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-version 1.1, 1999/12/08 05:47:44
+version 1.14, 2005/03/30 10:53:28
 Line 1
 Line 1
 Line 1
+ @comment $OpenXM: OpenXM/src/asir-doc/parts/risa.texi,v 1.13 2005/03/24 23:40:50 takayama Exp $
  @node Risa/Asir,,, Top
  @chapter Risa/Asir
  @menu
+ \BJP
  * Risa $B$*$h$S(B Asir::
  * Asir $B$NFCD'(B::
- * $B%$%s%9%H%l!<%7%g%s(B::
+ * Installation::
  * $B%3%^%s%I%i%$%s%*%W%7%g%s(B::
  * $B4D6-JQ?t(B::
  * $B5/F0$+$i=*N;$^$G(B::
  * $B3d$j9~$_(B::
  * $B%(%i!<=hM}(B::
  * $B7W;;7k2L$*$h$SFC<l$J?t(B::
+ \E
+ \BEG
+ * Risa and Asir::
+ * Features of Asir::
+ * Installation::
+ * Command line options::
+ * Environment variable::
+ * Starting and Terminating an Asir session::
+ * Interruption::
+ * Error handling::
+ * Referencing results and special numbers::
+ \E
  @end menu
+ \BJP
  @node Risa $B$*$h$S(B Asir,,, Risa/Asir
  @section Risa $B$*$h$S(B Asir
+ \E
+ \BEG
+ @node Risa and Asir,,, Risa/Asir
+ @section @b{Risa} and @b{Asir}
+ \E
  @noindent
+ \BJP
  @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.
  @b{Risa} $B$N9=@.$O<!$NDL$j$G$"$k(B.
+ \E
+ \BEG
+ @b{Risa} is the name of whole libraries of a computer algebra system
+ which is under development at FUJITSU LABORATORIES LIMITED.
+ The structure of @b{Risa} is as follows.
+ \E
  @itemize @bullet
  @item
- @code{$B4pK\1i;;It(B}
+ \JP @code{$B4pK\1i;;It(B}
+ \EG @b{The basic algebraic engine}
+ @*
+ \BJP
  $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)
  $B$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
  $B%j$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
- $B8@8l%$%s%?%U%'!<%9(B @b{Asir} $B$N4pK\1i;;It$H$7$FMQ$$$i$l$F$$$k0lJ}(B,
+ $B8@8l%$%s%?%U%'!<%9(B @b{Asir} $B$N4pK\1i;;It$H$7$FMQ$$$i$l$F$$$k(B.
- $B?t<07W;;$rI,MW$H$9$k$5$^$6$^$J%W%m%0%i%`Cf$K%j%s%/$7$FMQ$$$k$3$H$,$G$-$k(B.
+ @comment $B0lJ}(B, $B?t<07W;;$rI,MW$H$9$k$5$^$6$^$J%W%m%0%i%`Cf$K%j%s%/$7$FMQ$$$k$3$H$,$G$-$k(B.
- ($BL$8x3+(B)
+ \E
- @item
+ \BEG
- @code{$B%a%b%j4IM}It(B}
+ This is the part which performs basic algebraic operations,
+ such as arithmetic operations, to algebraic objects, e.g., numbers and
+ polynomials, which are already converted into internal forms.
+ It exists, like @samp{libc.a} of UNIX, as a library of ordinary UNIX system.
+ The algebraic engine is written mainly in C language and
+ partly in assembler.
+ It serves as the basic operation part of @b{Asir}, a standard
+ language interface of @b{Risa}.
+ @comment It can also be linked to various programs that need some symbolic
+ @comment and algebraic computation.
+ \E
+ @item
+ \JP @code{$B%a%b%j4IM}It(B}
+ \EG @b{Memory Manager}
+ @*
+ \BJP
  @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
- $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
+ $B%=%U%H%&%'%"(B (@code{gc-6.1alpha5}) $B$rMQ$$$F$$$k(B. $B$3$l$O%,!<%Y%8%3%l%/%7%g%s(B
  ($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
  $BItJ,$O$9$Y$F$3$l$K$h$jI,MW$J%a%b%j$rF@$F$$$k(B.
+ \E
+ \BEG
+ @b{Risa} employs, as its memory management component (the memory
+ manager), a free software distributed by Boehm (@code{gc-6.1alpha5}).
+ It is proposed by @code{[Boehm,Weiser]}, and developed by Boehm and
+ his colleagues.
+ The memory manager has a memory allocator which automatically
+ reclaims garbages, i.e., allocated but unused memories,
+ and refreshes them for further use.
+ The algebraic engine gets all its necessary memories through the memory
+ manager.
+ \E
  @item
  @b{Asir}
+ @*
+ \BJP
  @b{Asir} $B$O(B, @b{Risa} $B$N7W;;%(%s%8%s$N8@8l%$%s%?%U%'!<%9$G(B
  $B$"$k(B. @b{Risa} $B$G$O(B, $BHf3SE*MF0W$K%f!<%6MQ$N8@8l%$%s%?%U%'!<%9$r:n$k(B
  $B$3$H$,$G$-$k(B. @b{Asir} $B$O$=$N0l$D$NNc$H$7$F:n$C$?$b$N$G(B, C $B8@8l$K6a(B
  $B$$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
  $B$N%G%P%C%,$bHw$($F$$$k(B.
+ \E
+ \BEG
+ @b{Asir} is a standard language interface of @b{Risa}'s algebraic
+ engine. It is one of the possible language interfaces, because
+ one can develop one's own language interface easily on @b{Risa}
+ system.
+ @b{Asir} is an example of such language interfaces.
+ @b{Asir} has very similar syntax and semantics as C language.
+ Furthermore, it has a debugger that provide a subset of commands of
+ @code{dbx}, a widely used debugger of C language.
+ \E
  @end itemize
+ \BJP
  @node Asir $B$NFCD'(B,,, Risa/Asir
  @section Asir $B$NFCD'(B
+ \E
+ \BEG
+ @node Features of Asir,,, Risa/Asir
+ @section Features of @b{Asir}
+ \E
  @noindent
+ \BJP
  @b{Asir} $B$O(B, $BA0=R$NDL$j(B, $B7W;;%(%s%8%s$N8@8l%$%s%?%U%'!<%9$G$"(B
  $B$k(B. $BDL>o(B @b{Asir} $B$H$$$&L>A0$N<B9T2DG=%U%!%$%k$H$7$FDs6!$5$l$k(B.
  $B8=:_%5%]!<%H$5$l$F$$$k5!G=$O35$M<!$NDL$j$G$"$k(B.
+ \E
+ \BEG
+ As mentioned in the previous section, @b{Asir} is a standard language
+ interface for@b{Risa}'s algebraic engine.
+ Usually, it is provided as an executable file named @code{asir}.
+ Main features supported for the current version of Asir is as follows.
+ \E
  @itemize @bullet
+ \BJP
  @item
  C $B8@8lIw$N%f!<%68@8l(B
-Line 88  C $B8@8lIw$N%f!<%68@8l(B
+Line 171  C $B8@8lIw$N%f!<%68@8l(B
 Line 88  C $B8@8lIw$N%f!<%68@8l(B
 Line 171  C $B8@8lIw$N%f!<%68@8l(B
  UNIX $B>e$G$NJ,;67W;;5!G=(B (Open XM)
  @comment @item
  @comment $B%R%9%H%jCV495!G=$r$b$D(B X11 $B%$%s%?%U%'!<%9(B
+ \E
+ \BEG
+ @item
+ A C-like programming language
+ @item
+ Arithmetic operations (addition, subtraction, multiplication
+ and division) on numbers, polynomials and rational expressions
+ @item
+ Operations on vectors and matrices
+ @item
+ List processing operations at the minimum
+ @item
+ Several Built-in functions (factorization, GCD computation, Groebner basis
+ computation etc.)
+ @item
+ Useful user defined functions(e.g., factorization over algebraic number fields)
+ @item
+ A @code{dbx}-like debugger
+ @item
+ Plotting of implicit functions
+ @item
+ Numerical evaluation of mathematical expressions including elementary
+ transcendental functions at arbitrary precision. This feature is
+ in force only if @b{PARI} system (@pxref{pari}).
+ @item
+ Distributed computation over UNIX
+ \E
  @end itemize
- @node $B%$%s%9%H%l!<%7%g%s(B,,, Risa/Asir
+ @node Installation,,, Risa/Asir
- @section $B%$%s%9%H%l!<%7%g%s(B
+ @section Installation
- $B0J2<$N<jB3$-$GITL@$JE@(B, $BITET9g$JE@$,$"$C$?>l9g$NLd$$9g$o$;$O(B
+ \JP $B0J2<$N<jB3$-$GITL@$JE@(B, $BITET9g$JE@$,$"$C$?>l9g$NLd$$9g$o$;$O(B
+ \BEG
+ Any questions and any comments on this manual are welcome by e-mails
+ to the following address.
+ \E
  @example
- noro@@para.flab.fujitsu.co.jp
+ noro@@math.kobe-u.ac.jp
  @end example
  @noindent
- $B08$K(B e-mail $B$G$*4j$$$7$^$9(B.
+ \JP $B08$K(B e-mail $B$G$*4j$$$7$^$9(B.
  @menu
- * UNIX $BHG(B::
+ * UNIX binary version::
- * Windows $BHG(B::
+ * UNIX source code version::
+ * Windows version::
  @end menu
- @node UNIX $BHG(B,,, $B%$%s%9%H%l!<%7%g%s(B
+ @node UNIX binary version,,, Installation
- @subsection UNIX $BHG(B
+ @subsection UNIX binary version
  @noindent
- $BI,MW$J%U%!%$%k$O(B @samp{asir.tgz} $B$G$"$k(B.
+ \BJP
+ $B%?!<%2%C%H(B CPU/OS $B$KBP1~$9$k(B @samp{asir.tgz} $B$,I,MW$G$"$k(B.
  $B$3$l$i$OA4$F(B @code{gzip} $B$G05=L$7$F$"$k$N$G(B, $BF~<j8e(B @code{gzip} $B$G(B
  $BE83+$9$k(B. $B$^$:(B, $B%$%s%9%H!<%k$9$k%G%#%l%/%H%j$r7h$a$k(B. $B%G%U%)%k%H$G$O(B
  @samp{/usr/local/lib} $B$K(B @samp{asir} $B$H$$$&%G%#%l%/%H%j$H$7$F(B
  $B%$%s%9%H!<%k$5$l$k$3$H$r2>Dj$7$F$$$k(B. $B0J2<$3$N%G%#%l%/%H%j$r%i%$%V%i%j(B
  $B%G%#%l%/%H%j$H8F$V(B.
+ \E
+ \BEG
+ A file @samp{asir.tgz} suitable for the target machine/architecture
+ is required. After getting it,
+ you have to unpack it by @code{gzip}. First of all, determine
+ a derectory where binaries and library files are installed.
+ We call the directory the @b{library directory}.
+ The following installs the files in @samp{/usr/local/lib/asir}.
+ \E
  @example
  # gzip -dc asir.tgz | ( cd /usr/local/lib; tar xf - )
  @end example
- $B8D?ME*$K;HMQ$9$k>l9g$K$O(B, @samp{$HOME}$B$J$I$KCV$$$F$b$h$$(B.
+ \JP $B8D?ME*$K;HMQ$9$k>l9g$K$O(B, @samp{$HOME}$B$J$I$KCV$$$F$b$h$$(B.
+ \BEG
+ In this case you don't have to set any environment variable.
+ You can install them elsewhere.
+ \E
  @example
  % gzip -dc asir.tgz | ( cd $HOME; tar xf - )
  @end example
  @noindent
+ \BJP
  $B$3$N>l9g(B, $B%i%$%V%i%j%G%#%l%/%H%j$NL>A0$r4D6-JQ?t(B
  @code{ASIR_LIBDIR} $B$K@_Dj$9$kI,MW$,$"$k(B.
+ \E
+ \BEG
+ In this case you have to set the name of the library directory
+ to the environment variable @code{ASIR_LIBDIR}.
+ \E
  @example
  % setenv ASIR_LIBDIR $HOME/asir
  @end example
  @noindent
+ \BJP
  Asir $BK\BN$O(B, $B%i%$%V%i%j%G%#%l%/%H%j$N(B @samp{asir} $B$G$"$k(B.
  @samp{/usr/local/bin} $B$"$k$$$O%f!<%6$N<B9T%U%!%$%k%5!<%A%Q%9(B
  $B$N$I$3$+$K%7%s%\%j%C%/%j%s%/$r:n$k$HJXMx$G$"$k(B.
+ \E
+ \BEG
+ @b{Asir} itself is in the library directory. It will be convenient
+ to create a symbolic link to it from @samp{/usr/local/bin} or
+ the user's search path.
+ \E
  @example
  # ln -s /usr/local/lib/asir/asir /usr/local/bin/asir
  @end example
  @noindent
- $B$3$N>uBV$G(B @samp{asir} $B$r5/F0$7$F$_$k(B.
+ \JP $B$3$l$G(B @samp{asir} $B$,5/F0$G$-$k(B.
+ \BEG
+ Then you can start @samp{asir}.
+ \E
  @example
  % /usr/local/bin/asir
- asir_key not found.
+ This is Risa/Asir, Version 20000821.
- ID for this machine is XXXXXXXX.
+ Copyright (C) FUJITSU LABORATORIES LIMITED.
- See the file ASIR_INSTALL to get the correct key.
+-2000. All rights reserved.
+ [0]
  @end example
- @noindent
+ @node UNIX source code version,,, Installation
- $B$9$k$H(B, $B$3$N$h$&$J%a%C%;!<%8$,=P$F(B @samp{asir} $B$O=*N;$9$k(B. UNIX $BHG(B
+ @subsection UNIX source code version
- $B$G$O(B, $B%^%7%s$4$H$K(B @code{key} $B$H8F$P$l$kJ8;zNs$,I,MW$G$"$k(B.
- @code{key} $B$rF~<j$9$k$?$a$K$O(B,
- @example
+ \BEG
- risa@@para.flab.fujitsu.co.jp
+ First of all you have to determine the install directory.
- @end example
+ In the install directory, the following subdirectories are put:
+ \E
- @noindent
+ \BJP
- $B08$K(B,
+ $B$^$:(B, $B%$%s%9%H!<%k@h$N%G%#%l%/%H%j$r7h$a$kI,MW$,$"$k(B.
+ $B$3$3$K$O(B, $B0J2<$N%5%V%G%#%l%/%H%j$,CV$+$l$k(B.
+ \E
- @example
+ @itemize @bullet
- ASIR XXXXXXXX
+ @item bin
- @end example
- @noindent
+ \EG executables of PARI and Asir
- $B$H$$$&(B 1 $B9T$N$_$+$i$J$k(B e-mail $B$rAw$l$P$h$$(B. @code{XXXXXXXX} $B$OI=<($5$l$?(B
+ \JP PARI $B$*$h$S(B Asir $B$N<B9T2DG=%U%!%$%k(B
- @code{ID} $B$G$"$k(B. $B@^$jJV$7(B
+ @item lib
+ \EG library files of PARI and Asir
+ \JP PARI $B$*$h$S(B Asir $B$N%i%$%V%i%j(B
+ @item include
+ \EG header files of PARI
+ \JP PARI $B$N%X%C%@%U%!%$%k(B
+ @end itemize
+ \BEG
+ These subdirectories are created automatically if they does not exist.
+ If you can be a root, it is recommended to set the install directory
+ to @samp{/usr/local}.  In the following the directory is denoted by TARGETDIR.
+ \E
+ \BJP
+ $B$3$l$i$N%5%V%G%#%l%/%H%j$OL5$1$l$P<+F0E*$K:n$i$l$k(B.
+ root $B8"8B$,$"$k>l9g$K$O(B, @samp{/usr/local} $B$K%$%s%9%H!<%k$9$k$3$H$r(B
+ $B$*4+$a$9$k(B. $B0J2<(B, $B$3$N%G%#%l%/%H%j$r(B TARGETDIR $B$H=q$/(B.
+ \E
+ \BEG
+ Then, install PARI library. After getting @samp{pari.tgz},
+ unpack and install it as follows:
+ \E
+ \BJP
+ $B$^$:(B PARI $B%i%$%V%i%j$r%$%s%9%H!<%k$9$kI,MW$,$"$k(B.
+ @samp{pari.tgz} $B$rF~<j8e(B, $BE,Ev$J%G%#%l%/%H%j$GE83+(B, $B%$%s%9%H!<%k$9$k(B.
+ \E
  @example
- YYYYYYYY YYYYYYYY YYYYYYYY
+ % gzip -dc pari.tgz | tar xvf -
+ % cd pari
+ % ./Configure --prefix=TARGETDIR
+ % make all
+ % su
+ # make install
+ # make install-lib-sta
  @end example
- @noindent
+ \BJP
- $B$H$$$&7A$N(B 1 $B9T$N$_$+$i$J$k(B e-mail $B$,FO$/$N$G(B, $B$3$N(B 1 $B9T$r4^$`(B @samp{asir_key}
+ make $BCf$K%(%i!<$G;_$^$C$?$i(B, $B0J2<$r<B9T$9$k(B.
- $B$J$k%U%!%$%k$r%+%l%s%H%G%#%l%/%H%j$K:n$C$F(B @samp{asir} $B$r5/F0$7$F$_$k(B.
+ \E
+ \BEG
+ While executing 'make install', the procedure may stop due to
+ some error. Then try the following:
+ \E
  @example
- % /usr/local/bin/asir
+ % cd Oxxx
- This is Asir, Version 990831.
+ % make lib-sta
- Copyright (C) FUJITSU LABORATORIES LIMITED.
+ % su
-March 1994. All rights reserved.
+ # make install-lib-sta
- [0]
+ # make install-include
+ # exit
+ %
  @end example
- @noindent
+ \BEG
- $B$3$N$h$&$J%W%m%s%W%H$,=P$l$P(B, $BF~<j$7$?(B @code{key} $B$O$=$N%^%7%s$KBP$7$FM-8z(B
+ In the above example, xxx denotes the name of the target operating system.
- $B$G$"$k(B. @code{key} $B$r=q$$$F$*$/%U%!%$%k$K4X$7$F$O(B, $B4D6-JQ?t(B @code{ASIR_KEY}
+ Although GP is not built, the library necessary for building asir2000
- $B$N@bL@$N9`$G>\$7$/=R$Y$k$,(B, $B%i%$%V%i%j%G%#%l%/%H%j$K$3$3$G:n@.$7$?(B
+ will be generated.
- $B%U%!%$%k(B @samp{asir_key} $B$rCV$1$P(B, $B$=$N%^%7%s>e$GA4$F$N%f!<%6$,(B @samp{asir}
- $B$r;HMQ$G$-$k$h$&$K$J$k(B. @samp{asir_key} $B$K$OJ#?t$N%^%7%s$KBP$9$k(B @code{key}
- $B$r=q$1$k$N$G(B, $B%i%$%V%i%j%G%#%l%/%H%j$r6&M-$7$F$$$k>l9g$G$b(B @samp{asir_key}
- $B$K9T$rDI2C$7$F$$$1$P$h$$(B.
+ After getting @samp{asir2000.tgz}, unpack it
+ and install necessary files as follows.
+ \E
+ \BJP
+ $B>e$NNc$G(B, xxx $B$O8=:_%?!<%2%C%H$H$J$C$F$$$k(B OS $B$NL>A0$r<($9(B.
+ GP $B$O%$%s%9%H!<%k$5$l$J$$$,(B, asir2000 $B$N:n@.$KI,MW$J%U%!%$%k$O%$%s%9%H!<%k(B
+ $B$5$l$k(B.
+ @samp{asir2000.tgz} $B$rF~<j8e(B, $BE,Ev$J%G%#%l%/%H%j$G(B
+ $B$GE83+$7(B, $B0J2<$N<j=g$G%$%s%9%H!<%k$9$k(B.
+ \E
  @example
- # cp asir_key /usr/local/lib/asir
+ % gzip -dc asir.tgz | tar xf -
+ % cd asir2000
+ % ./configure --prefix=TARGETDIR --with-pari --enable-plot
+ % make
+ % su
+ # make install
+ # make install-lib
+ # make install-doc
+ # exit
  @end example
- @node Windows $BHG(B,,, $B%$%s%9%H%l!<%7%g%s(B
+ @node Windows version,,, Installation
- @subsection Windows $BHG(B
+ @subsection Windows version
  @noindent
- $BI,MW$J%U%!%$%k$O(B @samp{asirwin.tgz} $B$G$"$k(B. $BB>$K(B, @samp{gzip.exe},
+ \BJP
- @samp{tar.exe} $B$,I,MW$@$,(B, asirwin.tgz $B$HF1$8%G%#%l%/%H%j$KMQ0U$7$F(B
+ $BI,MW$J%U%!%$%k$O(B @samp{asirwin-ja.tgz} $B$G$"$k(B. $BB>$K(B, @samp{gzip.exe},
- $B$"$k(B. $B$3$l$i(B 3 $B$D$N%U%!%$%k$rF10l%G%#%l%/%H%j$K$*$-(B, DOS $B%W%m%s%W%H(B
+ @samp{tar.exe} $B$,I,MW$@$,(B, @samp{asirwin-ja.tgz} $B$HF1$8%G%#%l%/%H%j$KMQ0U$7$F(B
+ $B$"$k(B. $B$3$l$i(B 3 $B$D$N%U%!%$%k$rF10l%G%#%l%/%H%j$K$*$-(B, $B%3%^%s%I%W%m%s%W%H(B
+ (DOS $B%W%m%s%W%H(B)
  $B$+$i(B
+ \E
+ \BEG
+ The necessary file is @samp{asirwin-en.tgz}. To unpack it @samp{gzip.exe}
+ and @samp{tar.exe} are necessary. They are in the same
+ directory as @samp{asirwin-en.tgz} on the ftp server.
+ Putting them in the same directory, execute the following:
+ \E
  @example
- C:\...> tar xzf asirwin.tgz
+ \JP C:\...> tar xzf asirwin.tgz
+ \EG C:\...> tar xzf asirwin.tgz
  @end example
  @noindent
+ \BJP
  $B$r<B9T$9$l$P(B, @samp{Asir} $B$H$$$&%G%#%l%/%H%j(B (Asir $B%k!<%H%G%#%l%/%H%j(B)
- $B$,$G$-$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
+ $B$,$G$-$k(B.
- $BJL%W%m%;%9$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
+ @comment 990831 $BHG$G$O(B, GUI $B$HK\BN$,J,N%$5$l(B, $B$^$?%G%P%C%0%&%#%s%I%&$b(B
- $BEPO?$5$l$F$$$k$3$H$,I,MW$G$"$k(B.  Asir $B%k!<%H%G%#%l%/%H%j$N%5%V%G%#%l%/%H(B
+ @comment $BJL%W%m%;%9$H$7$F(B GUI $B$,8F$S=P$5$l$k$?$a(B, Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/(B
- $B%j(B @samp{bin} $B$K(B @samp{asirgui.exe} (GUI), @samp{engine.exe} ($BK\BN(B) $B$,(B
+ @comment $BEPO?$5$l$F$$$k$3$H$,I,MW$G$"$k(B.
- $BCV$+$l$F$$$k(B. @samp{asirgui.exe} $B$N=i2s$NN)$A>e$2$O(B, $B%(%/%9%W%m!<%i$+$i9T(B
+ Asir $B%k!<%H%G%#%l%/%H%j$N%5%V%G%#%l%/%H(B
- $B$&(B. $B$3$l$K$h$j(B
+ @samp{bin} $B$K(B @samp{asirgui.exe} (GUI), @samp{engine.exe} ($BK\BN(B) $B$,(B
+ $BCV$+$l$F$$$k(B.
+ @samp{asirgui.exe} $B$r%@%V%k%/%j%C%/$9$l$P(B Asir $B$,N)$A>e$,$k(B.
+ @comment @samp{asirgui.exe} $B$N=i2s$NN)$A>e$2$O(B, $B%(%/%9%W%m!<%i$+$i9T(B
+ @comment $B$&(B. $B$3$l$K$h$j(B
+ \E
- @example
+ \BEG
- HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory
+ Then a directory @samp{Asir} (@b{Asir root directory}) is created,
- @end example
+ which has subdirectories named @samp{bin} and @samp{lib}.
+ Asir can be invoked by double-clicking @samp{asirgui.exe}.
+ @comment To set up it,
+ @comment invoke @samp{bin\asirgui.exe} from Explorer and
+ @comment click @code{OK}.  Then the name of @b{Asir root directory} is set to the
+ @comment following registries.
+ \E
- @noindent
+ @comment @example
- $B$H$$$&%l%8%9%H%j$K(B Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/EPO?$5$l$k(B.
+ @comment \JP HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory
+ @comment \EG HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory
+ @comment @end example
+ @comment @noindent
+ @comment \JP $B$H$$$&%l%8%9%H%j$K(B Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/EPO?$5$l$k(B.
+ \BJP
  @node $B%3%^%s%I%i%$%s%*%W%7%g%s(B,,, Risa/Asir
  @section $B%3%^%s%I%i%$%s%*%W%7%g%s(B
+ \E
+ \BEG
+ @node Command line options,,, Risa/Asir
+ @section Command line options
+ \E
  @noindent
- $B%3%^%s%I%i%$%s%*%W%7%g%s$O<!$NDL$j(B.
+ \JP $B%3%^%s%I%i%$%s%*%W%7%g%s$O<!$NDL$j(B.
+ \EG Command-line options for the command @samp{asir} are as follows.
  @table @code
  @item -heap @var{number}
+ \BJP
  @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.
  $B%G%U%)%k%H$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
  $B$rJQ99$9$k>l9g(B, @code{-heap} $B$rMQ$$$k(B. $BC10L$O%V%m%C%/$G$"$k(B.
  heap $B$NBg$-$5$O(B, @code{heap()} $BH!?t$GD4$Y$k$3$H$,$G$-$k(B ($BC10L$O%P%$%H(B).
+ \E
+ \BEG
+ In @b{Risa/Asir}, 4KB is used as an unit, called block,
+ for memory allocation.
+ By default, 16 blocks (64KB) are allocated initially.
+ This value can be changed by giving an option @code{-heap}
+ a number parameter in unit block.
+ Size of the heap area is obtained by a Built-in function heap(),
+ the result of which is a number in Bytes.
+ \E
  @item -adj @var{number}
+ \BJP
  $B$3$NCM$,Bg$-$$$[$I(B, $B;HMQ%a%b%jNL$OBg$-$/$J$k$,(B, GC $B;~4V$,>/$J$/$J(B
  $B$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
  $B$k(B. $B$3$NCM$,(B 1 $B0J2<$K$J$k$H(B GC $B$r$7$J$$@_Dj$K$J$k$N$GMWCm0U$G$"$k(B. heap
  $B$r$J$k$Y$/?-$P$5$:$K(B, GC $B$r<gBN$K$7$F%a%b%j4IM}$7$?$$>l9g$K$O(B, $B$3$NCM$r(B
  $BBg$-$/(B ($BNc$($P(B 8) $B@_Dj$9$k(B.
+ \E
+ \BEG
+ Heap area will be stretched by the memory manager,
+ if the size of reclaimed memories is less than 1/@var{number}
+ of currently allocated heap area.
+ The default value for @var{number} is 3.
+ If you do not prefer to stretch heap area by some reason, perhaps by
+ restriction of available memories, but if prefer to resort to
+ reclaiming garbages as far as possible,
+ then a large value should be chosen for @var{number}, e.g., 8.
+ \E
  @item -norc
- $B=i4|2=%U%!%$%k(B @samp{$HOME/.asirrc} $B$rFI$^$J$$(B.
+ \JP $B=i4|2=%U%!%$%k(B @samp{$HOME/.asirrc} $B$rFI$^$J$$(B.
+ \BEG
+ When this option is specified, @b{Asir} does not read the
+ initial file @samp{$HOME/.asirrc}.
+ \E
+ @item -quiet
+ \JP $B5/F0;~$NCx:n8"I=<($r9T$o$J$$(B.
+ \BEG Be quiet at boot time.
+ \E
  @item -f @var{file}
+ \BJP
  $BI8=`F~NO$NBe$o$j$K(B, @var{file} $B$+$iF~NO$rFI$_9~$s$G<B9T$9$k(B.
  $B%(%i!<$N:]$K$O$?$@$A$K=*N;$9$k(B.
+ \E
+ \BEG
+ Instead of the standard input, @var{file} is used as the input.
+ Upon an error, the execution immediately terminates.
+ \E
  @item -paristack @var{number}
+ \BJP
  @b{PARI} (@pxref{pari}) $B@lMQ$NNN0h$NBg$-$5$r;XDj$9$k(B. $BC10L$O%P%$%H(B. $B%G%U%)(B
  $B%k%H$G$O(B 1 MB.
+ \E
+ \BEG
+ This option specifies the private memory size for @code{PARI} (@pxref{pari}).
+ The unit is Bytes. By default, it is set to 1 MB.
+ \E
  @item -maxheap @var{number}
+ \BJP
  heap $BNN0h$N>e8B$r;XDj$9$k(B. $BC10L$O%P%$%H(B. $B%G%U%)%k%H$G$OL5@)8B(B. UNIX $B$N(B
  $B>l9g(B, $B<B:]$K$O(B @code{limit} $B%3%^%s%I$GI=<($5$l$k(B @code{datasize} $B$NCM(B
  $B$K@)8B$5$l$F$$$k$?$a(B, @code{-maxheap} $B$N;XDj$,$J$/$F$b0lDjNL0J>e$K(B
  heap $B$r3MF@$G$-$J$$>l9g$,$"$k$N$GCm0U(B.)
+ \E
+ \BEG
+ This option sets an upper limit of the heap size. The unit is Bytes.
+ Note that the size is already limited by the value of @code{datasize}
+ displayed by the command @code{limit} on UNIX.
+ \E
  @end table
+ \BJP
  @node $B4D6-JQ?t(B,,, Risa/Asir
  @section $B4D6-JQ?t(B
+ \E
+ \BEG
+ @node Environment variable,,, Risa/Asir
+ @section Environment variable
+ \E
  @noindent
+ \BJP
  @b{Asir} $B$N<B9T$K4X$9$k$$$/$D$+$N4D6-JQ?t$,B8:_$9$k(B. UNIX $B>e$G$O4D6-JQ?t(B
  $B$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
  $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
  $B$G$O(B, @samp{c:\autoexec.bat} $B$K=q$$$F(B reboot $B$9$k(B.
+ \E
+ \BEG
+ There exist several environment variables concerning with an execution
+ of @b{Asir}. On UNIX, an environment variable is set from shells, or
+ in rc files of shells. On Windows NT, it can be set from [Control Panel]
+ ->[Environment]. On Windows 95/98, it can be set in @samp{c:\autoexec.bat}.
+ Note that the setting takes effect after rebooting the machine on Windows
+/98.
+ \E
  @itemize @bullet
  @item
- @code{ASIR_KEY}
- UNIX $BHG$G$O(B, @b{Asir} $B$,5/F0$5$l$?%^%7%s$KBP$9$k(B @code{key} $B$,$J$1(B
- $B$l$P$=$N%^%7%s>e$G(B @b{Asir} $B$OF0:n$7$J$$(B. @code{key} $B$O(B 16 $B?J(B 8
- $B7e(B 3 $B%o!<%I$+$i$J$j(B,
- @example
- % cat asir_key
- cf6f236c 61a35091 dddc4529 geisha
- 82281685 d1929945 a8bd24ca yorktown
-b75d30 63f8df93 3e881113 nyanchu
- @end example
- $B$H$$$&7A$GJ#?tBf$N%^%7%s$KBP$9$k(B @code{key} $B$r0l$D$N%U%!%$%k$K$^$H$a$F(B
- $B=q$/$3$H$,$G$-$k(B. @code{key} $B$N8e$m$OL5;k$5$l$k$N$G(B, $B%3%a%s%H$r=q$/(B
- $B$3$H$,$G$-$k(B. @code{key} $B$r4^$`%U%!%$%k$O(B, $B0J2<$N=g$G%5!<%A$5$l$k(B.
- @enumerate
- @item
- $B4D6-JQ?t(B @code{ASIR_KEY} $B$K;XDj$5$l$?%U%!%$%k(B
- @item
- $B%+%l%s%H%G%#%l%/%H%j$N(B @samp{asir_key}
- @item
- $B4D6-JQ?t(B @code{ASIR_LIBDIR} $B$G;XDj$5$l$?%G%#%l%/%H%j(B ($B;XDj$,$J$1$l$P(B
- @samp{/usr/local/lib/asir}) $B$N(B @samp{asir_key}
- @end enumerate
- @item
  @code{ASIR_LIBDIR}
+ @*
+ \BJP
  @b{Asir} $B$N%i%$%V%i%j%G%#%l%/%H%j(B, $B$9$J$o$A%f!<%68@8l$G=q$+$l$?%U%!%$%k(B
  $B$J$I$,$*$+$l$k%G%#%l%/%H%j(B. $B;XDj$,$J$$>l9g(B UNIX $BHG$G$O(B
  @samp{/usr/local/lib/asir}, Windows $BHG$G$O(B Asir $B%a%$%s%G%#%l%/%H%j$N2<$N(B
  @samp{lib} $B%G%#%l%/%H%j$,MQ$$$i$l$k(B.
+ $B$3$N4D6-JQ?t$O(B @code{ASIRLOADPATH} $B$KE}9g$5$lGQ;_$5$l$kM=Dj(B.
+ \E
+ \BEG
+ The library directory of @b{Asir}, i.e., the directory where
+ , for example, files containing programs written in @b{Asir}.
+ If not specified, on UNIX, @samp{/usr/local/lib/asir} is used by default.
+ On Windows, @samp{lib} in @b{Asir root directory} is used by default.
+ This environment will be useful in a case where @b{Asir} binaries
+ are installed on a private directory of the user.
+ This environmental variable will become obsolete.
+ \E
+ @item
+ @code{ASIR_CONTRIB_DIR}
+ @*
+ \BJP
+ @b{Asir} $B$N(B asir-contrib $B%G%#%l%/%H%j(B, $B$9$J$o$A(B OpenXM/asir-contrib
+ $B%W%m%8%'%/%H$G=q$+$l$?%Q%C%1!<%8$d%G!<%?$J$I$,$*$+$l$k%G%#%l%/%H%j(B.
+ $B;XDj$,$J$$>l9g(B UNIX $BHG$G$O(B
+ @samp{/usr/local/lib/asir-contrib},
+ Windows $BHG$G$O(B Asir $B%a%$%s%G%#%l%/%H%j$N2<$N(B @samp{lib-asir-contrib}
+ $B%G%#%l%/%H%j$,MQ$$$i$l$k(B.
+ $B$3$N4D6-JQ?t$O(B @code{ASIRLOADPATH} $B$KE}9g$5$lGQ;_$5$l$kM=Dj(B.
+ This environmental variable will become obsolete.
+ \E
+ \BEG
+ The asir-contrib library directory of @b{Asir}, i.e., the directory where
+ packages and data developed by the OpenXM/asir-contrib project files are put.
+ If not specified, on UNIX, @samp{/usr/local/lib/asir-contrib}
+ is used by default.
+ On Windows, @samp{lib-asir-contrib} in @b{Asir root directory}
+ is used by default.
+ This environment will be useful in a case where @b{Asir} binaries
+ are installed on a private directory of the user.
+ \E
  @item
  @code{ASIRLOADPATH}
+ @*
+ \BJP
  $B%m!<%I$5$l$k%U%!%$%k$,$"$k%G%#%l%/%H%j$r(B UNIX $B$N>l9g(B ':',
  Windows$B$N>l9g(B ';' $B$G6h@Z$C$FJB$Y$k(B. $B%G%#%l(B
  $B%/%H%j$O:8$+$i=g$K%5!<%A$5$l$k(B. $B$3$N;XDj$,$J$$>l9g(B, $B$*$h$S;XDj$5$l$?(B
  $B%U%!%$%k$,(B @code{ASIRLOADPATH} $B$K$J$+$C$?>l9g(B, $B%i%$%V%i%j%G%#%l%/%H%j(B
  $B$b%5!<%A$5$l$k(B.
+ \E
+ \BEG
+ This environment specifies directories which contains files to be
+ loaded by @b{Asir} command @code{load()}.
+ Directories are separated by a `:' on UNIX, a ';' on Windows respectively.
+ The search order is from the left to the right.
+ After searching out all directories in @code{ASIRLOADPATH},
+ or in case of no specification at all,
+ the library directory will be searched.
+ \E
  @item
  @code{HOME}
+ @*
+ \BJP
  @var{-norc} $B%*%W%7%g%s$D$-$G5/F0$7$J$$>l9g(B, @samp{$HOME/.asirrc}$B$,$"$l$P(B,
  $BM=$a$3$N%U%!%$%k$r<B9T$9$k(B. @code{HOME} $B$,@_Dj$5$l$F$$$J$$>l9g(B, UNIX $BHG(B
  $B$G$O$J$K$bFI$^$J$$$,(B, Windows $BHG$G$O(B Asir $B%a%$%s%G%#%l%/%H%j(B
  (@code{get_rootdir()} $B$GJV$5$l$k%G%#%l%/%H%j(B) $B$N(B @samp{.asirrc} $B$rC5$7(B,
  $B$"$l$P$=$l$r<B9T$9$k(B.
+ \E
+ \BEG
+ If @b{Asir} is invoked without @var{-norc}, @samp{$HOME/.asirrc}, if exists,
+ is executed. If @code{HOME} is not set, nothing is done on UNIX. On Windows,
+ @samp{.asirrc} in @b{Asir root directory} is executed if it exists.
+ \E
  @end itemize
+ \BJP
  @node $B5/F0$+$i=*N;$^$G(B,,, Risa/Asir
  @section $B5/F0$+$i=*N;$^$G(B
+ \E
+ \BEG
+ @node Starting and Terminating an Asir session,,, Risa/Asir
+ @section Starting and Terminating an @b{Asir} session
+ \E
  @noindent
- @b{Asir} $B$r5/F0$9$k$H(B,
+ \JP @b{Asir} $B$r5/F0$9$k$H(B,
+ \BEG
+ Run @b{Asir}, then the copyright notice and the first prompt
+ will appear on your screen,
+ and a new @b{Asir} session will be started.
+ \E
  @example
  [0]
  @end example
  @noindent
+ \BJP
  $B$J$k%W%m%s%W%H$,I=<($5$l(B, $B%;%C%7%g%s$,3+;O$9$k(B. @samp{$HOME/.asirrc}
  (Windows $BHG$N>l9g(B, @code{HOME} $B@_Dj$5$l$F$$$J$$>l9g$K$O(B @code{get_rootdir()}
  $B$GJV$5$l$k%G%#%l%/%H%j$K$"$k(B @samp{.asirrc})
  $B$,B8:_$7$F$$$k>l9g(B, $B$3$N%U%!%$%k$r(B @b{Asir} $B%f!<%68@8l$G$+$+$l$?(B
  $B%U%!%$%k$H8+$J$7(B, $B2r<a<B9T$9$k(B.
+ \E
+ \BEG
+ When initialization file @samp{$HOME/.asirrc} exists,
+ @b{Asir} interpreter executes it at first taking it as a program
+ file written in @b{Asir}.
+ \E
  @noindent
+ \BJP
  $B%W%m%s%W%H$OF~NO$NHV9f$rI=$9(B. $B%;%C%7%g%s$O(B, @code{end;} $B$^$?$O(B
  @code{quit;} $B$rF~NO$9$k$3$H$K$h$j=*N;$9$k(B. $BF~NO$O(B, @samp{;} $B$^$?$O(B
  @samp{$} $B$^$G$r0l6h@Z$j$H$7$FI>2A$5$l$k(B. @samp{;} $B$N$H$-7k2L$OI=<($5$l(B,
  @samp{$} $B$N$H$-I=<($5$l$J$$(B.
+ \E
+ \BEG
+ The prompt indicates the sequential number of your input commands to
+ @b{Asir}.
+ The session will terminate when you input @code{end;} or @code{quit;}
+ to @b{Asir}.
+ Input commands are evaluated statement by statement.
+ A statement normally ends with its terminator
+ @samp{;} or @samp{$}.
+ (There are some exceptions. See, syntax of @b{Asir}.)
+ The result will be displayed when the command, i.e. statement,
+ is terminated by a @samp{;},
+ and will not when terminated by a @samp{$}.
+ \E
  @example
  % asir
-Line 382  a
+Line 751  a
 Line 382  a
 Line 751  a
  @end example
  @noindent
+ \BJP
  $B$3$NNc$G$O(B, @code{A}, @code{a}, @code{x}, @code{y} $B$J$kJ8;z$,;HMQ$5$l$F$$$k(B.
  @code{A} $B$O%W%m%0%i%`$K$*$1$kJQ?t$G(B, @code{a}, @code{x}, @code{y} $B$O?t3XE*(B
  $B$J0UL#$G$NITDj85$G$"$k(B. $B0lHL$K%W%m%0%i%`JQ?t$OBgJ8;z$G;O$^$j(B,
-Line 390  a
+Line 760  a
 Line 390  a
 Line 760  a
  $B0lJ}(B, $BITDj85$O$=$l<+?H$GCM$r;}$D$3$H$O$G$-$:(B, $B=>$C$F(B, $BITDj85$KBP$9$k(B
  $BBeF~$O5v$5$l$J$$(B. $B8e$K<($9$,(B, $BITDj85$KBP$9$kBeF~$O(B, $BAH$_9~$_H!?t(B @code{subst()}
  $B$K$h$jL@<(E*$K9T$o$l$k(B.
+ \E
+ \BEG
+ In the above example, names @code{A}, @code{a}, @code{x} and @code{y}
+ are used to identify mathematical and programming objects.
+ There, the name @code{A} denotes a program variable
+ (some times called simply as a program variable.)
+ while the other names, @code{a}, @code{x} and @code{y}, denote
+ mathematical objects, that is, indeterminates.
+ In general, program variables have names which begin with
+ capital letters, while names of indeterminates begin with
+ small letters.
+ As you can see in the example, program variables are used to hold and
+ keep objects, such as numbers and expressions, as their values,
+ just like variables in C programming language.
+ Whereas, indeterminates cannot have values so that assignment to
+ indeterminates are illegal.
+ If one wants to get a result by substituting a value for an indeterminate
+ in an expression, it is achieved by the function @code{subst} as the
+ value of the function.
+ \E
+ \BJP
  @node $B3d$j9~$_(B,,, Risa/Asir
  @section $B3d$j9~$_(B
+ \E
+ \BEG
+ @node Interruption,,, Risa/Asir
+ @section Interruption
+ \E
  @noindent
+ \BJP
  $B7W;;$r<B9TCf$K3d$j9~$_$r$+$1$?$$>l9g(B, $B3d$j9~$_%-%c%i%/%?(B($BDL>o$O(B
- @kbd{C-c}, DOS $BHG$G$O(B @kbd{C-x}, Mac $BHG$G$O(B
+ @kbd{C-c}, Windows, DOS $BHG$G$O(B @kbd{C-x} $B$rF~NO$9$k(B.
- @code{command+}@samp{.} ) $B$rF~NO$9$k(B.
+ \E
+ \BEG
+ To interrupt the @b{Asir} execution, input an interrupt character
+ from the keyboard.  A @kbd{C-c} is usually used for it.
+ (Notice: @kbd{C-x} on Windows and DOS.)
+ \E
  @example
  @@ (x+y)^1000;
-Line 405  a
+Line 807  a
 Line 405  a
 Line 807  a
  @end example
  @noindent
- $B3FA*Br;h$N0UL#$O<!$NDL$j(B.
+ \JP $B3FA*Br;h$N0UL#$O<!$NDL$j(B.
+ \EG Here, the meaning of options are as follows.
  @table @code
+ \BJP
  @item q
  @b{Asir} $B$r=*N;$9$k(B. ($B3NG'$"$j(B)
  @item t
-Line 417  a
+Line 821  a
 Line 417  a
 Line 821  a
  @item d
  $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}.
  @item u
- @code{register_handler()} (@pxref{ox_reset register_handler}) $B$GEPO?$5$l$?(B
+ @code{register_handler()} (@pxref{ox_reset ox_intr register_handler}) $B$GEPO?$5$l$?(B
  $B4X?t$r<B9T8e%H%C%W%l%Y%k$KLa$k(B. ($B3NG'$"$j(B)
  @item w
  $BCfCGE@$^$G$NH!?t$N8F$S=P$7Ns$rI=<($9$k(B.
  @item ?
  $B3FA*Br;h$N0UL#$r@bL@$9$k(B.
+ \E
+ \BEG
+ @item q
+ Terminates @b{Asir} session. (Confirmation requested.)
+ @item t
+ Returns to toplevel. (Confirmation requested.)
+ @item c
+ Resumes to continue the execution.
+ @item d
+ Enters debugging mode at the next statement of the @b{Asir} program,
+ if @b{Asir} has been executing a program loaded from a file.
+ Note that it will sometimes take a long time before entering
+ debugging mode when @b{Asir} is executing basic functions in the
+ algebraic engine, (e.g., arithmetic operation, factorization etc.)
+ Detailed description about the debugger will be given in @ref{Debugger}.
+ @item u
+ After executing a function registered by @code{register_handler()}
+ (@pxref{ox_reset ox_intr register_handler}), returns to toplevel. A confirmation
+ is prompted.
+ @item w
+ Displays the calling sequence up to the interruption.
+ @item ?
+ Show a brief description of options.
+ \E
  @end table
+ \BJP
  @node $B%(%i!<=hM}(B,,, Risa/Asir
  @section $B%(%i!<=hM}(B
+ \E
+ \BEG
+ @node Error handling,,, Risa/Asir
+ @section Error handling
+ \E
  @noindent
+ \BJP
  $BAH$_9~$_H!?t$KIT@5$J7?$N0z?t$rEO$7$?>l9g$J$I$K$O<B9T$,CfCG$5$l$k$,(B,
  $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
  $B%b!<%I$KF~$k(B. $B$3$N>uBV$G(B
-Line 436  a
+Line 871  a
 Line 436  a
 Line 871  a
  $BI=<($5$l$k%(%i!<%a%C%;!<%8$O$5$^$6$^$G$"$j(B, $BFbIt$NH!?tL>$K0z$-B3$$$F(B
  $B%a%C%;!<%8$,I=<($5$l$k(B. $B$3$l$O(B, $B8F$S=P$5$l$?AH$_9~$_H!?t(B
  $B$HI,$:$7$bBP1~$O$7$J$$(B.
+ \E
+ \BEG
+ When arguments with illegal types are given to a built-in function,
+ an error will be detected and the execution will be quit.
+ In many cases, when an error is detected in a built-in function,
+ @b{Asir} automatically enters debugging mode before coming back
+ to toplevel.
+ At that time, one can examine the state of the program,
+ for example, inspect argument values just before the error occurred.
+ Messages reported there are various depending on cases.  They are
+ reported after the internal function name.  The internal function name
+ sometimes differs from the built-in function name that is specified by
+ the user program.
+ \E
  @noindent
+ \BJP
  $B$=$NB>(B, $B$5$^$6$^$J860x$K$h$jFbIt1i;;H!?t$K$*$$$F%(%i!<$,@8$:$k$3$H$,(B
  $B$"$k(B. UNIX $BHG$N>l9g(B, $B$3$l$O<!$N$$$:$l$+$N(B
  @code{internal error} $B$H$7$FJs9p$5$l(B, $BDL>o$N%(%i!<$HF1MM$K07$C$F(B,
  $B%G%P%C%0%b!<%I$KF~$k(B.
+ \E
+ \BEG
+ In the execution of internal functions, errors may happen by various
+ reasons.  The UNIX version of @b{Asir} will report those errors as one of
+ the following @code{internal error}'s, and enters debugging mode just
+ like normal errors.
+ \E
  @table @code
  @item SEGV
  @itemx BUS ERROR
+ @*
+ \BJP
  $BAH$_9~$_H!?t$K$h$C$F$O(B, $B0z?t$N7?$r87L)$K%A%'%C%/$;$:$K1i;;%k!<%A%s$K0z(B
  $B$-EO$7$F$7$^$&$b$N$bB8:_$7$F$$$k(B. $B$3$N$h$&$J>u67$K$*$$$F(B,
  $BIT@5$J%]%$%s%?(B, $B$"$k$$$O(B NULL $B%]%$%s%?$K$h$k%"%/%;%90cH?$,$"$C$?>l9g(B, $B$3$l$i(B
  $B$N%(%i!<$H$J$k(B.
+ \E
+ \BEG
+ Some of the built-in functions transmit their arguments to internal
+ operation routines without strict type-checking.  In such cases,
+ one of these two errors will be reported
+ when an access violation caused by an illegal pointer or a NULL pointer
+ is detected.
+ \E
  @item BROKEN PIPE
+ @*
+ \BJP
  $B%W%m%;%94VDL?.$K$*$$$F(B, $BAj<j@h$N%W%m%;%9$H$N4V$N%9%H%j!<%`(B
  $B$,4{$KB8:_$7$F$$$J$$>l9g(B ($BNc$($P4{$KAj<j@h$N%W%m%;%9$,=*N;$7$F$$$k>l9g$J$I(B)
  $B$K(B, $B$=$N%9%H%j!<%`$KF~=PNO$7$h$&$H$7$?>l9g$K$3$N%(%i!<$H$J$k(B.
+ \E
+ \BEG
+ In the process communication, this error will be reported if a process
+ attempts to read from or to write onto the partner process when the
+ stream to the partner process does not already exist, (e.g., terminated
+ process.)
+ \E
  @end table
  @noindent
+ \BJP
  $B$3$l$i$O<B:]$K$O(B, $BAH$_9~$_H!?t$NF~8}$K$*$$$F(B, $B0z?t$r40A4$K%A%'%C%/(B
  $B$9$k$3$H$K$h$jBgItJ,$OKI$2$k$,(B, $B<j4V$,B?$/$+$+$k$3$H$H(B, $B>l9g$K(B
  $B$h$C$F$O8zN($rMn$9$3$H$K$b$J$k$?$a(B, $B$"$($F0z?t%A%'%C%/$O%f!<%6(B
  $BG$$;$K$7$F$"$k(B.
+ \E
+ \BEG
+ For UNIX version, even in such a case, the process itself does not
+ terminate because such an error can be caught by @code{signal()} and
+ recovered.
+ To remove this weak point, complete type
+ checking of all arguments are indispensable at the entry of a built-in
+ function, which requires an enormous amount of re-making efforts.
+ \E
+ \BJP
  @node $B7W;;7k2L$*$h$SFC<l$J?t(B,,, Risa/Asir
  @section $B7W;;7k2L(B, $BFC<l$J?t(B
+ \E
+ \BEG
+ @node Referencing results and special numbers,,, Risa/Asir
+ @section Referencing results and special numbers
+ \E
  @noindent
- @code{@@} $B$O%(%9%1!<%WJ8;z$H$7$F;HMQ$5$l$k(B. $B8=:_<!$N$h$&$J5,Dj$,$"$k(B.
+ \JP @code{@@} $B$O%(%9%1!<%WJ8;z$H$7$F;HMQ$5$l$k(B. $B8=:_<!$N$h$&$J5,Dj$,$"$k(B.
+ \BEG
+ An @code{@@} used for an escape character; rules currently in force
+ are as follows.
+ \E
  @table @code
+ \BJP
  @item @@@var{n}
  @var{n} $BHVL\$N7W;;7k2L(B.
  @item @@@@
-Line 486  a
+Line 980  a
 Line 486  a
 Line 980  a
 $B85BN(B GF(2) $B>e$N0lJQ?tB?9`<0$NJQ?t(B ($BITDj85(B).
  @item @@>, @@<, @@>=, @@<=, @@==, @@&&, @@||
  quantifier elimination $B$K$*$1$k(B, $B0l3,=R8lO@M}1i;;;R(B
+ \E
+ \BEG
+ @item @@@var{n}
+ The evaluated result of @var{n}-th input command
+ @item @@@@
+ The evaluated result of the last command
+ @item @@i
+ The unit of imaginary number, square root of -1.
+ @item @@pi
+ The number pi,
+ the ratio of a circumference of the circle and its diameter.
+ @item @@e
+ Napier's number, the base of natural logarithm.
+ @item @@
+ A generator of GF(2^m), a finite field of characteristic 2, over GF(2).
+ It is a root of an irreducible univariate polynomial over GF(2)
+ which is set as the defining polynomial of GF(2^m).
+ @item @@>, @@<, @@>=, @@<=, @@==, @@&&, @@||
+ Fist order logical operators. They are used in quantifier elimination.
+ \E
  @end table
  @example
-Line 508  x^4-x^3+x^2-x+1
+Line 1022  x^4-x^3+x^2-x+1
 Line 508  x^4-x^3+x^2-x+1
 Line 1022  x^4-x^3+x^2-x+1
  @end example
  @noindent
+ \BJP
  $B%H%C%W%l%Y%k$G7W;;$5$l$?CM$O$3$N$h$&$K%R%9%H%j$H$7$F<h$j=P$72DG=$G$"$k$,(B,
  $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,
  $BBg$-$J<0$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
  $BG=@-$,$"$k(B. $B$3$N$h$&$J>l9g(B, @code{delete_history()}
  (@pxref{delete_history,,@code{delete_history}}) $B$,M-8z$G$"$k(B.
+ \E
+ \BEG
+ As you can see in the above example,
+ results of toplevel computation can be referred to
+ by @code{@@} convention.
+ This is convenient for users, while it sometimes imposes a heavy
+ burden to the garbage collector.
+ It may happen that GC time will rapidly increase after computing
+ a very large expression at the toplevel.
+ In such cases @code{delete_history()}
+ (@pxref{delete_history,,@code{delete_history}}) takes effect.
+ \E

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