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version 1.1, 1999/12/08 05:47:44

version 1.2, 1999/12/21 02:47:32

Line 1

@comment $OpenXM$

@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::

Line 11

Line 13

* $B3d$j9~$_(B::

* $B%(%i!<=hM}(B::

* $B7W;;7k2L$*$h$SFC<l$J?t(B::

\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::

@end menu

\BJP

@node Risa $B$*$h$S(B Asir,,, Risa/Asir

@section Risa $B$*$h$S(B Asir

\BEG

@node Risa and Asir,,, Risa/Asir

@section @b{Risa} and @b{Asir}

@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.

\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.

@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)

\BEG

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.

@item

@code{$B%a%b%j4IM}It(B}

\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

($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.

\BEG

@b{Risa} employs, as its memory management component (the memory

manager), a free software distributed by Boehm (@code{gc-5.0alpha2}).

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.

@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.

\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.

@end itemize

\BJP

@node Asir $B$NFCD'(B,,, Risa/Asir

@section Asir $B$NFCD'(B

\BEG

@node Features of Asir,,, Risa/Asir

@section Features of @b{Asir}

@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.

\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.

@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

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

\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

@end itemize

\BJP

@node $B%$%s%9%H%l!<%7%g%s(B,,, Risa/Asir

@section $B%$%s%9%H%l!<%7%g%s(B

\BEG

@node Installation,,, Risa/Asir

@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 well come by e-mails

to the following address.

@example

noro@@para.flab.fujitsu.co.jp

noryo@@flab.fujitsu.co.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

\BJP

* UNIX $BHG(B::

* Windows $BHG(B::

\BEG

* UNIX version::

* Windows version::

@end menu

\BJP

@node UNIX $BHG(B,,, $B%$%s%9%H%l!<%7%g%s(B

@subsection UNIX $BHG(B

\BEG

@node UNIX version,,, Installation

@subsection UNIX version

@noindent

\BJP

$BI,MW$J%U%!%$%k$O(B @samp{asir.tgz} $B$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.

\BEG

A file @samp{asir.tgz} suitable for the taget 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}.

@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.

@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.

\BEG

In this case you have to set the name of the library directory

to the environment variable @code{ASIR_LIBDIR}.

@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.

\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.

@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$3$N>uBV$G(B @samp{asir} $B$r5/F0$7$F$_$k(B.

\BEG

Start @samp{asir}, and @b{Asir} will immediately terminate leaving you

a message as follows.

@example

% /usr/local/bin/asir

Line 156 See the file ASIR_INSTALL to get the correct key.

Line 328 See the file ASIR_INSTALL to get the correct key.

@end example

@noindent

\BJP

$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

$B$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,

Line 164 See the file ASIR_INSTALL to get the correct key.

Line 337 See the file ASIR_INSTALL to get the correct key.

risa@@para.flab.fujitsu.co.jp

@end example

@noindent

$B08$K(B,

@example

ASIR XXXXXXXX

@end example

@noindent

$B$H$$$&(B 1 $B9T$N$_$+$i$J$k(B e-mail $B$rAw$l$P$h$$(B. @code{XXXXXXXX} $B$OI=<($5$l$?(B

@code{ID} $B$G$"$k(B. $B@^$jJV$7(B

Line 182 YYYYYYYY YYYYYYYY YYYYYYYY

Line 353 YYYYYYYY YYYYYYYY YYYYYYYY

@noindent

$B$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}

$B$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.

\BEG

For UNIX version of @b{Asir}, you need a @code{key}, a string,

for each machine you want to run @b{Asir}.

In order to get the @code{key}, you just need to send an e-mail

consisting of a single line like

@example

ASIR XXXXXXXX

@end example

to address

@example

risa@@para.flab.fujitsu.co.jp

@end example

@noindent

Here, @code{XXXXXXXX} is the machine ID notified in the first message

from @b{Asir}.

After a while, an e-mail will be returned containing only one line like

@example

YYYYYYYY YYYYYYYY YYYYYYYY

@end example

@noindent

Then, you shall create a new file in the current directory

named @samp{asir_key} containing the returned string in one line.

All after this, call again @samp{asir}.

@example

% /usr/local/bin/asir

This is Asir, Version 990831.

Line 192 Copyright (C) FUJITSU LABORATORIES LIMITED.

Line 397 Copyright (C) FUJITSU LABORATORIES LIMITED.

@end example

@noindent

\BJP

$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

$B$G$"$k(B. @code{key} $B$r=q$$$F$*$/%U%!%$%k$K4X$7$F$O(B, $B4D6-JQ?t(B @code{ASIR_KEY}

$B$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

Line 199 Copyright (C) FUJITSU LABORATORIES LIMITED.

Line 405 Copyright (C) FUJITSU LABORATORIES LIMITED.

$B$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.

\BEG

If you get such a prompt (@samp{[0]}) from @b{Asir},

the key you have is valid to the machine you are currently running

@code{asir}.

When the file @samp{asir_key} is located on the library directory,

all the users of the machine can execute @samp{asir}.

The file @samp{asir_key} can contain several lines for

several @code{key}'s.

This enables users to run several machines sharing the same library

directory by simply adding lines for machines to be used.

We shall describe about the file for @code{key}'s in detail in

@ref{Environment variable}.

@example

# cp asir_key /usr/local/lib/asir

@end example

\BJP

@node Windows $BHG(B,,, $B%$%s%9%H%l!<%7%g%s(B

@subsection Windows $BHG(B

\BEG

@node Windows version,,, Installation

@subsection Windows version

@noindent

\BJP

$BI,MW$J%U%!%$%k$O(B @samp{asirwin.tgz} $B$G$"$k(B. $BB>$K(B, @samp{gzip.exe},

@samp{tar.exe} $B$,I,MW$@$,(B, asirwin.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, DOS $B%W%m%s%W%H(B

$B$+$i(B

\BEG

The necessary file is @samp{asirwin.tgz}. To unpack it @samp{gzip.exe}

and @samp{tar.exe} are necessary. They are in the same

directory as @samp{asirwin.tgz} on the ftp server.

Putting them in the same directory, execute the following:

@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

$BJL%W%m%;%9$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

Line 225 C:\...> tar xzf asirwin.tgz

Line 462 C:\...> tar xzf asirwin.tgz

$B%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} $B$N=i2s$NN)$A>e$2$O(B, $B%(%/%9%W%m!<%i$+$i9T(B

$B$&(B. $B$3$l$K$h$j(B

\BEG

Then a directory @samp{Asir} (@b{Asir root directory}) is created,

which has subdirectories named @samp{bin} and @samp{lib}. To set up it,

invoke @samp{bin\asirgui.exe} from Explorer and

click @code{OK}. Then the name of @b{Asir root directory} is set to the

following registries.

@example

HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory

\JP HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory

\EG HKEY_LOCAL_MACHINE\SOFTWARE\FUJITSU\Asir\99.03.31\Directory

@end example

@noindent

$B$H$$$&%l%8%9%H%j$K(B Asir $B%k!<%H%G%#%l%/%H%j$,@5$7$/EPO?$5$l$k(B.

\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

\BEG

@node Command line options,,, Risa/Asir

@section Command line options

@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).

\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.

@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.

\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.

@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}.

@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.

\BEG

Instead of the standard input, @var{file} is used as the input.

Upon an error, the execution immediately terminates.

@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.

\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.

@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.)

\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.

@end table

\BJP

@node $B4D6-JQ?t(B,,, Risa/Asir

@section $B4D6-JQ?t(B

\BEG

@node Environment variable,,, Risa/Asir

@section Environment variable

@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.

\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

95/98.

@itemize @bullet

@item

@code{ASIR_KEY}

\BJP

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,

\BEG

@b{Asir} shall not work unless a @code{key} for the machine

on which @b{Asir} is invoked is given.

The @code{key} consists of a string which denotes 3 word hexadecimal

number, each of which has 8 hexadecimal digits.

In order to run @b{Asir} for several machines,

several @code{key}'s can be written together on a same file as follows.

@example

% cat asir_key

cf6f236c 61a35091 dddc4529 geisha

Line 296 cf6f236c 61a35091 dddc4529 geisha

Line 620 cf6f236c 61a35091 dddc4529 geisha

34b75d30 63f8df93 3e881113 nyanchu

@end example

\BJP

$B$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.

\BEG

The text after each @code{key} is neglected to the end-of-line.

This is convenient to comment on the respective @code{key}.

Files containing @code{key}'s are searched by the following order.

@enumerate

@item

$B4D6-JQ?t(B @code{ASIR_KEY} $B$K;XDj$5$l$?%U%!%$%k(B

\JP $B4D6-JQ?t(B @code{ASIR_KEY} $B$K;XDj$5$l$?%U%!%$%k(B

\EG File set to environment @code{ASIR_KEY}

@item

$B%+%l%s%H%G%#%l%/%H%j$N(B @samp{asir_key}

\JP $B%+%l%s%H%G%#%l%/%H%j$N(B @samp{asir_key}

\EG File @samp{asir_key} on the current directory.

@item

\BJP

$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}

\BEG

Files on the directory specified by environment @code{ASIR_LIBDIR}.

(File @samp{asir_key} on @samp{/usr/local/lib/asir/},

if environment @code{ASIR_LIBDIR} is not set.)

@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.

\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.

@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.

\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.

@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.

\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.

@end itemize

\BJP

@node $B5/F0$+$i=*N;$^$G(B,,, Risa/Asir

@section $B5/F0$+$i=*N;$^$G(B

\BEG

@node Starting and Terminating an Asir session,,, Risa/Asir

@section Starting and Terminating an @b{Asir} session

@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.

@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.

\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}.

@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.

\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{$}.

@example

% asir

Line 382 a

Line 783 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 792 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.

\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.

\BJP

@node $B3d$j9~$_(B,,, Risa/Asir

@section $B3d$j9~$_(B

\BEG

@node Interruption,,, Risa/Asir

@section Interruption

@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

@code{command+}@samp{.} ) $B$rF~NO$9$k(B.

\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} for DOS version; @code{command+}@samp{.} for Macintosh

version.)

@example

@@ (x+y)^1000;

Line 405 a

Line 841 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 423 a

Line 861 a

$BCfCGE@$^$G$NH!?t$N8F$S=P$7Ns$rI=<($9$k(B.

@item ?

$B3FA*Br;h$N0UL#$r@bL@$9$k(B.

\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 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.

@end table

\BJP

@node $B%(%i!<=hM}(B,,, Risa/Asir

@section $B%(%i!<=hM}(B

\BEG

@node Error handling,,, Risa/Asir

@section Error handling

@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 905 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.

\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.

@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.

\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.

@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.

\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.

@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.

\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.)

@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.

\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.

\BJP

@node $B7W;;7k2L$*$h$SFC<l$J?t(B,,, Risa/Asir

@section $B7W;;7k2L(B, $BFC<l$J?t(B

\BEG

@node Referencing results and special numbers,,, Risa/Asir

@section Referencing results and special numbers

@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.

@table @code

\BJP

@item @@@var{n}

@var{n} $BHVL\$N7W;;7k2L(B.

@item @@@@

Line 486 a

Line 1014 a

2 $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

\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.

@end table

@example

Line 508 x^4-x^3+x^2-x+1

Line 1056 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.

\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.

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>