 </body>
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