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Initial revision

@node $B7?(B,,, Top
@chapter $B7?(B

@menu
* Asir $B$G;HMQ2DG=$J7?(B::
* $B?t$N7?(B::
* $BITDj85$N7?(B::
@end menu

@node Asir $B$G;HMQ2DG=$J7?(B,,, $B7?(B
@section @b{Asir} $B$G;HMQ2DG=$J7?(B

@noindent
@b{Asir} $B$K$*$$$F$O(B, $B2DFI$J7A<0$GF~NO$5$l$?$5$^$6$^$JBP>]$O(B, $B%Q!<%6$K$h$j(B
$BCf4V8@8l$KJQ49$5$l(B, $B%$%s%?%W%j%?$K$h$j(B @b{Risa} $B$N7W;;%(%s%8%s$r8F$S=P$7(B
$B$J$,$iFbIt7A<0$KJQ49$5$l$k(B. $BJQ49$5$l$?BP>]$O(B, $B<!$N$$$:$l$+$N7?$r;}$D(B. 
$B3FHV9f$O(B, $BAH$_9~$_H!?t(B @code{type()} $B$K$h$jJV$5$l$kCM$KBP1~$7$F$$$k(B. 
$B3FNc$O(B, @b{Asir} $B$N%W%m%s%W%H$KBP$9$kF~NO$,2DG=$J7A<0$N$$$/$D$+$r(B
$B<($9(B. 

@table @code
@item 0
@b{0}

$B<B:]$K$O(B 0 $B$r<1JL;R$K$b$DBP>]$OB8:_$7$J$$(B. 0 $B$O(B, C $B$K$*$1$k(B 0 $B%]%$%s%?$K(B
$B$h$jI=8=$5$l$F$$$k(B. $B$7$+$7(B, $BJX59>e(B @b{Asir} $B$N(B @code{type(0)} $B$O(B
$BCM(B 0 $B$rJV$9(B. 

@item 1
@b{$B?t(B}

@example
1 2/3  14.5  3+2*@@i 
@end example

$B?t$O(B, $B$5$i$K$$$/$D$+$N7?$KJ,$1$i$l$k(B. $B$3$l$K$D$$$F$O2<$G=R$Y$k(B. 

@item 2
@b{$BB?9`<0(B} ($B?t$G$J$$(B)

@example
x  afo  (2.3*x+y)^10
@end example

$BB?9`<0$O(B, $BA4$FE83+$5$l(B, $B$=$N;~E@$K$*$1$kJQ?t=g=x$K=>$C$F(B, $B:F5"E*$K(B
1 $BJQ?tB?9`<0$H$7$F9_QQ$N=g$K@0M}$5$l$k(B (@xref{$BJ,;6I=8=B?9`<0(B}). 
$B$3$N;~(B, $B$=$NB?9`<0$K8=$l$k=g=x:GBg$NJQ?t$r(B @b{$B<gJQ?t(B} $B$H8F$V(B. 

@item 3
@b{$BM-M}<0(B} ($BB?9`<0$G$J$$(B)

@example
(x+1)/(y^2-y-x)  x/x
@end example

$BM-M}<0$O(B, $BJ,JlJ,;R$,LsJ,2DG=$G$b(B, $BL@<(E*$K(B @code{red()} $B$,8F$P$l$J$$(B
$B8B$jLsJ,$O9T$o$l$J$$(B. $B$3$l$O(B, $BB?9`<0$N(B GCD $B1i;;$,6K$a$F=E$$1i;;$G$"$k(B
$B$?$a$G(B, $BM-M}<0$N1i;;$OCm0U$,I,MW$G$"$k(B. 

@item 4
@b{$B%j%9%H(B}

@example
[]  [1,2,[3,4],[x,y]]
@end example

$B%j%9%H$OFI$_=P$7@lMQ$G$"$k(B. @code{[]} $B$O6u%j%9%H$r0UL#$9$k(B. $B%j%9%H$KBP$9$k(B
$BA`:n$H$7$F$O(B, @code{car()}, @code{cdr()}, @code{cons()} $B$J$I$K$h$kA`:n$NB>$K(B, 
$BFI$_=P$7@lMQ$NG[Ns$H$_$J$7$F(B, @code{[@var{index}]} $B$rI,MW$J$@$1$D$1$k$3$H$K$h$j(B
$BMWAG$N<h$j=P$7$r9T$&$3$H$,$G$-$k(B. $BNc$($P(B

@example
[0] L = [[1,2,3],[4,[5,6]],7]$
[1] L[1][1];
[5,6]
@end example

$BCm0U$9$Y$-$3$H$O(B, $B%j%9%H(B, $BG[Ns(B ($B9TNs(B, $B%Y%/%H%k(B) $B6&$K(B, $B%$%s%G%C%/%9$O(B
0 $B$+$i;O$^$k$3$H$H(B, $B%j%9%H$NMWAG$N<h$j=P$7$r%$%s%G%C%/%9$G9T$&$3$H$O(B, 
$B7k6I$O@hF,$+$i%]%$%s%?$r$?$I$k$3$H$KAjEv$9$k$?$a(B, $BG[Ns$KBP$9$kA`:n$K(B
$BHf3S$7$FBg$-$J%j%9%H$G$O;~4V$,$+$+$k>l9g$,$"$k$H$$$&$3$H$G$"$k(B. 

@item 5
@b{$B%Y%/%H%k(B}

@example
newvect(3)  newvect(2,[a,1])
@end example

$B%Y%/%H%k$O(B, @code{newvect()} $B$GL@<(E*$K@8@.$9$kI,MW$,$"$k(B. $BA0<T$NNc$G(B
$B$O(B2 $B@.J,$N(B 0 $B%Y%/%H%k$,@8@.$5$l(B, $B8e<T$G$O(B, $BBh(B 0 $B@.J,$,(B @code{a}, $BBh(B 1 
$B@.J,$,(B @code{1} $B$N%Y%/%H%k$,@8@.$5$l$k(B. $B=i4|2=$N$?$a$N(B $BBh(B 2 $B0z?t$O(B, $BBh(B
1 $B0z?t0J2<$ND9$5$N%j%9%H$r<u$1IU$1$k(B. $B%j%9%H$NMWAG$O:8$+$iMQ$$$i$l(B, $BB-(B
$B$j$J$$J,$O(B 0 $B$,Jd$o$l$k(B. $B@.J,$O(B @code{[@var{index}]} $B$K$h$j<h$j=P$;$k(B. $B<B:](B
$B$K$O(B, $B3F@.J,$K(B, $B%Y%/%H%k(B, $B9TNs(B, $B%j%9%H$r4^$`G$0U$N7?$NBP>]$rBeF~$G$-$k(B
$B$N$G(B, $BB?<!85G[Ns$r%Y%/%H%k$GI=8=$9$k$3$H$,$G$-$k(B. 

@example
[0] A3 = newvect(3);
[ 0 0 0 ]
[1] for (I=0;I<3;I++)A3[I] = newvect(3);
[2] for (I=0;I<3;I++)for(J=0;J<3;J++)A3[I][J]=newvect(3);
[3] A3;
[ [ [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] ] [ [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] ] [ [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] ] ]
[4] A3[0];
[ [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] ]
[5] A3[0][0];
[ 0 0 0 ]
@end example

@item 6
@b{$B9TNs(B}

@example
newmat(2,2)  newmat(2,3,[[x,y],[z]])
@end example

$B9TNs$N@8@.$b(B @code{newmat()} $B$K$h$jL@<(E*$K9T$o$l$k(B. $B=i4|2=$b(B, $B0z?t(B
$B$,%j%9%H$N%j%9%H$H$J$k$3$H$r=|$$$F$O%Y%/%H%k$HF1MM$G(B, $B%j%9%H$N3FMWAG(B
($B$3$l$O$^$?%j%9%H$G$"$k(B) $B$O(B, $B3F9T$N=i4|2=$K;H$o$l(B, $BB-$j$J$$ItJ,$K$O(B
0 $B$,Kd$a$i$l$k(B. $B9TNs$b(B, $B3FMWAG$K$OG$0U$NBP>]$rBeF~$G$-$k(B. $B9TNs$N3F(B
$B9T$O(B, $B%Y%/%H%k$H$7$F<h$j=P$9$3$H$,$G$-$k(B. 

@example
[0] M=newmat(2,3);
[ 0 0 0 ]
[ 0 0 0 ]
[1] M[1];
[ 0 0 0 ]
[2] type(@@@@);
5
@end example

@item 7
@b{$BJ8;zNs(B}

@example
""  "afo"
@end example

$BJ8;zNs$O(B, $B<g$K%U%!%$%kL>$J$I$KMQ$$$i$l$k(B. $BJ8;zNs$KBP$7$F$O2C;;$N$_$,(B
$BDj5A$5$l$F$$$F(B, $B7k2L$O(B 2 $B$D$NJ8;zNs$N7k9g$G$"$k(B. 

@example
[0] "afo"+"take";
afotake
@end example
@item 8
@b{$B9=B$BN(B}

@example
newstruct(afo)
@end example

$B9=B$BN$K4X$7$F$O(B, $B>O$r2~$a$F2r@b$9$kM=Dj$G$"$k(B. 

@item 9
@b{$BJ,;6I=8=B?9`<0(B}

@example
2*<<0,1,2,3>>-3*<<1,2,3,4>>
@end example

$B$3$l$O(B, $B$[$H$s$I%0%l%V%J4pDl@lMQ$N7?$G(B, $BDL>o$N7W;;$G$3$N7?$,I,MW$H(B
$B$J$k$3$H$O$^$:$J$$$,(B, $B%0%l%V%J4pDl7W;;%Q%C%1!<%8<+BN$,%f!<%68@8l(B
$B$G=q$+$l$F$$$k$?$a(B, $B%f!<%6$,A`:n$G$-$k$h$&FHN)$7$?7?$H$7$F(B  @b{Asir}
$B$G;HMQ$G$-$k$h$&$K$7$F$"$k(B. $B$3$l$K$D$$$F$O(B @xref{$B%0%l%V%J4pDl$N7W;;(B}.

@item 10
@b{$BId9f$J$7%^%7%s(B 32bit $B@0?t(B}

@item 11
@b{$B%(%i!<%*%V%8%'%/%H(B}

$B0J>eFs$D$O(B, Open XM $B$K$*$$$FMQ$$$i$l$kFC<l%*%V%8%'%/%H$G$"$k(B. 

@item 12
@b{GF(2) $B>e$N9TNs(B}

$B8=:_(B, $BI8?t(B 2 $B$NM-8BBN$K$*$1$k4pDlJQ49$N$?$a$N%*%V%8%'%/%H$H$7$FMQ$$$i$l(B
$B$k(B. 

@item 13
@b{MATHCAP $B%*%V%8%'%/%H(B}

Open XM $B$K$*$$$F(B, $B<BAu$5$l$F$$$k5!G=$rAw<u?.$9$k$?$a$N%*%V%8%'%/%H$G$"$k(B. 

@item 14
@b{first order formula}

quantifier elimination $B$GMQ$$$i$l$k0l3,=R8lO@M}<0(B. 
@end table

@node $B?t$N7?(B,,, $B7?(B
@section $B?t$N7?(B

@table @code
@item 0
@b{$BM-M}?t(B}

$BM-M}?t$O(B, $BG$0UB?G\D9@0?t(B (@b{bignum}) $B$K$h$j<B8=$5$l$F$$$k(B. $BM-M}?t$O>o$K(B
$B4{LsJ,?t$GI=8=$5$l$k(B. 

@item 1
@b{$BG\@:EYIbF0>.?t(B}

$B%^%7%s$NDs6!$9$kG\@:EYIbF0>.?t$G$"$k(B. @b{Asir} $B$N5/F0;~$K$O(B, 
$BDL>o$N7A<0$GF~NO$5$l$?IbF0>.?t$O$3$N7?$KJQ49$5$l$k(B. $B$?$@$7(B, 
@code{ctrl()} $B$K$h$j(B @b{bigfloat} $B$,A*Br$5$l$F$$$k>l9g$K$O(B
@b{bigfloat} $B$KJQ49$5$l$k(B. 

@example
[0] 1.2;
1.2
[1] 1.2e-1000; 
0
[2] ctrl("bigfloat",1);
1
[3] 1.2e-1000;         
1.20000000000000000513 E-1000
@end example

$BG\@:EYIbF0>.?t$HM-M}?t$N1i;;$O(B, $BM-M}?t$,IbF0>.?t$KJQ49$5$l$F(B, 
$BIbF0>.?t$H$7$F1i;;$5$l$k(B. 

@item 2
@b{$BBe?tE*?t(B}

@xref{$BBe?tE*?t$K4X$9$k1i;;(B}.

@item 3
@b{bigfloat}

@b{bigfloat} $B$O(B, @b{Asir} $B$G$O(B @b{PARI} $B%i%$%V%i%j$K$h$j(B
$B<B8=$5$l$F$$$k(B. @b{PARI} $B$K$*$$$F$O(B, @b{bigfloat} $B$O(B, $B2>?tIt(B
$B$N$_G$0UB?G\D9$G(B, $B;X?tIt$O(B 1 $B%o!<%I0JFb$N@0?t$K8B$i$l$F$$$k(B. 
@code{ctrl()} $B$G(B @b{bigfloat} $B$rA*Br$9$k$3$H$K$h$j(B, $B0J8e$NIbF0>.?t(B
$B$NF~NO$O(B @b{bigfloat} $B$H$7$F07$o$l$k(B. $B@:EY$O%G%U%)%k%H$G$O(B
10 $B?J(B 9 $B7eDxEY$G$"$k$,(B, @code{setprec()} $B$K$h$j;XDj2DG=$G$"$k(B. 

@example
[0] ctrl("bigfloat",1);
1
[1] eval(2^(1/2));
1.414213562373095048763788073031
[2] setprec(100);      
9
[3] eval(2^(1/2));
1.41421356237309504880168872420969807856967187537694807317654396116148
@end example

@code{eval()} $B$O(B, $B0z?t$K4^$^$l$kH!?tCM$r2DG=$J8B$j?tCM2=$9$kH!?t$G$"$k(B. 
@code{setprec()} $B$G;XDj$5$l$?7e?t$O(B, $B7k2L$N@:EY$rJ]>Z$9$k$b$N$G$O$J$/(B, 
@b{PARI} $BFbIt$GMQ$$$i$l$kI=8=$N%5%$%:$r<($9$3$H$KCm0U$9$Y$-$G$"$k(B. 
(@ref{eval}, @xref{pari})

@item 4
@b{$BJ#AG?t(B}

$BJ#AG?t$O(B, $BM-M}?t(B, $BG\@:EYIbF0>.?t(B, @b{bigfloat} $B$r<BIt(B, $B5uIt$H$7$F(B
@code{a+b*@@i} (@@i $B$O5u?tC10L(B) $B$H$7$FM?$($i$l$k?t$G$"$k(B. $B<BIt(B, $B5uIt$O(B
$B$=$l$>$l(B @code{real()}, @code{imag()} $B$G<h$j=P$;$k(B. 

@item 5
@b{$B>.I8?t$NM-8BAGBN$N85(B}

$B$3$3$G8@$&>.I8?t$H$O(B, $BI8?t$,(B 2^27 $BL$K~$N$b$N$N$3$H$G$"$k(B. $B$3$N$h$&$JM-8B(B
$BBN$O(B, $B8=:_$N$H$3$m%0%l%V%J4pDl7W;;$K$*$$$FFbItE*$KMQ$$$i$l(B, $BM-8BBN78?t$N(B
$BJ,;6I=8=B?9`<0$N78?t$r<h$j=P$9$3$H$GF@$i$l$k(B. $B$=$l<+?H$OB0$9$kM-8BBN$K4X(B
$B$9$k>pJs$O;}$?$:(B, @code{setmod()} $B$G@_Dj$5$l$F$$$kAG?t(B @var{p} $B$rMQ$$$F(B 
GF(@var{p}) $B>e$G$N1i;;$,E,MQ$5$l$k(B.

@item 6
@b{$BBgI8?t$NM-8BAGBN$N85(B}

$BI8?t$H$7$FG$0U$NAG?t$,$H$l$k(B. 
$B$3$N7?$N?t$O(B, $B@0?t$KBP$7(B@code{simp_ff} $B$rE,MQ$9$k$3$H$K$h$jF@$i$l$k(B. 


@item 7
@b{$BI8?t(B 2 $B$NM-8BBN$N85(B}

$BI8?t(B 2 $B$NG$0U$NM-8BBN$N85$rI=8=$9$k(B. $BI8?t(B 2 $B$NM-8BBN(B F $B$O(B, $B3HBg<!?t(B 
[F:GF(2)] $B$r(B n $B$H$9$l$P(B, GF(2) $B>e4{Ls$J(B n $B<!B?9`<0(B f(t) $B$K$h$j(B
F=GF(2)[t]/(f(t)) $B$H$"$i$o$5$l$k(B. $B$5$i$K(B, GF(2)[t] $B$N85(B g $B$O(B, f(t) 
$B$b4^$a$F<+A3$J;EJ}$G%S%C%HNs$H$_$J$5$l$k$?$a(B, $B7A<0>e$O(B, F $B$N85$O(B,
g mod f $B$O(B, g, f  $B$r$"$i$o$9(B 2 $B$D$N%S%C%HNs$GI=8=$9$k$3$H$,$G$-$k(B. 

F $B$N85$rF~NO$9$k$$$/$D$+$NJ}K!$,MQ0U$5$l$F$$$k(B. 

@itemize @bullet
@item
@code{@@}

@code{@@} $B$O$=$N8e$m$K?t;z(B, $BJ8;z$rH<$C$F(B, $B%R%9%H%j$dFC<l$J?t$r$"$i$o$9$,(B, 
$BC1FH$G8=$l$?>l9g$K$O(B, F=GF(2)[t]/(f(t)) $B$K$*$1$k(B t mod f $B$r$"$i$o$9(B. 
$B$h$C$F(B, @@ $B$NB?9`<0$H$7$F(B F $B$N85$rF~NO$G$-$k(B. (@@^10+@@+1 $B$J$I(B)

@item
@code{ptogf2n}

$BG$0UJQ?t$N(B 1 $BJQ?tB?9`<0$r(B, @code{ptogf2n} $B$K$h$jBP1~$9$k(B F $B$N85$KJQ49$9$k(B. 

@item
@code{ntogf2n}

$BG$0U$N<+A3?t$r(B, $B<+A3$J;EJ}$G(B F $B$N85$H$_$J$9(B. $B<+A3?t$H$7$F$O(B, 10 $B?J(B, 
16 $B?J(B (0x $B$G;O$^$k(B), 2 $B?J(B (0b $B$G;O$^$k(B) $B$GF~NO$,2DG=$G$"$k(B. 

@item
@code{$B$=$NB>(B}

$BB?9`<0$N78?t$r4]$4$H(B F $B$N85$KJQ49$9$k$h$&$J>l9g(B, @code{simp_ff}
$B$K$h$jJQ49$G$-$k(B. 

@end itemize
@end table

$BBgI8?tAGBN$NI8?t(B, $BI8?t(B 2 $B$NM-8BBN$NDj5AB?9`<0$O(B, @code{setmod_ff}
$B$G@_Dj$9$k(B. 
$BM-8BBN$N85$I$&$7$N1i;;$G$O(B, @code{setmod_ff} $B$K$h$j@_Dj$5$l$F$$$k(B
modulus $B$G(B, $BB0$9$kBN$,J,$+$j(B, $B$=$NCf$G1i;;$,9T$o$l$k(B. 
$B0lJ}$,M-M}?t$N>l9g$K$O(B, $B$=$NM-M}?t$O<+F0E*$K8=:_@_Dj$5$l$F$$$k(B
$BM-8BBN$N85$KJQ49$5$l(B, $B1i;;$,9T$o$l$k(B. 

@node $BITDj85$N7?(B,,, $B7?(B
@section $BITDj85$N7?(B

@noindent
$BB?9`<0$NJQ?t$H$J$jF@$kBP>]$r(B@b{$BITDj85(B}$B$H$h$V(B. @b{Asir} $B$G$O(B, 
$B1Q>.J8;z$G;O$^$j(B, $BG$0U8D$N%"%k%U%!%Y%C%H(B, $B?t;z(B, @samp{_} $B$+$i$J$kJ8;zNs(B
$B$rITDj85$H$7$F07$&$,(B, $B$=$NB>$K$b%7%9%F%`$K$h$jITDj85$H$7$F07$o$l$k$b$N(B
$B$,$$$/$D$+$"$k(B. @b{Asir} $B$NFbIt7A<0$H$7$F$O(B, $B$3$l$i$OA4$FB?9`<0$H$7$F$N(B
$B7?$r;}$D$,(B, $B?t$HF1MM(B, $BITDj85$N7?$K$h$j6hJL$5$l$k(B.

@table @code
@item 0
@b{$B0lHLITDj85(B}

$B1Q>.J8;z$G;O$^$kJ8;zNs(B. $BB?9`<0$NJQ?t$H$7$F:G$bIaDL$KMQ$$$i$l$k(B. 

@example
[0] [vtype(a),vtype(aA_12)];
[0,0]
@end example

@item 1
@b{$BL$Dj78?t(B}

@code{uc()} $B$O(B, @samp{_} $B$G;O$^$kJ8;zNs$rL>A0$H$9$kITDj85$r@8@.$9$k(B. 
$B$3$l$i$O(B, $B%f!<%6$,F~NO$G$-$J$$$H$$$&$@$1$G(B, $B0lHLITDj85$HJQ$o$i$J$$$,(B, 
$B%f!<%6$,F~NO$7$?ITDj85$H>WFM$7$J$$$H$$$&@-<A$rMxMQ$7$FL$Dj78?t$N(B
$B<+F0@8@.$J$I$KMQ$$$k$3$H$,$G$-$k(B. 

@example
[1] U=uc();                 
_0
[2] vtype(U);
1
@end example

@item 2
@b{$BH!?t7A<0(B}

$BAH$_9~$_H!?t(B, $B%f!<%6H!?t$N8F$S=P$7$O(B, $BI>2A$5$l$F2?$i$+$N(B @b{Asir} $B$N(B
$BFbIt7A<0$KJQ49$5$l$k$,(B, @code{sin(x)}, @code{cos(x+1)} $B$J$I$O(B, $BI>2A8e(B
$B$b$=$N$^$^$N7A$GB8:_$9$k(B. $B$3$l$OH!?t7A<0$H8F$P$l(B, $B$=$l<+?H$,(B 1 $B$D$N(B
$BITDj85$H$7$F07$o$l$k(B. $B$^$?$d$dFC<l$JNc$H$7$F(B, $B1_<~N((B @code{@@pi} $B$d(B
$B<+A3BP?t$NDl(B @code{@@e} $B$bH!?t7A<0$H$7$F07$o$l$k(B. 

@example
[3] V=sin(x);         
sin(x)
[4] vtype(V);
2
[5] vars(V^2+V+1);
[sin(x)]
@end example

@item 3
@b{$BH!?t;R(B}

$BH!?t8F$S=P$7$O(B, @var{fname(args)} $B$H$$$&7A$G9T$J$o$l$k$,(B, @var{fname} $B$N(B
$BItJ,$rH!?t;R$H8F$V(B. $BH!?t;R$K$O(B, $BH!?t$N<oN`$K$h$jAH$_9~$_H!?t;R(B,
$B%f!<%6Dj5AH!?t;R(B, $B=iEyH!?t;R$J$I$,$"$k$,(B, $BH!?t;R$OC1FH$GITDj85$H$7$F(B
$B5!G=$9$k(B. 

@example
[6] vtype(sin);
3
@end example
@end table