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Up to [local] / OpenXM / src / asir-doc / parts

Imported OpenXM/src/asir-doc. 

@node $BIUO?(B,,, Top
@appendix $BIUO?(B

@menu
* $BJ8K!$N>\:Y(B::
* $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::
* $BF~NO%$%s%?%U%'!<%9(B::
* $BJQ99E@(B::
* $BJ88%(B::
@end menu

@node $BJ8K!$N>\:Y(B,,, $BIUO?(B
@section $BJ8K!$N>\:Y(B

@example
<$B<0(B>: (@xref{$B$5$^$6$^$J<0(B})
    @samp{(}<$B<0(B>@samp{)}
    <$B<0(B> <$BFs9`1i;;;R(B> <$B<0(B>
    @samp{+} <$B<0(B>
    @samp{-} <$B<0(B>
    <$B:8JUCM(B>
    <$B:8JUCM(B> <$BBeF~1i;;;R(B> <$B<0(B>
    <$B:8JUCM(B> @samp{++}
    <$B:8JUCM(B> @samp{--}
    @samp{++} <$B:8JUCM(B>
    @samp{--} <$B:8JUCM(B>
    @samp{!} <$B<0(B>
    <$B<0(B> @samp{?} <$B<0(B> @samp{:} <$B<0(B>
    <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)}
    <$BJ8;zNs(B>
    <$B;X?t%Y%/%H%k(B>
    <$B%"%H%`(B>
    <$B%j%9%H(B>
@end example

@example
<$B:8JUCM(B>:
    <$BJQ?t(B> [@samp{[}<$B<0(B>@samp{]}]*
@end example

@example
<$BFs9`1i;;;R(B>:
    @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B) 
    @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
@end example

@example
<$BBeF~1i;;;R(B>:
    @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{%=} @samp{^=} 
@end example

@example
<$B<0JB$S(B>:
    <$B6u(B>
    <$B<0(B> [@samp{,} <$B<0(B>]*
@end example

@example
<$B%j%9%H(B>:
    @samp{[} <$B<0JB$S(B> @samp{]}
@end example

@example
<$BJQ?t(B>: (@xref{$BJQ?t$*$h$SITDj85(B})
    $BBgJ8;z$G;O$^$kJ8;zNs(B (X,Y,Japan $B$J$I(B)
@end example

@example
<$BH!?t(B>:
   $B>.J8;z$G;O$^$kJ8;zNs(B (fctr,gcd $B$J$I(B)
@end example

@example
<$B%"%H%`(B>:
   <$BITDj85(B>
   <$B?t(B>
@end example

@example
<$BITDj85(B>: (@xref{$BJQ?t$*$h$SITDj85(B})
   $B>.J8;z$G;O$^$kJ8;zNs(B (a,bCD,c1_2 $B$J$I(B)
@end example

@example
<$B?t(B>: (@xref{$B?t$N7?(B})
   <$BM-M}?t(B>
   <$BIbF0>.?t(B>
   <$BBe?tE*?t(B>
   <$BJ#AG?t(B>
@end example

@example
<$BM-M}?t(B>:
   0, 1, -2, 3/4
@end example

@example
<$BIbF0>.?t(B>:
   0.0, 1.2e10
@end example

@example
<$BBe?tE*?t(B>: (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
   newalg(x^2+1), alg(0)^2+1
@end example

@example
<$BJ#AG?t(B>:
   1+@code{@@i}, 2.3*@code{@@i}
@end example

@example
<$BJ8;zNs(B>:
   @samp{"} $B$G0O$^$l$?J8;zNs(B 
@end example

@example
<$B;X?t%Y%/%H%k(B>: (@xref{$B%0%l%V%J4pDl$N7W;;(B})
   @samp{<<} <$B<0JB$S(B> @samp{>>}
@end example

@example
<$BJ8(B>: (@xref{$BJ8(B})
    <$B<0(B> <$B=*C<(B>
    <$BJ#J8(B>
    @samp{break} <$B=*C<(B>
    @samp{continue} <$B=*C<(B>
    @samp{return} <$B=*C<(B>
    @samp{return} <$B<0(B> <$B=*C<(B>
    @samp{if} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>
    @samp{if} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B> @samp{else} <$BJ8(B>
    @samp{for} @samp{(} <$B<0JB$S(B> @samp{;} <$B<0JB$S(B> @samp{;} <$B<0JB$S(B> @samp{)} <$BJ8(B>
    @samp{do} <$BJ8(B> @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$B=*C<(B> 
    @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>
    @samp{def} <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)} @samp{@{} <$BJQ?t@k8@(B> <$BJ8JB$S(B> @samp{@}}
    @samp{end(quit)} <$B=*C<(B> 
@end example

@example
<$B=*C<(B>:
    @samp{;} @samp{$}
@end example

@example
<$BJQ?t@k8@(B>:
    [@samp{extern} <$BJQ?t(B> [@samp{,} <$BJQ?t(B>]* <$B=*C<(B>]*
@end example

@example
<$BJ#J8(B>:
    @samp{@{} <$BJ8JB$S(B> @samp{@}}
@end example

@example
<$BJ8JB$S(B>:
    [<$BJ8(B>]*
@end example

@node $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B,,, $BIUO?(B
@section $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B

@noindent
$BI8=`%i%$%V%i%j%G%#%l%/%H%j(B ($B%G%U%)%k%H$G$O(B @samp{/usr/local/lib/asir}) $B$K$O(B
$B$$$/$D$+$N%f!<%6Dj5AH!?t%U%!%$%k$,$*$+$l$F$$$k(B. $B$3$l$i$N$&$A$N<g$J$b$N$K$D$$$F(B
$B@bL@$9$k(B. 

@table @samp
@item fff
$BBgI8?tAGBN$*$h$SI8?t(B 2 $B$NM-8BBN>e$N0lJQ?tB?9`<00x?tJ,2r(B (@xref{$BM-8BBN$K4X$9$k1i;;(B})
@item gr
$B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B.  (@xref{$B%0%l%V%J4pDl$N7W;;(B})
@item sp
$BBe?tE*?t$N1i;;$*$h$S0x?tJ,2r(B, $B:G>.J,2rBN(B. (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
@item alpi
@itemx bgk
@itemx cyclic
@itemx katsura
@itemx kimura
$B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B. 
(@xref{katsura hkatsura cyclic hcyclic})
@item defs.h
$B$$$/$D$+$N%^%/%mDj5A(B. (@xref{$B%W%j%W%m%;%C%5(B})
@item fctrtest
$B@0?t>e$NB?9`<0$N0x?tJ,2r$N%F%9%H(B. REDUCE $B$N(B @samp{factor.tst} $B$*$h$S(B
$B=EJ#EY$NBg$-$$$$$/$D$+$NNc$r4^$`(B. $B$3$l$O(B, @code{load()} $B$9$k$H(B
$BD>$A$K7W;;$,;O$^$k(B. $BF~<j$7$?(B @b{Asir} $B$,@5$7$/F0:n$7$F$$$k$+$N(B
$B%F%9%H$K$b;H$&$3$H$,$G$-$k(B. 
@item fctrdata
@samp{fctrtest} $B$G;H$o$l$F$$$kNc$r4^$`(B, $B0x?tJ,2r%F%9%HMQ$NNc(B. 
@code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@xref{asq af}) $BMQ$NNc$G$"$k(B. 
@example
[45] load("sp")$
[84] load("fctrdata")$
[175] cputime(1)$
0msec
[176] Alg[5];
x^9-15*x^6-87*x^3-125
0msec
[177] af(Alg[5],[newalg(Alg[5])]);
[[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
[75*x^2+(-10*#0^7+175*#0^4+395*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
[25*x^2+(25*#0)*x+(#0^8-15*#0^5-87*#0^2),1],[x^2+(#0)*x+(#0^2),1],
[x+(-#0),1]]
3.600sec + gc : 1.040sec
@end example
@item ifplot
$BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
$B6J@~$NNc(B, $BJQ?t(B @code{H, D, C, S} $B$K$O%H%i%s%W$N%O!<%H(B, $B%@%$%d(B, $B%/%i%V(B, 
$B%9%Z!<%I(B ($B$i$7$-(B) $B6J@~$NNc$,F~$C$F$$$k(B. 
@item num
$B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
@item mat
$B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
@item ratint
$BM-M}H!?t$NITDj@QJ,(B. @samp{sp}, @samp{gr} $B$,I,MW(B. @code{ratint()} $B$H$$$&(B
$BH!?t$,Dj5A$5$l$F$$$k$,(B, $B$=$NJV$97k2L$O$d$dJ#;($G$"$k(B. $BNc$G@bL@$9$k(B. 
@example
[0] load("gr")$
[45] load("sp")$
[84] load("ratint")$
[102] ratint(x^6/(x^5+x+1),x);
[1/2*x^2,
[[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),161*t#2^3-23*t#2^2+15*t#2-1],
[(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
@end example
$B$3$NNc$G$O(B, @code{x^6/(x^5+x+1)} $B$NITDj@QJ,$N7W;;$r9T$C$F$$$k(B. 
$B7k2L$O(B 2 $B$D$NMWAG$+$i$J$k%j%9%H$G(B, $BBh(B 1 $BMWAG$OITDj@QJ,$NM-M}ItJ,(B, 
$BBh(B 2 $BMWAG$OBP?tItJ,$rI=$9(B. $BBP?tItJ,$O99$K%j%9%H$H$J$C$F$$$F(B, $B3FMWAG$O(B, 
@code{[root*log(poly),defpoly]} $B$H$$$&7A$r$7$F$$$k(B. $B$3$l$O(B, $BITDj@QJ,$K(B
$B$*$$$F$O(B, @code{defpoly} $B$NA4$F$N:,(B @code{root} $B$KBP$7$F(B @code{root*log(poly)}
$B$r:n$j$=$l$i$rB-$79g$o$;$k$H$$$&0UL#$G$"$k(B. $B$3$3$G(B @code{poly} $B$O(B
@code{root} $B$r4^$s$G$$$F(B, @code{root} $B$rF~$lBX$($k>l9g$K$O(B @code{poly}
$B$KBP$7$F$bF1$8A`:n$r9T$&$b$N$H$9$k(B. $B$3$NA`:n$r(B, $B7k2L$NBh(B 2 $BMWAG$N(B
$B3F@.J,$KBP$7$F9T$C$F(B, $BA4$F$rB-$79g$o$;$?$b$N$,BP?tItJ,$H$J$k(B. 
@item primdec
$BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
(@code{[Shimoyama,Yokoyama]} $B;2>H(B).
$B=`AG%$%G%"%kJ,2r$O(B @code{primadec()}, $BAG%$%G%"%kJ,2r$O(B, @code{primedec()}
$B$H$$$&4X?t$G(B, $BMQ0U$5$l$F$$$k(B. $B0z?t$O(B, $BB?9`<0%j%9%H$HJQ?t$G$"$k(B. 
$BM-M}<078?t$NB?9`<0%$%G%"%k$d(B, 0$B<!85$G$J$$%$%G%"%k$b07$($k(B. 
@code{primadec} $B$O(B, $B=`AG@.J,$H$=$NAG@.J,$N%Z%"%j%9%H$N%j%9%H$rJV$9(B. 
@code{primedec} $B$O(B, $BAG@.J,$N%j%9%H$rJV$9(B. 
$B$=$N7k2L$O$$$:$l$b%0%l%V%J4pDl$K$J$C$F$$$k$,(B, $B$=$N(B
$BJQ?t=g=x$O(B, $B$=$l$>$lBg0hJQ?t(B @code{PRIMAORD}, @code{PRIMEORD}
 $B$NCM(B 0,1 $B$"$k$$$O(B 2 $B$K$h$C$F7h$^$k(B. 
@example
[84] load("primdec")$
[102] primedec([p*q*x-q^2*y^2+q^2*y,-p^2*x^2+p^2*x+p*q*y,
(q^3*y^4-2*q^3*y^3+q^3*y^2)*x-q^3*y^4+q^3*y^3,
-q^3*y^4+2*q^3*y^3+(-q^3+p*q^2)*y^2],[p,q,x,y]);
[[y,x],[y,p],[x,q],[q,p],[x-1,q],[y-1,p],[(y-1)*x-y,q*y^2-2*q*y-p+q]]
[103] primadec([x,z*y,w*y^2,w^2*y-z^3,y^3],[x,y,z,w]);
[[[x,z*y,y^2,w^2*y-z^3],[z,y,x]],[[w,x,z*y,z^3,y^3],[w,z,y,x]]]
@end example
@end table

@node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B
@section $BF~NO%$%s%?%U%'!<%9(B

$B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B
$B$7$F%3%^%s%I%i%$%sJT=8$*$h$S%R%9%H%jCV$-49$($,AH$_9~$^$l$F$$$k(B. UNIX $BHG$G$O(B
$B$3$N$h$&$J5!G=$OAH$_9~$^$l$F$$$J$$$,(B, $B0J2<$G=R$Y$k$h$&$JF~NO%$%s%?%U%'!<%9(B
$B$,MQ0U$5$l$F$$$k(B. $B$3$l$i$O(B @b{Asir} $B%P%$%J%j$H$H$b$K(B ftp $B2DG=$G$"$k(B. 
ftp server $B$K4X$7$F$O(B @xref{$BF~<jJ}K!(B}.

@menu
* fep::
* asir.el::
@end menu

@node fep,,, $BF~NO%$%s%?%U%'!<%9(B
@subsection fep

@noindent
fep $B$H$O(B, SRA $B$N2NBe;a$K$h$j3+H/$5$l$?%3%^%s%I%i%$%sJT=8(B, $B%R%9%H%jCV$-49$((B
$BMQ$NF~NO%U%m%s%H%(%s%I$G$"$k(B. $B$3$N%W%m%0%i%`$N85$G(B @samp{asir} $B$r5/F0$9$k(B
$B$3$H$K$h$j(B vi $B$"$k$$$O(B emacs $BIw$N%3%^%s%I%i%$%sJT=8$*$h$S(B csh $BIw$N%R%9%H%j(B
$BCV$-49$($,2DG=$K$J$k(B. 

@example
% fep asir
...
[0] fctr(x^5-1);
[[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
[1] !!                              /* !!+Return                      */
fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */
...                                 /* $BJT=8(B+Return                    */
fctr(x^5+1);
[[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]
@end example

@noindent
fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $B%*%j%8%J%k$N$b$N$O(B make $B$G$-$k(B
$B5!<o(B (OS) $B$,8B$i$l$F$$$k(B. $B$$$/$D$+$N5!<o>e$GF0:n$9$k$h$&$K2f!9$,2~B$$7$?$b$N(B
$B$,(B, ftp $B$GF~<j2DG=$G$"$k(B.

@node asir.el,,, $BF~NO%$%s%?%U%'!<%9(B
@subsection asir.el

@noindent
@samp{asir.el} $B$O(B, @b{Asir} $B$N(B GNU Emacs $B%$%s%?%U%'!<%9$G$"$k(B ($BCx<T$O(B
$B5\Eh8w<#;a(B (@code{YVE25250@@pcvan.or.jp}).  @samp{asir.el} $B$K$*$$$F$O(B, 
$BDL>o$N(B emacs $B$G2DG=$JJT=85!G=$NB>$K(B, $B%U%!%$%kL>(B, $B%3%^%s%IL>$N(B completion
$B$,<B8=$5$l$F$$$k(B. 

@noindent
@samp{asir.el} $B$O(B PC-VAN $B$G(B
$B4{$K8x3+$5$l$F$$$k$,(B, $B:#2s$N2~D{$KH<$&JQ99$r9T$C$?$b$N$,(B, $B$d$O$j(B ftp $B$G(B
$BF~<j2DG=$G$"$k(B. 

@noindent
$B%;%C%H%"%C%W(B, $B;HMQJ}K!$O(B, @samp{asir.el} $B$N@hF,$K5-=R$5$l$F$$$k(B. 

@node $BJQ99E@(B,,, $BIUO?(B
@section $BJQ99E@(B

@menu
* Version 990831::
* Version 950831::
* Version 940420::
@end menu

@node Version 990831,,, $BJQ99E@(B
@subsection Version 990831

4 $BG/$V$j$NBg2~D{(B. $B@0?t$N(B 32bit $B2=B>(B, $BCf?H$O$:$$$V$sJQ$o$C$F$$$k$b$N$N(B, 
$B8+3]$1$O$=$l$[$IJQ$o$C$F$$$k$h$&$K$O8+$($J$$(B. $B$`$7$m(B, Windows $BHG$J$I$O(B, 
plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 

$B5lHG$N%f!<%6$,$b$C$H$bCm0U$9$Y$-E@$O(B, $B5lHG$G:n$C$?(B bsave file $B$rFI$_9~$`(B
$B>l9g$O(B @code{bload27} $B$r;H$&I,MW$,$"$k(B, $B$H$$$&E@$G$"$k(B. 

@node Version 950831,,, $BJQ99E@(B
@subsection Version 950831

@menu
* $B%G%P%C%,(B($BJQ99(B)::
* $BAH$_9~$_H!?t(B($BJQ99(B)::
* $B%0%l%V%J4pDl(B($BJQ99(B)::
* $B$=$NB>(B($BJQ99(B)::
@end menu

@node $B%G%P%C%,(B($BJQ99(B),,, Version 950831
@subsubsection $B%G%P%C%,(B

@itemize @bullet
@item
$BG$0U$N;~E@$K%G%P%C%0%b!<%I$KF~$l$k(B.
@item
@code{finish} $B%3%^%s%I$NDI2C(B. 
@item
@code{up}, @code{down}, @code{frame} $B%3%^%s%I$K$h$k(B, $BG$0U$N%9%?%C%/%U%l!<%`(B
$B$N;2>H(B. 
@item
@code{trace} $B%3%^%s%I$NDI2C(B. 
@end itemize

@node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831
@subsubsection $BAH$_9~$_H!?t(B

@itemize @bullet
@item
@code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B. 
@item
@code{sdivm()} $B$J$I(B, $BM-8BBN>e$G$NB?9`<0=|;;$NDI2C(B. 
@item
@code{det()}, @code{res()} $B$J$I$K$*$1$k(B, $BM-8BBN>e$G$N7W;;$N%5%]!<%H(B
@item
@code{vtol()} ($B%Y%/%H%k$+$i%j%9%H$X$NJQ49(B) $B$NDI2C(B. 
@item
@code{map()} $B$NDI2C(B. 
@end itemize

@node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831
@subsubsection $B%0%l%V%J4pDl(B

@itemize @bullet
@item
$B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B. 
@item
@code{grm()}, @code{hgrm()} $B$,(B @code{gr()}, @code{hgr()} $B$KJQ99(B. 
@item
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@item
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@item
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@item
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@item
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@end itemize

@node $B$=$NB>(B($BJQ99(B),,, Version 950831
@subsubsection $B$=$NB>(B

@itemize @bullet
@item
$BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.
@item
$BBe?tBN>e$N(B GCD $B7W;;$K$*$1$k%b%8%e%i7W;;$N1~MQ(B.
@item
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@item
Windows $B$X$N0\?"(B.
@end itemize

@node Version 940420,,, $BJQ99E@(B
@subsection Version 940420

@noindent
$B:G=i$N8x3+HG(B. 

@node $BJ88%(B,,, $BIUO?(B
@section $BJ88%(B
@table @code
@item [Batut et al.]
Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",
1993.
@item [Becker,Weispfenning] 
Becker, T., Weispfenning, V., "Groebner Bases", Graduate Texts in Math. 141,
Springer-Verlag, 1993.
@item [Boehm,Weiser] 
Boehm, H., Weiser, M., "Garbage Collection in an Uncooperative
Environment", Software Practice & Experience, September 1988, 807-820.
@item [Gebauer,Moeller] 
Gebauer, R., Moeller, H. M., "An installation of Buchberger's algorithm",
J. of Symbolic Computation 6, 275-286.
@item [Giovini et al.] 
Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C., 
""One sugar cube, please" OR Selection strategies in the Buchberger algorithm",
Proc. ISSAC'91, 49-54.
@item [Noro,Takeshima] 
Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",
Proc. ISSAC'92, 387-396.
@item [Noro,Yokoyama] 
Noro, M., Yokoyama, K., "New methods for the change-of-ordering in Groebner
basis computation", ISIS Research Report ISIS-RR-95-8E, 1995.
@item [Shimoyama,Yokoyama]
Shimoyama, T., Yokoyama, K.,
"Localization and primary decomposition of polynomial ideals",
to appear in J. Symb. Comp.
@item [Traverso]
Traverso, C., "Groebner trace algorithms", Proc. ISSAC '88(LNCS 358), 125-138.
@end table