1<TeXmacs|1.0.7.16>
2
3<style|tmdoc>
4
5<\body>
6  <tmdoc-title|Example of a <name|Reduce> session>
7
8  Here follows a sample session (with mathematical input mode).
9
10  <\session|reduce|default>
11    <\output>
12      \;
13
14      Reduce (Free PSL version), 31-Jan-2012 ...
15
16      \;
17    </output>
18
19    <\unfolded-io-math>
20      REDUCE]\ 
21    <|unfolded-io-math>
22      a\<assign\><around*|(|x+y|)><rsup|2>
23    <|unfolded-io-math>
24      <with|color|black|mode|math|math-display|true|a<with|math-font-family|rm|:=>x<rsup|2>+2*x*y+y<rsup|2>>
25    </unfolded-io-math>
26
27    <\unfolded-io-math>
28      REDUCE]\ 
29    <|unfolded-io-math>
30      x\<assign\>z+1$ a;
31    <|unfolded-io-math>
32      \;
33
34      <with|color|black|mode|math|math-display|true|y<rsup|2>+2*y*z+2*y+z<rsup|2>+2*z+1>
35    </unfolded-io-math>
36
37    <\unfolded-io-math>
38      REDUCE]\ 
39    <|unfolded-io-math>
40      x\<assign\>z-1$ a;
41    <|unfolded-io-math>
42      \;
43
44      <with|color|black|mode|math|math-display|true|y<rsup|2>+2*y*z-2*y+z<rsup|2>-2*z+1>
45    </unfolded-io-math>
46
47    <\unfolded-io-math>
48      REDUCE]\ 
49    <|unfolded-io-math>
50      clear x; a;
51    <|unfolded-io-math>
52      \;
53
54      <with|color|black|mode|math|math-display|true|x<rsup|2>+2*x*y+y<rsup|2>>
55    </unfolded-io-math>
56
57    <\unfolded-io-math>
58      REDUCE]\ 
59    <|unfolded-io-math>
60      <frac|x<rsup|2>+y<rsup|2>|x<rsup|2>-y<rsup|2>>-<frac|x<rsup|2>-y<rsup|2>|x<rsup|2>+y<rsup|2>>
61    <|unfolded-io-math>
62      <with|color|black|mode|math|math-display|true|<frac|4*x<rsup|2>*y<rsup|2>|x<rsup|4>-y<rsup|4>>>
63    </unfolded-io-math>
64
65    <\unfolded-io-math>
66      REDUCE]\ 
67    <|unfolded-io-math>
68      <around*|(|<sqrt|x>-<sqrt|y>|)><rsup|4>
69    <|unfolded-io-math>
70      <with|color|black|mode|math|math-display|true|-4*<sqrt|y>*<sqrt|x>*x-4*<sqrt|y>*<sqrt|x>*y+x<rsup|2>+6*x*y+y<rsup|2>>
71    </unfolded-io-math>
72
73    <\input-math>
74      REDUCE]\ 
75    <|input-math>
76      load_package trigsimp
77    </input-math>
78
79    <\unfolded-io-math>
80      REDUCE]\ 
81    <|unfolded-io-math>
82      trigsimp<around*|(|sin<around*|(|\<alpha\>|)>*cos<around*|(|\<beta\>|)>,combine|)>
83    <|unfolded-io-math>
84      <with|color|black|mode|math|math-display|true|<frac|sin<around*|(|\<alpha\>-\<beta\>|)>+sin<around*|(|\<alpha\>+\<beta\>|)>|2>>
85    </unfolded-io-math>
86
87    <\unfolded-io-math>
88      REDUCE]\ 
89    <|unfolded-io-math>
90      sin<around*|(|-x|)>; cos<around*|(|<frac|\<pi\>|6>|)>;
91      log<around*|(|\<mathe\><rsup|x>|)>;
92      <around*|(|2+3*\<mathi\>|)><rsup|2>;
93    <|unfolded-io-math>
94      <with|color|black|mode|math|math-display|true|-sin<around*|(|x|)>>
95
96      <with|color|black|mode|math|math-display|true|<frac|<sqrt|3>|2>>
97
98      <with|color|black|mode|math|math-display|true|x>
99
100      <with|color|black|mode|math|math-display|true|<with|math-font-family|rm|12>*i-5>
101    </unfolded-io-math>
102
103    <\unfolded-io-math>
104      REDUCE]\ 
105    <|unfolded-io-math>
106      a\<assign\>\<mathe\><rsup|c*x>*cos<around*|(|x|)>
107    <|unfolded-io-math>
108      <with|color|black|mode|math|math-display|true|a<with|math-font-family|rm|:=>e<rsup|c*x>*cos<around*|(|x|)>>
109    </unfolded-io-math>
110
111    <\unfolded-io-math>
112      REDUCE]\ 
113    <|unfolded-io-math>
114      df<around*|(|a,x|)>
115    <|unfolded-io-math>
116      <with|color|black|mode|math|math-display|true|e<rsup|c*x>*<around*|(|cos<around*|(|x|)>*c-sin<around*|(|x|)>|)>>
117    </unfolded-io-math>
118
119    <\input-math>
120      REDUCE]\ 
121    <|input-math>
122      clear a
123    </input-math>
124
125    <\unfolded-io-math>
126      REDUCE]\ 
127    <|unfolded-io-math>
128      <big|int><sqrt|x<rsup|2>+a>*\<mathd\>x
129    <|unfolded-io-math>
130      <with|color|black|mode|math|math-display|true|<frac|<sqrt|a+x<rsup|2>>*x+log<around*|(|<frac|<sqrt|a+x<rsup|2>>+x|<sqrt|a>>|)>*a|2>>
131    </unfolded-io-math>
132
133    <\input-math>
134      REDUCE]\ 
135    <|input-math>
136      load_package defint
137    </input-math>
138
139    <\unfolded-io-math>
140      REDUCE]\ 
141    <|unfolded-io-math>
142      <big|int><rsub|0><rsup|\<infty\>><frac|sin<around*|(|x|)>|x>*\<mathd\>x
143    <|unfolded-io-math>
144      <with|color|black|mode|math|math-display|true|<frac|\<pi\>|2>>
145    </unfolded-io-math>
146
147    <\unfolded-io-math>
148      REDUCE]\ 
149    <|unfolded-io-math>
150      <big|sum><rsub|n=0><rsup|m>n<rsup|2>
151    <|unfolded-io-math>
152      <with|color|black|mode|math|math-display|true|<frac|m*<around*|(|2*m<rsup|2>+3*m+1|)>|6>>
153    </unfolded-io-math>
154
155    <\unfolded-io-math>
156      REDUCE]\ 
157    <|unfolded-io-math>
158      <big|sum><rsub|n=1><rsup|10><frac|1|n<rsup|2>>
159    <|unfolded-io-math>
160      <with|color|black|mode|math|math-display|true|<frac|<with|math-font-family|rm|1968329>|<with|math-font-family|rm|1270080>>>
161    </unfolded-io-math>
162
163    <\input-math>
164      REDUCE]\ 
165    <|input-math>
166      load_package sum
167    </input-math>
168
169    <\unfolded-io-math>
170      REDUCE]\ 
171    <|unfolded-io-math>
172      <big|sum><rsub|n=1><rsup|\<infty\>><frac|1|n<rsup|2>>
173    <|unfolded-io-math>
174      <with|color|black|mode|math|math-display|true|<frac|\<pi\><rsup|2>|6>>
175    </unfolded-io-math>
176
177    <\input-math>
178      REDUCE]\ 
179    <|input-math>
180      load_package tps
181    </input-math>
182
183    <\unfolded-io-math>
184      REDUCE]\ 
185    <|unfolded-io-math>
186      sinx\<assign\>ps<around*|(|sin<around*|(|x|)>,x,0|)>
187    <|unfolded-io-math>
188      <with|color|black|mode|math|math-display|true|<with|math-font-family|rm|sinx:=>*x-<frac|1|6>*x<rsup|3>+<frac|1|<with|math-font-family|rm|120>>*x<rsup|5>+O<around*|(|x<rsup|7>|)>>
189    </unfolded-io-math>
190
191    <\unfolded-io-math>
192      REDUCE]\ 
193    <|unfolded-io-math>
194      cosx\<assign\>ps<around*|(|cos<around*|(|x|)>,x,0|)>
195    <|unfolded-io-math>
196      <with|color|black|mode|math|math-display|true|<with|math-font-family|rm|cosx:=>*1-<frac|1|2>*x<rsup|2>+<frac|1|<with|math-font-family|rm|24>>*x<rsup|4>-<frac|1|<with|math-font-family|rm|720>>*x<rsup|6>+O<around*|(|x<rsup|7>|)>>
197    </unfolded-io-math>
198
199    <\unfolded-io-math>
200      REDUCE]\ 
201    <|unfolded-io-math>
202      a\<assign\>sinx<rsup|2>+cosx<rsup|2>
203    <|unfolded-io-math>
204      <with|color|black|mode|math|math-display|true|a<with|math-font-family|rm|:=>1+O<around*|(|x<rsup|7>|)>>
205    </unfolded-io-math>
206
207    <\unfolded-io-math>
208      REDUCE]\ 
209    <|unfolded-io-math>
210      psexplim 10$ a;
211    <|unfolded-io-math>
212      \;
213
214      <with|color|black|mode|math|math-display|true|1+O<around*|(|x<rsup|<with|math-font-family|rm|11>>|)>>
215    </unfolded-io-math>
216
217    <\input-math>
218      REDUCE]\ 
219    <|input-math>
220      clear a,sinx,cosx
221    </input-math>
222
223    <\unfolded-io-math>
224      REDUCE]\ 
225    <|unfolded-io-math>
226      solve<around*|(|a*x<rsup|2>+b*x+c=0,x|)>
227    <|unfolded-io-math>
228      <with|color|black|mode|math|math-display|true|<around*|{|x=<frac|<sqrt|-4*a*c+b<rsup|2>>-b|2*a><space|0.25spc><with|math-font-family|rm|,<space|0.25spc>><space|0.25spc>x=<frac|-<around*|(|<sqrt|-4*a*c+b<rsup|2>>+b|)>|2*a>|}>>
229    </unfolded-io-math>
230
231    <\unfolded-io-math>
232      REDUCE]\ 
233    <|unfolded-io-math>
234      solve<around*|(|<around*|{|a*x+b*y=u,c*x+d*y=v|}>,<around*|{|x,y|}>|)>
235    <|unfolded-io-math>
236      <with|color|black|mode|math|math-display|true|<around*|{|<around*|{|x=<frac|-b*v+d*u|a*d-b*c><space|0.25spc><with|math-font-family|rm|,<space|0.25spc>><space|0.25spc>y=<frac|a*v-c*u|a*d-b*c>|}>|}>>
237    </unfolded-io-math>
238
239    <\unfolded-io-math>
240      REDUCE]\ 
241    <|unfolded-io-math>
242      m\<assign\><matrix|<tformat|<table|<row|<cell|a>|<cell|b>>|<row|<cell|c>|<cell|d>>>>>
243    <|unfolded-io-math>
244      <with|color|black|mode|math|math-display|true|m<with|math-font-family|rm|:=><around*|(|<tabular*|<tformat|<table|<row|<cell|a>|<cell|b>>|<row|<cell|c>|<cell|d>>>>>|)>>
245    </unfolded-io-math>
246
247    <\unfolded-io-math>
248      REDUCE]\ 
249    <|unfolded-io-math>
250      mi\<assign\>m<rsup|-1>
251    <|unfolded-io-math>
252      <with|color|black|mode|math|math-display|true|<with|math-font-family|rm|mi:=><around*|(|<tabular*|<tformat|<table|<row|<cell|<frac|d|a*d-b*c>>|<cell|<frac|-b|a*d-b*c>>>|<row|<cell|<frac|-c|a*d-b*c>>|<cell|<frac|a|a*d-b*c>>>>>>|)>>
253    </unfolded-io-math>
254
255    <\unfolded-io-math>
256      REDUCE]\ 
257    <|unfolded-io-math>
258      m*mi
259    <|unfolded-io-math>
260      <with|color|black|mode|math|math-display|true|<around*|(|<tabular*|<tformat|<table|<row|<cell|1>|<cell|0>>|<row|<cell|0>|<cell|1>>>>>|)>>
261    </unfolded-io-math>
262
263    <\input-math>
264      REDUCE]\ 
265    <|input-math>
266      clear m,mi
267    </input-math>
268
269    <\unfolded-io-math>
270      REDUCE]\ 
271    <|unfolded-io-math>
272      <det|<tformat|<table|<row|<cell|a>|<cell|b>>|<row|<cell|c>|<cell|d>>>>>
273    <|unfolded-io-math>
274      <with|color|black|mode|math|math-display|true|a*d-b*c>
275    </unfolded-io-math>
276
277    <\input-math>
278      REDUCE]\ 
279    <|input-math>
280      for all x,y let log<around*|(|x*y|)>=log<around*|(|x|)>+log<around*|(|y|)>,
281
282      log<around*|(|<frac|x|y>|)>=log<around*|(|x|)>-log<around*|(|y|)>,
283
284      log<around*|(|x<rsup|y>|)>=y*log<around*|(|x|)>
285    </input-math>
286
287    <\unfolded-io-math>
288      REDUCE]\ 
289    <|unfolded-io-math>
290      log<around*|(|x*\<mathe\><rsup|y>|)>
291    <|unfolded-io-math>
292      <with|color|black|mode|math|math-display|true|log<around*|(|x|)>+y>
293    </unfolded-io-math>
294
295    <\input-math>
296      REDUCE]\ 
297    <|input-math>
298      for all x,y clear log<around*|(|x*y|)>,log<around*|(|<frac|x|y>|)>,log<around*|(|x<rsup|y>|)>
299    </input-math>
300
301    <\unfolded-io-math>
302      REDUCE]\ 
303    <|unfolded-io-math>
304      procedure fac<around*|(|n|)>;
305
306      if n\<gtr\>1 then n*fac<around*|(|n-1|)> else 1;
307    <|unfolded-io-math>
308      <with|color|black|mode|math|math-display|true|math-font-family|rm|fac>
309    </unfolded-io-math>
310
311    <\unfolded-io-math>
312      REDUCE]\ 
313    <|unfolded-io-math>
314      load_package rdebug
315    <|unfolded-io-math>
316      *** fluid \0lispsystem!*' cannot become global
317
318      *** \0break_prompt' has not been defined, because it is flagged LOSE
319
320      \;
321    </unfolded-io-math>
322
323    <\unfolded-io-math>
324      REDUCE]\ 
325    <|unfolded-io-math>
326      tr fac
327    <|unfolded-io-math>
328      \;
329
330      (fac)
331
332      \;
333    </unfolded-io-math>
334
335    <\unfolded-io-math>
336      REDUCE]\ 
337    <|unfolded-io-math>
338      fac<around*|(|5|)>
339    <|unfolded-io-math>
340      fac being entered
341
342      \ \ \ n: \ \ 5
343
344      \;
345
346      \ \ fac (level 2) being entered
347
348      \ \ \ \ \ n: 4
349
350      \;
351
352      \ \ \ \ fac (level 3) being entered
353
354      \ \ \ \ \ \ \ n: \ \ \ \ \ \ 3
355
356      \;
357
358      \ \ \ \ \ \ fac (level 4) being entered
359
360      \ \ \ \ \ \ \ \ \ n: \ \ \ \ 2
361
362      \;
363
364      \ \ \ \ \ \ \ \ fac (level 5) being entered
365
366      \ \ \ \ \ \ \ \ \ \ \ n: \ \ 1
367
368      \;
369
370      \ \ \ \ \ \ \ \ fac (level 5) = 1
371
372      \;
373
374      \ \ \ \ \ \ fac (level 4) = 2
375
376      \;
377
378      \ \ \ \ fac (level 3) = 6
379
380      \;
381
382      \ \ fac (level 2) = 24
383
384      \;
385
386      fac = 120
387
388      \;
389
390      <with|color|black|mode|math|math-display|true|120>
391    </unfolded-io-math>
392
393    <\input-math>
394      REDUCE]\ 
395    <|input-math>
396      untr fac
397    </input-math>
398
399    <\input-math>
400      REDUCE]\ 
401    <|input-math>
402      load_package gnuplot
403    </input-math>
404
405    <\input-math>
406      REDUCE]\ 
407    <|input-math>
408      plot<around*|(|<frac|sin<around*|(|x|)>|x>,x=<around*|(|-4*\<pi\>\<ldots\>4*\<pi\>|)>|)>
409    </input-math>
410
411    <\unfolded-io-math>
412      REDUCE]\ 
413    <|unfolded-io-math>
414      bye
415    <|unfolded-io-math>
416      \;
417
418      Quitting
419
420      <script-dead>
421    </unfolded-io-math>
422
423    <\input-math>
424      REDUCE]\ 
425    <|input-math>
426      \;
427    </input-math>
428  </session>
429
430  <tmdoc-copyright|2012|Andrey Grozin>
431
432  <tmdoc-license|Permission is granted to copy, distribute and/or modify this
433  document under the terms of the GNU Free Documentation License, Version 1.1
434  or any later version published by the Free Software Foundation; with no
435  Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
436  Texts. A copy of the license is included in the section entitled "GNU Free
437  Documentation License".>
438</body>
439
440<\initial>
441  <\collection>
442    <associate|language|english>
443    <associate|preamble|false>
444  </collection>
445</initial>