Annotation of OpenXM/src/asir-doc/parts/risa.texi, Revision 1.9
1.9 ! noro 1: @comment $OpenXM: OpenXM/src/asir-doc/parts/risa.texi,v 1.8 2000/01/26 01:37:32 noro Exp $
1.1 noro 2: @node Risa/Asir,,, Top
3: @chapter Risa/Asir
4:
5: @menu
1.2 noro 6: \BJP
1.1 noro 7: * Risa $B$*$h$S(B Asir::
8: * Asir $B$NFCD'(B::
1.9 ! noro 9: * Installation::
1.1 noro 10: * $B%3%^%s%I%i%$%s%*%W%7%g%s(B::
11: * $B4D6-JQ?t(B::
12: * $B5/F0$+$i=*N;$^$G(B::
13: * $B3d$j9~$_(B::
14: * $B%(%i!<=hM}(B::
15: * $B7W;;7k2L$*$h$SFC<l$J?t(B::
1.2 noro 16: \E
17: \BEG
18: * Risa and Asir::
19: * Features of Asir::
20: * Installation::
21: * Command line options::
22: * Environment variable::
23: * Starting and Terminating an Asir session::
24: * Interruption::
25: * Error handling::
26: * Referencing results and special numbers::
27: \E
1.1 noro 28: @end menu
29:
1.2 noro 30: \BJP
1.1 noro 31: @node Risa $B$*$h$S(B Asir,,, Risa/Asir
32: @section Risa $B$*$h$S(B Asir
1.2 noro 33: \E
34: \BEG
35: @node Risa and Asir,,, Risa/Asir
36: @section @b{Risa} and @b{Asir}
37: \E
1.1 noro 38:
39: @noindent
1.2 noro 40: \BJP
1.1 noro 41: @b{Risa} $B$O(B, $BIY;NDL8&$G3+H/Cf$N?t<0=hM}%7%9%F%`(B/$B%i%$%V%i%j$NAm>N$G$"$k(B.
42: @b{Risa} $B$N9=@.$O<!$NDL$j$G$"$k(B.
1.2 noro 43: \E
44: \BEG
45: @b{Risa} is the name of whole libraries of a computer algebra system
46: which is under development at FUJITSU LABORATORIES LIMITED.
47: The structure of @b{Risa} is as follows.
48: \E
1.1 noro 49:
50: @itemize @bullet
51: @item
1.2 noro 52: \JP @code{$B4pK\1i;;It(B}
53: \EG @b{The basic algebraic engine}
1.8 noro 54: @*
1.2 noro 55: \BJP
1.1 noro 56: $B$3$l$O(B, @b{Risa} $B$NFbIt7A<0$KJQ49$5$l$?%*%V%8%'%/%H(B ($B?t(B, $BB?9`<0$J$I(B)
57: $B$N4V$N1i;;$r<B9T$9$kItJ,$G$"$j(B, UNIX $B$N(B @samp{libc.a} $B$J$I$HF1MM$N(B, $B%i%$%V%i(B
58: $B%j$H$7$FB8:_$9$k(B. $B%(%s%8%s$O(B, C $B$*$h$S(B $B%"%;%s%V%i$G5-=R$5$l(B, $B8e=R$9$k(B
1.2 noro 59: $B8@8l%$%s%?%U%'!<%9(B @b{Asir} $B$N4pK\1i;;It$H$7$FMQ$$$i$l$F$$$k(B.
60: @comment $B0lJ}(B, $B?t<07W;;$rI,MW$H$9$k$5$^$6$^$J%W%m%0%i%`Cf$K%j%s%/$7$FMQ$$$k$3$H$,$G$-$k(B.
61: \E
62: \BEG
63: This is the part which performs basic algebraic operations,
64: such as arithmetic operations, to algebraic objects, e.g., numbers and
65: polynomials, which are already converted into internal forms.
66: It exists, like @samp{libc.a} of UNIX, as a library of ordinary UNIX system.
67: The algebraic engine is written mainly in C language and
68: partly in assembler.
69: It serves as the basic operation part of @b{Asir}, a standard
70: language interface of @b{Risa}.
71: @comment It can also be linked to various programs that need some symbolic
72: @comment and algebraic computation.
73: \E
74:
1.1 noro 75: @item
1.2 noro 76: \JP @code{$B%a%b%j4IM}It(B}
77: \EG @b{Memory Manager}
1.8 noro 78: @*
1.2 noro 79: \BJP
1.1 noro 80: @b{Risa} $B$G$O(B, $B%a%b%j4IM}It$H$7$F(B, @code{[Boehm,Weiser]} $B$K$h$k%U%j!<(B
81: $B%=%U%H%&%'%"(B (@code{gc-5.0alpha2}) $B$rMQ$$$F$$$k(B. $B$3$l$O%,!<%Y%8%3%l%/%7%g%s(B
82: ($B0J2<(B GC $B$H8F$V(B) $B$r<+F0E*$K9T$&%a%b%j3d$jEv$F5!9=$r;}$A(B, @b{Risa} $B$N3F(B
83: $BItJ,$O$9$Y$F$3$l$K$h$jI,MW$J%a%b%j$rF@$F$$$k(B.
1.2 noro 84: \E
85: \BEG
86: @b{Risa} employs, as its memory management component (the memory
87: manager), a free software distributed by Boehm (@code{gc-5.0alpha2}).
88: It is proposed by @code{[Boehm,Weiser]}, and developed by Boehm and
89: his colleagues.
90: The memory manager has a memory allocator which automatically
91: reclaims garbages, i.e., allocated but unused memories,
92: and refreshes them for further use.
93: The algebraic engine gets all its necessary memories through the memory
94: manager.
95: \E
1.1 noro 96:
97: @item
98: @b{Asir}
1.8 noro 99: @*
1.2 noro 100: \BJP
1.1 noro 101: @b{Asir} $B$O(B, @b{Risa} $B$N7W;;%(%s%8%s$N8@8l%$%s%?%U%'!<%9$G(B
102: $B$"$k(B. @b{Risa} $B$G$O(B, $BHf3SE*MF0W$K%f!<%6MQ$N8@8l%$%s%?%U%'!<%9$r:n$k(B
103: $B$3$H$,$G$-$k(B. @b{Asir} $B$O$=$N0l$D$NNc$H$7$F:n$C$?$b$N$G(B, C $B8@8l$K6a(B
104: $B$$J8K!$r$b$D(B. $B$^$?(B, C $B$N%G%P%C%,$H$7$F9-$/MQ$$$i$l$F$$$k(B @code{dbx} $BIw(B
105: $B$N%G%P%C%,$bHw$($F$$$k(B.
1.2 noro 106: \E
107: \BEG
108: @b{Asir} is a standard language interface of @b{Risa}'s algebraic
109: engine. It is one of the possible language interfaces, because
110: one can develop one's own language interface easily on @b{Risa}
111: system.
112: @b{Asir} is an example of such language interfaces.
113: @b{Asir} has very similar syntax and semantics as C language.
114: Furthermore, it has a debugger that provide a subset of commands of
115: @code{dbx}, a widely used debugger of C language.
116: \E
1.1 noro 117: @end itemize
118:
1.2 noro 119: \BJP
1.1 noro 120: @node Asir $B$NFCD'(B,,, Risa/Asir
121: @section Asir $B$NFCD'(B
1.2 noro 122: \E
123: \BEG
124: @node Features of Asir,,, Risa/Asir
125: @section Features of @b{Asir}
126: \E
1.1 noro 127:
128: @noindent
1.2 noro 129: \BJP
1.1 noro 130: @b{Asir} $B$O(B, $BA0=R$NDL$j(B, $B7W;;%(%s%8%s$N8@8l%$%s%?%U%'!<%9$G$"(B
131: $B$k(B. $BDL>o(B @b{Asir} $B$H$$$&L>A0$N<B9T2DG=%U%!%$%k$H$7$FDs6!$5$l$k(B.
132: $B8=:_%5%]!<%H$5$l$F$$$k5!G=$O35$M<!$NDL$j$G$"$k(B.
1.2 noro 133: \E
134: \BEG
135: As mentioned in the previous section, @b{Asir} is a standard language
136: interface for@b{Risa}'s algebraic engine.
137: Usually, it is provided as an executable file named @code{asir}.
138: Main features supported for the current version of Asir is as follows.
139: \E
1.1 noro 140:
141: @itemize @bullet
1.2 noro 142: \BJP
1.1 noro 143: @item
144: C $B8@8lIw$N%f!<%68@8l(B
145:
146: @item
147: $B?t(B, $BB?9`<0(B, $BM-M}<0$N2C8:>h(B($B=|(B)
148:
149: @item
150: $B%Y%/%H%k(B, $B9TNs$N1i;;(B
151:
152: @item
153: $B:G>.8B$N%j%9%H=hM}(B
154:
155: @item
156: $BAH$_9~$_H!?t(B ($B0x?tJ,2r(B, GCD, $B%0%l%V%J4pDl$J$I(B)
157:
158: @item
159: $B%f!<%6Dj5AH!?t$K$h$k%D!<%k(B ($BBe?tBN>e$N0x?tJ,2r$J$I(B)
160:
161: @item
162: @code{dbx} $BIw$N%G%P%C%,(B
163:
164: @item
165: $B1"H!?t$NIA2h(B
166:
167: @item
168: @b{PARI} (@pxref{pari}) $B$K$h$k=iEyD61[H!?t$r4^$`<0$NI>2A(B
169:
170: @item
171: UNIX $B>e$G$NJ,;67W;;5!G=(B (Open XM)
172: @comment @item
173: @comment $B%R%9%H%jCV495!G=$r$b$D(B X11 $B%$%s%?%U%'!<%9(B
1.2 noro 174: \E
175: \BEG
176: @item
177: A C-like programming language
178:
179: @item
180: Arithmetic operations (addition, subtraction, multiplication
181: and division) on numbers, polynomials and rational expressions
182:
183: @item
184: Operations on vectors and matrices
185:
186: @item
187: List processing operations at the minimum
188:
189: @item
190: Several Built-in functions (factorization, GCD computation, Groebner basis
191: computation etc.)
192:
193: @item
194: Useful user defined functions(e.g., factorization over algebraic number fields)
195:
196: @item
197: A @code{dbx}-like debugger
198:
199: @item
200: Plotting of implicit functions
201:
202: @item
203: Numerical evaluation of mathematical expressions including elementary
204: transcendental functions at arbitrary precision. This feature is
205: in force only if @b{PARI} system (@pxref{pari}).
206:
207: @item
208: Distributed computation over UNIX
209: \E
1.1 noro 210: @end itemize
211:
1.2 noro 212: @node Installation,,, Risa/Asir
213: @section Installation
214:
215: \JP $B0J2<$N<jB3$-$GITL@$JE@(B, $BITET9g$JE@$,$"$C$?>l9g$NLd$$9g$o$;$O(B
216: \BEG
1.9 ! noro 217: Any questions and any comments on this manual are welcome by e-mails
1.2 noro 218: to the following address.
219: \E
1.1 noro 220:
221: @example
1.9 ! noro 222: risa-admin@@sec.flab.fujitsu.co.jp
1.1 noro 223: @end example
224:
225: @noindent
1.2 noro 226: \JP $B08$K(B e-mail $B$G$*4j$$$7$^$9(B.
1.1 noro 227:
228: @menu
1.9 ! noro 229: * UNIX binary version::
! 230: * UNIX source code version::
1.2 noro 231: * Windows version::
1.1 noro 232: @end menu
233:
1.9 ! noro 234: @node UNIX binary version,,, Installation
! 235: @subsection UNIX binary version
1.1 noro 236:
237: @noindent
1.2 noro 238: \BJP
1.9 ! noro 239: $B%?!<%2%C%H(B CPU/OS $B$KBP1~$9$k(B @samp{asir.tgz} $B$,I,MW$G$"$k(B.
1.1 noro 240: $B$3$l$i$OA4$F(B @code{gzip} $B$G05=L$7$F$"$k$N$G(B, $BF~<j8e(B @code{gzip} $B$G(B
241: $BE83+$9$k(B. $B$^$:(B, $B%$%s%9%H!<%k$9$k%G%#%l%/%H%j$r7h$a$k(B. $B%G%U%)%k%H$G$O(B
242: @samp{/usr/local/lib} $B$K(B @samp{asir} $B$H$$$&%G%#%l%/%H%j$H$7$F(B
243: $B%$%s%9%H!<%k$5$l$k$3$H$r2>Dj$7$F$$$k(B. $B0J2<$3$N%G%#%l%/%H%j$r%i%$%V%i%j(B
244: $B%G%#%l%/%H%j$H8F$V(B.
1.2 noro 245: \E
246: \BEG
1.9 ! noro 247: A file @samp{asir.tgz} suitable for the target machine/architecture
1.2 noro 248: is required. After getting it,
249: you have to unpack it by @code{gzip}. First of all, determine
250: a derectory where binaries and library files are installed.
251: We call the directory the @b{library directory}.
252: The following installs the files in @samp{/usr/local/lib/asir}.
253: \E
1.1 noro 254:
255: @example
256: # gzip -dc asir.tgz | ( cd /usr/local/lib; tar xf - )
257: @end example
258:
1.2 noro 259: \JP $B8D?ME*$K;HMQ$9$k>l9g$K$O(B, @samp{$HOME}$B$J$I$KCV$$$F$b$h$$(B.
260: \BEG
261: In this case you don't have to set any environment variable.
1.1 noro 262:
1.2 noro 263: You can install them elsewhere.
264: \E
1.1 noro 265: @example
266: % gzip -dc asir.tgz | ( cd $HOME; tar xf - )
267: @end example
268:
269: @noindent
1.2 noro 270: \BJP
1.1 noro 271: $B$3$N>l9g(B, $B%i%$%V%i%j%G%#%l%/%H%j$NL>A0$r4D6-JQ?t(B
272: @code{ASIR_LIBDIR} $B$K@_Dj$9$kI,MW$,$"$k(B.
1.2 noro 273: \E
274: \BEG
275: In this case you have to set the name of the library directory
276: to the environment variable @code{ASIR_LIBDIR}.
277: \E
1.1 noro 278:
279: @example
280: % setenv ASIR_LIBDIR $HOME/asir
281: @end example
282:
283: @noindent
1.2 noro 284: \BJP
1.1 noro 285: Asir $BK\BN$O(B, $B%i%$%V%i%j%G%#%l%/%H%j$N(B @samp{asir} $B$G$"$k(B.
286: @samp{/usr/local/bin} $B$"$k$$$O%f!<%6$N<B9T%U%!%$%k%5!<%A%Q%9(B
287: $B$N$I$3$+$K%7%s%\%j%C%/%j%s%/$r:n$k$HJXMx$G$"$k(B.
1.2 noro 288: \E
289: \BEG
290: @b{Asir} itself is in the library directory. It will be convenient
291: to create a symbolic link to it from @samp{/usr/local/bin} or
292: the user's search path.
293: \E
1.1 noro 294:
295: @example
296: # ln -s /usr/local/lib/asir/asir /usr/local/bin/asir
297: @end example
298:
299: @noindent
1.9 ! noro 300: \JP $B$3$l$G(B @samp{asir} $B$,5/F0$G$-$k(B.
1.2 noro 301: \BEG
1.9 ! noro 302: Then you can start @samp{asir}.
1.2 noro 303: \E
1.1 noro 304:
305: @example
306: % /usr/local/bin/asir
1.9 ! noro 307: This is Risa/Asir, Version 20000821.
! 308: Copyright (C) FUJITSU LABORATORIES LIMITED.
! 309: 1994-2000. All rights reserved.
! 310: [0]
1.1 noro 311: @end example
312:
1.9 ! noro 313: @node UNIX source code version,,, Installation
! 314: @subsection UNIX source code version
1.1 noro 315:
1.9 ! noro 316: \BEG
! 317: First of all you have to install PARI library. The following is
! 318: a sample of installation of PARI on FreeBSD.
1.2 noro 319: \E
1.9 ! noro 320: \BJP
! 321: $B$^$:(B PARI $B%i%$%V%i%j$r(B install $B$9$kI,MW$,$"$k(B. $B0J2<$O(B FreeBSD $B>e$G$N(B
! 322: PARI $B$N(B installation $B$NNc$G$"$k(B.
1.2 noro 323: \E
1.1 noro 324:
325: @example
1.9 ! noro 326: % su
! 327: # gzip -dc pari-2.0.17.beta.tgz | tar xf -
! 328: # cd pari-2.0.17.beta
! 329: # ./Configure
! 330: # make install
! 331: # make install-lib-sta
1.1 noro 332: @end example
333:
1.2 noro 334: \BJP
1.9 ! noro 335: @samp{asir2000-src.tgz} $B$rF~<j8e(B, $BE,Ev$J%G%#%l%/%H%j(B
! 336: $B$K$*$$$F(B, @code{gzip} $B$GE83+$7(B, $B0J2<$N<j=g$G(B install $B$9$k(B.
! 337: \E
! 338: \BEG
! 339: After getting @samp{asir2000-src.tgz}, unpack it by @code{gzip}
! 340: and install necessary files as follows.
1.2 noro 341: \E
1.1 noro 342:
343: @example
1.9 ! noro 344: % gzip -dc asir.tgz | tar xf -
! 345: % cd asir2000
! 346: % ./configure -oxhome /usr/local -pari -plot
! 347: % xmkmf -a
! 348: % make
! 349: % su
! 350: # make install
! 351: # make install-lib
! 352: # make install-doc
1.1 noro 353: @end example
354:
1.2 noro 355: \BJP
1.9 ! noro 356: $B>e$NNc$G(B, @samp{/usr/local} $B$O%U%!%$%k$,(B install $B$5$l$k%G%#%l%/%H%j$r(B
! 357: $BI=$9(B. $BB($A(B, $B%P%$%J%j%U%!%$%k(B @samp{asir} $B$O(B @samp{/usr/local/bin}
! 358: $B$K(B install $B$5$l(B, $B%i%$%V%i%j$*$h$SJ8=q%U%!%$%k$O(B @samp{/usr/local/lib}
! 359: $B$K(B install $B$5$l$k(B. @code{-oxhome} $B$N0z?t$H$7$F;XDj$5$l$k%G%#%l%/%H%j(B
! 360: $B$O(B, PARI $B$N(B install $B@h$b$=$3$G$"$k$3$H$r0UL#$9$k(B. $B$b$7(B @b{Asir} $B$,(B
! 361: install $B$5$l$k%G%#%l%/%H%j$rJQ99$9$k>l9g(B, @samp{include/Risa.tmpl}
! 362: $B$N(B, $BJQ?t(B @code{PARIINC} $B$*$h$S(B @code{PARILIB} $B$NCM$rE,59JQ99$9$k(B
! 363: $BI,MW$,$"$k(B.
1.2 noro 364: \E
365: \BEG
1.9 ! noro 366: In the above example, @samp{/usr/local} indicates the destination of the
! 367: installation. That is, the binary file @samp{asir} is installed in
! 368: @samp{/usr/local/bin} and the library and documentation files are
! 369: installed in @samp{/usr/local/lib}. The directory name specified as an
! 370: argument of @code{-oxhome} also indicates that PARI files are installed
! 371: in that directory. If you change the destination directory, you have to
! 372: modify the values of @code{PARIINC} and @code{PARILIB} in
! 373: @samp{include/Risa.tmpl} appropriately.
! 374: \E
! 375:
1.2 noro 376: @node Windows version,,, Installation
377: @subsection Windows version
1.1 noro 378:
379: @noindent
1.2 noro 380: \BJP
1.1 noro 381: $BI,MW$J%U%!%$%k$O(B @samp{asirwin.tgz} $B$G$"$k(B. $BB>$K(B, @samp{gzip.exe},
382: @samp{tar.exe} $B$,I,MW$@$,(B, asirwin.tgz $B$HF1$8%G%#%l%/%H%j$KMQ0U$7$F(B
383: $B$"$k(B. $B$3$l$i(B 3 $B$D$N%U%!%$%k$rF10l%G%#%l%/%H%j$K$*$-(B, DOS $B%W%m%s%W%H(B
384: $B$+$i(B
1.2 noro 385: \E
386: \BEG
387: The necessary file is @samp{asirwin.tgz}. To unpack it @samp{gzip.exe}
388: and @samp{tar.exe} are necessary. They are in the same
389: directory as @samp{asirwin.tgz} on the ftp server.
390: Putting them in the same directory, execute the following:
391: \E
1.1 noro 392:
393: @example
1.2 noro 394: \JP C:\...> tar xzf asirwin.tgz
395: \EG C:\...> tar xzf asirwin.tgz
1.1 noro 396: @end example
397:
398: @noindent
1.2 noro 399: \BJP
1.1 noro 400: $B$r<B9T$9$l$P(B, @samp{Asir} $B$H$$$&%G%#%l%/%H%j(B (Asir $B%k!<%H%G%#%l%/%H%j(B)
401: $B$,$G$-$k(B. 990831 $BHG$G$O(B, GUI $B$HK\BN$,J,N%$5$l(B, $B$^$?%G%P%C%0%&%#%s%I%&$b(B
402: $BJL%W%m%;%9$H$7$F(B GUI $B$,8F$S=P$5$l$k$?$a(B, Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/(B
403: $BEPO?$5$l$F$$$k$3$H$,I,MW$G$"$k(B. Asir $B%k!<%H%G%#%l%/%H%j$N%5%V%G%#%l%/%H(B
404: $B%j(B @samp{bin} $B$K(B @samp{asirgui.exe} (GUI), @samp{engine.exe} ($BK\BN(B) $B$,(B
405: $BCV$+$l$F$$$k(B. @samp{asirgui.exe} $B$N=i2s$NN)$A>e$2$O(B, $B%(%/%9%W%m!<%i$+$i9T(B
406: $B$&(B. $B$3$l$K$h$j(B
1.2 noro 407: \E
408:
409: \BEG
410: Then a directory @samp{Asir} (@b{Asir root directory}) is created,
411: which has subdirectories named @samp{bin} and @samp{lib}. To set up it,
412: invoke @samp{bin\asirgui.exe} from Explorer and
413: click @code{OK}. Then the name of @b{Asir root directory} is set to the
414: following registries.
415: \E
1.1 noro 416:
417: @example
1.2 noro 418: \JP HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory
419: \EG HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory
1.1 noro 420: @end example
421:
422: @noindent
1.2 noro 423: \JP $B$H$$$&%l%8%9%H%j$K(B Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/EPO?$5$l$k(B.
1.1 noro 424:
1.2 noro 425: \BJP
1.1 noro 426: @node $B%3%^%s%I%i%$%s%*%W%7%g%s(B,,, Risa/Asir
427: @section $B%3%^%s%I%i%$%s%*%W%7%g%s(B
1.2 noro 428: \E
429: \BEG
430: @node Command line options,,, Risa/Asir
431: @section Command line options
432: \E
1.1 noro 433:
434: @noindent
1.2 noro 435: \JP $B%3%^%s%I%i%$%s%*%W%7%g%s$O<!$NDL$j(B.
436: \EG Command-line options for the command @samp{asir} are as follows.
1.1 noro 437:
438: @table @code
439:
440: @item -heap @var{number}
1.2 noro 441: \BJP
1.1 noro 442: @code{Risa/Asir} $B$G$O(B, 4KB $B$N%V%m%C%/$r%a%b%j3d$jEv$F$NC10L$H$7$FMQ$$$F$$$k(B.
443: $B%G%U%)%k%H$G$O(B, $B=i4|(B heap $B$H$7$F(B, 16 $B%V%m%C%/(B (64KB) $B3d$jEv$F$k$,(B, $B$=$l(B
444: $B$rJQ99$9$k>l9g(B, @code{-heap} $B$rMQ$$$k(B. $BC10L$O%V%m%C%/$G$"$k(B.
445: heap $B$NBg$-$5$O(B, @code{heap()} $BH!?t$GD4$Y$k$3$H$,$G$-$k(B ($BC10L$O%P%$%H(B).
1.2 noro 446: \E
447: \BEG
448: In @b{Risa/Asir}, 4KB is used as an unit, called block,
449: for memory allocation.
450: By default, 16 blocks (64KB) are allocated initially.
451: This value can be changed by giving an option @code{-heap}
452: a number parameter in unit block.
453: Size of the heap area is obtained by a Built-in function heap(),
454: the result of which is a number in Bytes.
455: \E
1.1 noro 456:
457: @item -adj @var{number}
1.2 noro 458: \BJP
1.1 noro 459: $B$3$NCM$,Bg$-$$$[$I(B, $B;HMQ%a%b%jNL$OBg$-$/$J$k$,(B, GC $B;~4V$,>/$J$/$J(B
460: $B$k(B. @var{number} $B$H$7$F(B 1 $B0J>e$N@0?t$,;XDj$G$-$k(B. $B%G%U%)%k%H$G$O(B 3 $B$G$"(B
461: $B$k(B. $B$3$NCM$,(B 1 $B0J2<$K$J$k$H(B GC $B$r$7$J$$@_Dj$K$J$k$N$GMWCm0U$G$"$k(B. heap
462: $B$r$J$k$Y$/?-$P$5$:$K(B, GC $B$r<gBN$K$7$F%a%b%j4IM}$7$?$$>l9g$K$O(B, $B$3$NCM$r(B
463: $BBg$-$/(B ($BNc$($P(B 8) $B@_Dj$9$k(B.
1.2 noro 464: \E
465: \BEG
466: Heap area will be stretched by the memory manager,
467: if the size of reclaimed memories is less than 1/@var{number}
468: of currently allocated heap area.
469: The default value for @var{number} is 3.
470: If you do not prefer to stretch heap area by some reason, perhaps by
471: restriction of available memories, but if prefer to resort to
472: reclaiming garbages as far as possible,
473: then a large value should be chosen for @var{number}, e.g., 8.
474: \E
1.1 noro 475:
476: @item -norc
1.2 noro 477: \JP $B=i4|2=%U%!%$%k(B @samp{$HOME/.asirrc} $B$rFI$^$J$$(B.
478: \BEG
479: When this option is specified, @b{Asir} does not read the
480: initial file @samp{$HOME/.asirrc}.
481: \E
1.1 noro 482:
483: @item -f @var{file}
1.2 noro 484: \BJP
1.1 noro 485: $BI8=`F~NO$NBe$o$j$K(B, @var{file} $B$+$iF~NO$rFI$_9~$s$G<B9T$9$k(B.
486: $B%(%i!<$N:]$K$O$?$@$A$K=*N;$9$k(B.
1.2 noro 487: \E
488: \BEG
489: Instead of the standard input, @var{file} is used as the input.
490: Upon an error, the execution immediately terminates.
491: \E
1.1 noro 492:
493: @item -paristack @var{number}
1.2 noro 494: \BJP
1.1 noro 495: @b{PARI} (@pxref{pari}) $B@lMQ$NNN0h$NBg$-$5$r;XDj$9$k(B. $BC10L$O%P%$%H(B. $B%G%U%)(B
496: $B%k%H$G$O(B 1 MB.
1.2 noro 497: \E
498: \BEG
499: This option specifies the private memory size for @code{PARI} (@pxref{pari}).
500: The unit is Bytes. By default, it is set to 1 MB.
501: \E
1.1 noro 502:
503: @item -maxheap @var{number}
1.2 noro 504: \BJP
1.1 noro 505: heap $BNN0h$N>e8B$r;XDj$9$k(B. $BC10L$O%P%$%H(B. $B%G%U%)%k%H$G$OL5@)8B(B. UNIX $B$N(B
506: $B>l9g(B, $B<B:]$K$O(B @code{limit} $B%3%^%s%I$GI=<($5$l$k(B @code{datasize} $B$NCM(B
507: $B$K@)8B$5$l$F$$$k$?$a(B, @code{-maxheap} $B$N;XDj$,$J$/$F$b0lDjNL0J>e$K(B
508: heap $B$r3MF@$G$-$J$$>l9g$,$"$k$N$GCm0U(B.)
1.2 noro 509: \E
510: \BEG
511: This option sets an upper limit of the heap size. The unit is Bytes.
512: Note that the size is already limited by the value of @code{datasize}
513: displayed by the command @code{limit} on UNIX.
514: \E
1.1 noro 515: @end table
516:
1.2 noro 517: \BJP
1.1 noro 518: @node $B4D6-JQ?t(B,,, Risa/Asir
519: @section $B4D6-JQ?t(B
1.2 noro 520: \E
521: \BEG
522: @node Environment variable,,, Risa/Asir
523: @section Environment variable
524: \E
1.1 noro 525:
526: @noindent
1.2 noro 527: \BJP
1.1 noro 528: @b{Asir} $B$N<B9T$K4X$9$k$$$/$D$+$N4D6-JQ?t$,B8:_$9$k(B. UNIX $B>e$G$O4D6-JQ?t(B
529: $B$O(B shell $B$N%3%^%s%I%i%$%s$+$iD>@\@_Dj$9$k$+(B, shell $B$N(B rc $B%U%!%$%k$G@_Dj(B
530: $B$9$k(B. Windows NT $B$G$O(B, [$B@_Dj(B]->[$B%7%9%F%`(B]->[$B4D6-(B] $B$G@_Dj$9$k(B. Windows 95/98
531: $B$G$O(B, @samp{c:\autoexec.bat} $B$K=q$$$F(B reboot $B$9$k(B.
1.2 noro 532: \E
533: \BEG
534: There exist several environment variables concerning with an execution
535: of @b{Asir}. On UNIX, an environment variable is set from shells, or
536: in rc files of shells. On Windows NT, it can be set from [Control Panel]
537: ->[Environment]. On Windows 95/98, it can be set in @samp{c:\autoexec.bat}.
538: Note that the setting takes effect after rebooting the machine on Windows
539: 95/98.
540: \E
1.1 noro 541: @itemize @bullet
542: @item
543: @code{ASIR_KEY}
1.8 noro 544: @*
1.2 noro 545: \BJP
1.1 noro 546: UNIX $BHG$G$O(B, @b{Asir} $B$,5/F0$5$l$?%^%7%s$KBP$9$k(B @code{key} $B$,$J$1(B
547: $B$l$P$=$N%^%7%s>e$G(B @b{Asir} $B$OF0:n$7$J$$(B. @code{key} $B$O(B 16 $B?J(B 8
548: $B7e(B 3 $B%o!<%I$+$i$J$j(B,
1.2 noro 549: \E
550: \BEG
551: @b{Asir} shall not work unless a @code{key} for the machine
552: on which @b{Asir} is invoked is given.
553: The @code{key} consists of a string which denotes 3 word hexadecimal
554: number, each of which has 8 hexadecimal digits.
555: In order to run @b{Asir} for several machines,
556: several @code{key}'s can be written together on a same file as follows.
557: \E
1.1 noro 558: @example
559: % cat asir_key
560: cf6f236c 61a35091 dddc4529 geisha
561: 82281685 d1929945 a8bd24ca yorktown
562: 34b75d30 63f8df93 3e881113 nyanchu
563: @end example
564:
1.2 noro 565: \BJP
1.1 noro 566: $B$H$$$&7A$GJ#?tBf$N%^%7%s$KBP$9$k(B @code{key} $B$r0l$D$N%U%!%$%k$K$^$H$a$F(B
567: $B=q$/$3$H$,$G$-$k(B. @code{key} $B$N8e$m$OL5;k$5$l$k$N$G(B, $B%3%a%s%H$r=q$/(B
568: $B$3$H$,$G$-$k(B. @code{key} $B$r4^$`%U%!%$%k$O(B, $B0J2<$N=g$G%5!<%A$5$l$k(B.
1.2 noro 569: \E
570: \BEG
571: The text after each @code{key} is neglected to the end-of-line.
572: This is convenient to comment on the respective @code{key}.
573: Files containing @code{key}'s are searched by the following order.
574: \E
1.1 noro 575:
576: @enumerate
577: @item
1.2 noro 578: \JP $B4D6-JQ?t(B @code{ASIR_KEY} $B$K;XDj$5$l$?%U%!%$%k(B
579: \EG File set to environment @code{ASIR_KEY}
1.1 noro 580:
581: @item
1.2 noro 582: \JP $B%+%l%s%H%G%#%l%/%H%j$N(B @samp{asir_key}
583: \EG File @samp{asir_key} on the current directory.
1.1 noro 584:
585: @item
1.2 noro 586: \BJP
1.1 noro 587: $B4D6-JQ?t(B @code{ASIR_LIBDIR} $B$G;XDj$5$l$?%G%#%l%/%H%j(B ($B;XDj$,$J$1$l$P(B
588: @samp{/usr/local/lib/asir}) $B$N(B @samp{asir_key}
1.2 noro 589: \E
590: \BEG
591: Files on the directory specified by environment @code{ASIR_LIBDIR}.
592: (File @samp{asir_key} on @samp{/usr/local/lib/asir/},
593: if environment @code{ASIR_LIBDIR} is not set.)
594: \E
595:
1.1 noro 596: @end enumerate
597:
598: @item
599: @code{ASIR_LIBDIR}
1.8 noro 600: @*
1.2 noro 601: \BJP
1.1 noro 602: @b{Asir} $B$N%i%$%V%i%j%G%#%l%/%H%j(B, $B$9$J$o$A%f!<%68@8l$G=q$+$l$?%U%!%$%k(B
603: $B$J$I$,$*$+$l$k%G%#%l%/%H%j(B. $B;XDj$,$J$$>l9g(B UNIX $BHG$G$O(B
604: @samp{/usr/local/lib/asir}, Windows $BHG$G$O(B Asir $B%a%$%s%G%#%l%/%H%j$N2<$N(B
605: @samp{lib} $B%G%#%l%/%H%j$,MQ$$$i$l$k(B.
1.2 noro 606: \E
607: \BEG
608: The library directory of @b{Asir}, i.e., the directory where
609: , for example, files containing programs written in @b{Asir}.
610: If not specified, on UNIX, @samp{/usr/local/lib/asir} is used by default.
611: On Windows, @samp{lib} in @b{Asir root directory} is used by default.
612: This environment will be useful in a case where @b{Asir} binaries
613: are installed on a private directory of the user.
614: \E
1.1 noro 615:
616: @item
617: @code{ASIRLOADPATH}
1.8 noro 618: @*
1.2 noro 619: \BJP
1.1 noro 620: $B%m!<%I$5$l$k%U%!%$%k$,$"$k%G%#%l%/%H%j$r(B UNIX $B$N>l9g(B ':',
621: Windows$B$N>l9g(B ';' $B$G6h@Z$C$FJB$Y$k(B. $B%G%#%l(B
622: $B%/%H%j$O:8$+$i=g$K%5!<%A$5$l$k(B. $B$3$N;XDj$,$J$$>l9g(B, $B$*$h$S;XDj$5$l$?(B
623: $B%U%!%$%k$,(B @code{ASIRLOADPATH} $B$K$J$+$C$?>l9g(B, $B%i%$%V%i%j%G%#%l%/%H%j(B
624: $B$b%5!<%A$5$l$k(B.
1.2 noro 625: \E
626: \BEG
627: This environment specifies directories which contains files to be
628: loaded by @b{Asir} command @code{load()}.
629: Directories are separated by a `:' on UNIX, a ';' on Windows respectively.
630: The search order is from the left to the right.
631: After searching out all directories in @code{ASIRLOADPATH},
632: or in case of no specification at all,
633: the library directory will be searched.
634: \E
1.1 noro 635: @item
636: @code{HOME}
1.8 noro 637: @*
1.2 noro 638: \BJP
1.1 noro 639: @var{-norc} $B%*%W%7%g%s$D$-$G5/F0$7$J$$>l9g(B, @samp{$HOME/.asirrc}$B$,$"$l$P(B,
640: $BM=$a$3$N%U%!%$%k$r<B9T$9$k(B. @code{HOME} $B$,@_Dj$5$l$F$$$J$$>l9g(B, UNIX $BHG(B
641: $B$G$O$J$K$bFI$^$J$$$,(B, Windows $BHG$G$O(B Asir $B%a%$%s%G%#%l%/%H%j(B
642: (@code{get_rootdir()} $B$GJV$5$l$k%G%#%l%/%H%j(B) $B$N(B @samp{.asirrc} $B$rC5$7(B,
643: $B$"$l$P$=$l$r<B9T$9$k(B.
1.2 noro 644: \E
645: \BEG
646: If @b{Asir} is invoked without @var{-norc}, @samp{$HOME/.asirrc}, if exists,
647: is executed. If @code{HOME} is not set, nothing is done on UNIX. On Windows,
648: @samp{.asirrc} in @b{Asir root directory} is executed if it exists.
649: \E
1.1 noro 650: @end itemize
651:
1.2 noro 652: \BJP
1.1 noro 653: @node $B5/F0$+$i=*N;$^$G(B,,, Risa/Asir
654: @section $B5/F0$+$i=*N;$^$G(B
1.2 noro 655: \E
656: \BEG
657: @node Starting and Terminating an Asir session,,, Risa/Asir
658: @section Starting and Terminating an @b{Asir} session
659: \E
1.1 noro 660:
661: @noindent
1.2 noro 662: \JP @b{Asir} $B$r5/F0$9$k$H(B,
663: \BEG
664: Run @b{Asir}, then the copyright notice and the first prompt
665: will appear on your screen,
666: and a new @b{Asir} session will be started.
667: \E
668:
1.1 noro 669: @example
670: [0]
671: @end example
672:
673: @noindent
1.2 noro 674: \BJP
1.1 noro 675: $B$J$k%W%m%s%W%H$,I=<($5$l(B, $B%;%C%7%g%s$,3+;O$9$k(B. @samp{$HOME/.asirrc}
676: (Windows $BHG$N>l9g(B, @code{HOME} $B@_Dj$5$l$F$$$J$$>l9g$K$O(B @code{get_rootdir()}
677: $B$GJV$5$l$k%G%#%l%/%H%j$K$"$k(B @samp{.asirrc})
678: $B$,B8:_$7$F$$$k>l9g(B, $B$3$N%U%!%$%k$r(B @b{Asir} $B%f!<%68@8l$G$+$+$l$?(B
679: $B%U%!%$%k$H8+$J$7(B, $B2r<a<B9T$9$k(B.
1.2 noro 680: \E
681: \BEG
682: When initialization file @samp{$HOME/.asirrc} exists,
683: @b{Asir} interpreter executes it at first taking it as a program
684: file written in @b{Asir}.
685: \E
1.1 noro 686:
687: @noindent
1.2 noro 688: \BJP
1.1 noro 689: $B%W%m%s%W%H$OF~NO$NHV9f$rI=$9(B. $B%;%C%7%g%s$O(B, @code{end;} $B$^$?$O(B
690: @code{quit;} $B$rF~NO$9$k$3$H$K$h$j=*N;$9$k(B. $BF~NO$O(B, @samp{;} $B$^$?$O(B
691: @samp{$} $B$^$G$r0l6h@Z$j$H$7$FI>2A$5$l$k(B. @samp{;} $B$N$H$-7k2L$OI=<($5$l(B,
692: @samp{$} $B$N$H$-I=<($5$l$J$$(B.
1.2 noro 693: \E
694: \BEG
695: The prompt indicates the sequential number of your input commands to
696: @b{Asir}.
697: The session will terminate when you input @code{end;} or @code{quit;}
698: to @b{Asir}.
699: Input commands are evaluated statement by statement.
700: A statement normally ends with its terminator
701: @samp{;} or @samp{$}.
702: (There are some exceptions. See, syntax of @b{Asir}.)
703: The result will be displayed when the command, i.e. statement,
704: is terminated by a @samp{;},
705: and will not when terminated by a @samp{$}.
706: \E
1.1 noro 707:
708: @example
709: % asir
710: [0] A;
711: 0
712: [1] A=(x+y)^5;
713: x^5+5*y*x^4+10*y^2*x^3+10*y^3*x^2+5*y^4*x+y^5
714: [2] A;
715: x^5+5*y*x^4+10*y^2*x^3+10*y^3*x^2+5*y^4*x+y^5
716: [3] a=(x+y)^5;
717: evalpv : invalid assignment
718: return to toplevel
719: [3] a;
720: a
721: [4] fctr(A);
722: [[1,1],[x+y,5]]
723: [5] quit;
724: %
725: @end example
726:
727: @noindent
1.2 noro 728: \BJP
1.1 noro 729: $B$3$NNc$G$O(B, @code{A}, @code{a}, @code{x}, @code{y} $B$J$kJ8;z$,;HMQ$5$l$F$$$k(B.
730: @code{A} $B$O%W%m%0%i%`$K$*$1$kJQ?t$G(B, @code{a}, @code{x}, @code{y} $B$O?t3XE*(B
731: $B$J0UL#$G$NITDj85$G$"$k(B. $B0lHL$K%W%m%0%i%`JQ?t$OBgJ8;z$G;O$^$j(B,
732: $BITDj85$O>.J8;z$G;O$^$k(B. $B$3$NNc$G$o$+$k$h$&$K(B, $B%W%m%0%i%`JQ?t$O(B,
733: $B?t(B, $B<0$J$I$r3JG<$7$F$*$/$?$a$N$b$N$G$"$j(B, C $B8@8l$J$I$K$*$1$kJQ?t$KBP1~$9$k(B.
734: $B0lJ}(B, $BITDj85$O$=$l<+?H$GCM$r;}$D$3$H$O$G$-$:(B, $B=>$C$F(B, $BITDj85$KBP$9$k(B
735: $BBeF~$O5v$5$l$J$$(B. $B8e$K<($9$,(B, $BITDj85$KBP$9$kBeF~$O(B, $BAH$_9~$_H!?t(B @code{subst()}
736: $B$K$h$jL@<(E*$K9T$o$l$k(B.
1.2 noro 737: \E
738: \BEG
739: In the above example, names @code{A}, @code{a}, @code{x} and @code{y}
740: are used to identify mathematical and programming objects.
741: There, the name @code{A} denotes a program variable
742: (some times called simply as a program variable.)
743: while the other names, @code{a}, @code{x} and @code{y}, denote
744: mathematical objects, that is, indeterminates.
745: In general, program variables have names which begin with
746: capital letters, while names of indeterminates begin with
747: small letters.
748: As you can see in the example, program variables are used to hold and
749: keep objects, such as numbers and expressions, as their values,
750: just like variables in C programming language.
751: Whereas, indeterminates cannot have values so that assignment to
752: indeterminates are illegal.
753: If one wants to get a result by substituting a value for an indeterminate
754: in an expression, it is achieved by the function @code{subst} as the
755: value of the function.
756: \E
1.1 noro 757:
1.2 noro 758: \BJP
1.1 noro 759: @node $B3d$j9~$_(B,,, Risa/Asir
760: @section $B3d$j9~$_(B
1.2 noro 761: \E
762: \BEG
763: @node Interruption,,, Risa/Asir
764: @section Interruption
765: \E
1.1 noro 766:
767: @noindent
1.2 noro 768: \BJP
1.1 noro 769: $B7W;;$r<B9TCf$K3d$j9~$_$r$+$1$?$$>l9g(B, $B3d$j9~$_%-%c%i%/%?(B($BDL>o$O(B
770: @kbd{C-c}, DOS $BHG$G$O(B @kbd{C-x}, Mac $BHG$G$O(B
771: @code{command+}@samp{.} ) $B$rF~NO$9$k(B.
1.2 noro 772: \E
773: \BEG
774: To interrupt the @b{Asir} execution, input an interrupt character
775: from the keyboard. A @kbd{C-c} is usually used for it.
776: (Notice: @kbd{C-x} for DOS version; @code{command+}@samp{.} for Macintosh
777: version.)
778: \E
1.1 noro 779:
780: @example
781: @@ (x+y)^1000;
782: @kbd{C-c}interrupt ?(q/t/c/d/u/w/?)
783: @end example
784:
785: @noindent
1.2 noro 786: \JP $B3FA*Br;h$N0UL#$O<!$NDL$j(B.
787: \EG Here, the meaning of options are as follows.
1.1 noro 788:
789: @table @code
1.2 noro 790: \BJP
1.1 noro 791: @item q
792: @b{Asir} $B$r=*N;$9$k(B. ($B3NG'$"$j(B)
793: @item t
794: $B%H%C%W%l%Y%k$KLa$k(B. ($B3NG'$"$j(B)
795: @item c
796: $B<B9T$r7QB3$9$k(B.
797: @item d
798: $B%G%P%C%0%b!<%I$KF~$k(B. $B%G%P%C%,$K4X$7$F$O(B @xref{$B%G%P%C%,(B}.
799: @item u
1.3 noro 800: @code{register_handler()} (@pxref{ox_reset ox_intr register_handler}) $B$GEPO?$5$l$?(B
1.1 noro 801: $B4X?t$r<B9T8e%H%C%W%l%Y%k$KLa$k(B. ($B3NG'$"$j(B)
802: @item w
803: $BCfCGE@$^$G$NH!?t$N8F$S=P$7Ns$rI=<($9$k(B.
804: @item ?
805: $B3FA*Br;h$N0UL#$r@bL@$9$k(B.
1.2 noro 806: \E
807: \BEG
808: @item q
809: Terminates @b{Asir} session. (Confirmation requested.)
810: @item t
811: Returns to toplevel. (Confirmation requested.)
812: @item c
813: Resumes to continue the execution.
814: @item d
815: Enters debugging mode at the next statement of the @b{Asir} program,
816: if @b{Asir} has been executing a program loaded from a file.
817: Note that it will sometimes take a long time before entering
818: debugging mode when @b{Asir} is executing basic functions in the
819: algebraic engine, (e.g., arithmetic operation, factorization etc.)
820: Detailed description about the debugger will be given in @ref{Debugger}.
821: @item u
822: After executing a function registered by @code{register_handler()}
1.3 noro 823: (@pxref{ox_reset ox_intr register_handler}), returns to toplevel. A confirmation
1.2 noro 824: is prompted.
825: @item w
826: Displays the calling sequence up to the interruption.
827: @item ?
828: Show a brief description of options.
829: \E
1.1 noro 830: @end table
831:
1.2 noro 832: \BJP
1.1 noro 833: @node $B%(%i!<=hM}(B,,, Risa/Asir
834: @section $B%(%i!<=hM}(B
1.2 noro 835: \E
836: \BEG
837: @node Error handling,,, Risa/Asir
838: @section Error handling
839: \E
1.1 noro 840:
841: @noindent
1.2 noro 842: \BJP
1.1 noro 843: $BAH$_9~$_H!?t$KIT@5$J7?$N0z?t$rEO$7$?>l9g$J$I$K$O<B9T$,CfCG$5$l$k$,(B,
844: $B%f!<%6H!?t$NCf$G%(%i!<$,5/$-$?>l9g$K$O%H%C%W%l%Y%k$KLa$kA0$K<+F0E*$K%G%P%C%0(B
845: $B%b!<%I$KF~$k(B. $B$3$N>uBV$G(B
846: $B%(%i!<$N>l=j(B, $BD>A0$N0z?t$NCM$J$I$rD4$Y$k$3$H$,$G$-$k(B.
847: $BI=<($5$l$k%(%i!<%a%C%;!<%8$O$5$^$6$^$G$"$j(B, $BFbIt$NH!?tL>$K0z$-B3$$$F(B
848: $B%a%C%;!<%8$,I=<($5$l$k(B. $B$3$l$O(B, $B8F$S=P$5$l$?AH$_9~$_H!?t(B
849: $B$HI,$:$7$bBP1~$O$7$J$$(B.
1.2 noro 850: \E
851: \BEG
852: When arguments with illegal types are given to a built-in function,
853: an error will be detected and the execution will be quit.
854: In many cases, when an error is detected in a built-in function,
855: @b{Asir} automatically enters debugging mode before coming back
856: to toplevel.
857: At that time, one can examine the state of the program,
858: for example, inspect argument values just before the error occurred.
859: Messages reported there are various depending on cases. They are
860: reported after the internal function name. The internal function name
861: sometimes differs from the built-in function name that is specified by
862: the user program.
863: \E
1.1 noro 864:
865: @noindent
1.2 noro 866: \BJP
1.1 noro 867: $B$=$NB>(B, $B$5$^$6$^$J860x$K$h$jFbIt1i;;H!?t$K$*$$$F%(%i!<$,@8$:$k$3$H$,(B
868: $B$"$k(B. UNIX $BHG$N>l9g(B, $B$3$l$O<!$N$$$:$l$+$N(B
869: @code{internal error} $B$H$7$FJs9p$5$l(B, $BDL>o$N%(%i!<$HF1MM$K07$C$F(B,
870: $B%G%P%C%0%b!<%I$KF~$k(B.
1.2 noro 871: \E
872: \BEG
873: In the execution of internal functions, errors may happen by various
874: reasons. The UNIX version of @b{Asir} will report those errors as one of
875: the following @code{internal error}'s, and enters debugging mode just
876: like normal errors.
877: \E
1.1 noro 878:
879: @table @code
880: @item SEGV
881: @itemx BUS ERROR
1.8 noro 882: @*
1.2 noro 883: \BJP
1.1 noro 884: $BAH$_9~$_H!?t$K$h$C$F$O(B, $B0z?t$N7?$r87L)$K%A%'%C%/$;$:$K1i;;%k!<%A%s$K0z(B
885: $B$-EO$7$F$7$^$&$b$N$bB8:_$7$F$$$k(B. $B$3$N$h$&$J>u67$K$*$$$F(B,
886: $BIT@5$J%]%$%s%?(B, $B$"$k$$$O(B NULL $B%]%$%s%?$K$h$k%"%/%;%90cH?$,$"$C$?>l9g(B, $B$3$l$i(B
887: $B$N%(%i!<$H$J$k(B.
1.2 noro 888: \E
889: \BEG
890: Some of the built-in functions transmit their arguments to internal
891: operation routines without strict type-checking. In such cases,
892: one of these two errors will be reported
893: when an access violation caused by an illegal pointer or a NULL pointer
894: is detected.
895: \E
1.1 noro 896:
897: @item BROKEN PIPE
1.8 noro 898: @*
1.2 noro 899: \BJP
1.1 noro 900: $B%W%m%;%94VDL?.$K$*$$$F(B, $BAj<j@h$N%W%m%;%9$H$N4V$N%9%H%j!<%`(B
901: $B$,4{$KB8:_$7$F$$$J$$>l9g(B ($BNc$($P4{$KAj<j@h$N%W%m%;%9$,=*N;$7$F$$$k>l9g$J$I(B)
902: $B$K(B, $B$=$N%9%H%j!<%`$KF~=PNO$7$h$&$H$7$?>l9g$K$3$N%(%i!<$H$J$k(B.
1.2 noro 903: \E
904: \BEG
905: In the process communication, this error will be reported if a process
906: attempts to read from or to write onto the partner process when the
907: stream to the partner process does not already exist, (e.g., terminated
908: process.)
909: \E
1.1 noro 910: @end table
911:
912: @noindent
1.2 noro 913: \BJP
1.1 noro 914: $B$3$l$i$O<B:]$K$O(B, $BAH$_9~$_H!?t$NF~8}$K$*$$$F(B, $B0z?t$r40A4$K%A%'%C%/(B
915: $B$9$k$3$H$K$h$jBgItJ,$OKI$2$k$,(B, $B<j4V$,B?$/$+$+$k$3$H$H(B, $B>l9g$K(B
916: $B$h$C$F$O8zN($rMn$9$3$H$K$b$J$k$?$a(B, $B$"$($F0z?t%A%'%C%/$O%f!<%6(B
917: $BG$$;$K$7$F$"$k(B.
1.2 noro 918: \E
919: \BEG
920: For UNIX version, even in such a case, the process itself does not
921: terminate because such an error can be caught by @code{signal()} and
922: recovered.
923: To remove this weak point, complete type
924: checking of all arguments are indispensable at the entry of a built-in
925: function, which requires an enormous amount of re-making efforts.
926: \E
1.1 noro 927:
1.2 noro 928: \BJP
1.1 noro 929: @node $B7W;;7k2L$*$h$SFC<l$J?t(B,,, Risa/Asir
930: @section $B7W;;7k2L(B, $BFC<l$J?t(B
1.2 noro 931: \E
932: \BEG
933: @node Referencing results and special numbers,,, Risa/Asir
934: @section Referencing results and special numbers
935: \E
1.1 noro 936:
937: @noindent
1.2 noro 938: \JP @code{@@} $B$O%(%9%1!<%WJ8;z$H$7$F;HMQ$5$l$k(B. $B8=:_<!$N$h$&$J5,Dj$,$"$k(B.
939: \BEG
940: An @code{@@} used for an escape character; rules currently in force
941: are as follows.
942: \E
1.1 noro 943: @table @code
1.2 noro 944: \BJP
1.1 noro 945: @item @@@var{n}
946: @var{n} $BHVL\$N7W;;7k2L(B.
947: @item @@@@
948: $BD>A0$N7W;;7k2L(B.
949: @item @@i
950: $B5u?tC10L(B.
951: @item @@pi
952: $B1_<~N((B.
953: @item @@e
954: $B<+A3BP?t$NDl(B.
955: @item @@
956: 2 $B85BN(B GF(2) $B>e$N0lJQ?tB?9`<0$NJQ?t(B ($BITDj85(B).
957: @item @@>, @@<, @@>=, @@<=, @@==, @@&&, @@||
958: quantifier elimination $B$K$*$1$k(B, $B0l3,=R8lO@M}1i;;;R(B
1.2 noro 959: \E
960: \BEG
961: @item @@@var{n}
962: The evaluated result of @var{n}-th input command
963: @item @@@@
964: The evaluated result of the last command
965: @item @@i
966: The unit of imaginary number, square root of -1.
967: @item @@pi
968: The number pi,
969: the ratio of a circumference of the circle and its diameter.
970: @item @@e
971: Napier's number, the base of natural logarithm.
972: @item @@
973: A generator of GF(2^m), a finite field of characteristic 2, over GF(2).
974: It is a root of an irreducible univariate polynomial over GF(2)
975: which is set as the defining polynomial of GF(2^m).
976: @item @@>, @@<, @@>=, @@<=, @@==, @@&&, @@||
977: Fist order logical operators. They are used in quantifier elimination.
978: \E
1.1 noro 979: @end table
980:
981: @example
982: [0] fctr(x^10-1);
983: [[1,1],[x-1,1],[x+1,1],[x^4+x^3+x^2+x+1,1],[x^4-x^3+x^2-x+1,1]]
984: [1] @@@@[3];
985: [x^4+x^3+x^2+x+1,1]
986: [2] eval(sin(@@pi/2));
987: 1.000000000000000000000000000000000000000000000000000000000
988: [3] eval(log(@@e),20);
989: 0.99999999999999999999999999998
990: [4] @@0[4][0];
991: x^4-x^3+x^2-x+1
992: [5] (1+@@i)^5;
993: (-4-4*@@i)
994: [6] eval(exp(@@pi*@@i));
995: -1.0000000000000000000000000000
996: [7] (@@+1)^9;
997: (@@^9+@@^8+@@+1)
998: @end example
999:
1000: @noindent
1.2 noro 1001: \BJP
1.1 noro 1002: $B%H%C%W%l%Y%k$G7W;;$5$l$?CM$O$3$N$h$&$K%R%9%H%j$H$7$F<h$j=P$72DG=$G$"$k$,(B,
1003: $B$3$N$3$H$O(B, $B%,%Y!<%8%3%l%/%?$K$H$C$F$OIiC4$r$b$?$i$92DG=@-$,$"$k(B. $BFC$K(B,
1004: $BBg$-$J<0$r%H%C%W%l%Y%k$G7W;;$7$?>l9g(B, $B$=$N8e$N(B GC $B;~4V$,5^B.$KA}Bg$9$k2D(B
1005: $BG=@-$,$"$k(B. $B$3$N$h$&$J>l9g(B, @code{delete_history()}
1006: (@pxref{delete_history,,@code{delete_history}}) $B$,M-8z$G$"$k(B.
1.2 noro 1007: \E
1008: \BEG
1009: As you can see in the above example,
1010: results of toplevel computation can be referred to
1011: by @code{@@} convention.
1012: This is convenient for users, while it sometimes imposes a heavy
1013: burden to the garbage collector.
1014: It may happen that GC time will rapidly increase after computing
1015: a very large expression at the toplevel.
1016: In such cases @code{delete_history()}
1017: (@pxref{delete_history,,@code{delete_history}}) takes effect.
1018: \E
1.1 noro 1019:
1020:
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