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Diff for /OpenXM/src/asir-doc/parts/type.texi between version 1.4 and 1.5

version 1.4, 2000/01/20 03:00:34 version 1.5, 2000/01/26 01:37:33
Line 1 
Line 1 
 @comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.3 1999/12/21 02:47:32 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.4 2000/01/20 03:00:34 noro Exp $
 \BJP  \BJP
 @node $B7?(B,,, Top  @node $B7?(B,,, Top
 @chapter $B7?(B  @chapter $B7?(B
Line 52  Each example shows possible forms of inputs for @b{Asi
Line 52  Each example shows possible forms of inputs for @b{Asi
   
 @table @code  @table @code
 @item 0 @b{0}  @item 0 @b{0}
   @*
 \BJP  \BJP
 $B<B:]$K$O(B 0 $B$r<1JL;R$K$b$DBP>]$OB8:_$7$J$$(B. 0 $B$O(B, C $B$K$*$1$k(B 0 $B%]%$%s%?$K(B  $B<B:]$K$O(B 0 $B$r<1JL;R$K$b$DBP>]$OB8:_$7$J$$(B. 0 $B$O(B, C $B$K$*$1$k(B 0 $B%]%$%s%?$K(B
 $B$h$jI=8=$5$l$F$$$k(B. $B$7$+$7(B, $BJX59>e(B @b{Asir} $B$N(B @code{type(0)} $B$O(B  $B$h$jI=8=$5$l$F$$$k(B. $B$7$+$7(B, $BJX59>e(B @b{Asir} $B$N(B @code{type(0)} $B$O(B
Line 321  For details @xref{Groebner basis computation}.
Line 321  For details @xref{Groebner basis computation}.
   
 \JP @item 11 @b{$B%(%i!<%*%V%8%'%/%H(B}  \JP @item 11 @b{$B%(%i!<%*%V%8%'%/%H(B}
 \EG @item 11 @b{error object}  \EG @item 11 @b{error object}
   @*
 \JP $B0J>eFs$D$O(B, Open XM $B$K$*$$$FMQ$$$i$l$kFC<l%*%V%8%'%/%H$G$"$k(B.  \JP $B0J>eFs$D$O(B, Open XM $B$K$*$$$FMQ$$$i$l$kFC<l%*%V%8%'%/%H$G$"$k(B.
 \EG These are special objects used for OpenXM.  \EG These are special objects used for OpenXM.
   
 \JP @item 12 @b{GF(2) $B>e$N9TNs(B}  \JP @item 12 @b{GF(2) $B>e$N9TNs(B}
 \EG @item 12 @b{matrix over GF(2)}  \EG @item 12 @b{matrix over GF(2)}
   @*
 \BJP  \BJP
 $B8=:_(B, $BI8?t(B 2 $B$NM-8BBN$K$*$1$k4pDlJQ49$N$?$a$N%*%V%8%'%/%H$H$7$FMQ$$$i$l(B  $B8=:_(B, $BI8?t(B 2 $B$NM-8BBN$K$*$1$k4pDlJQ49$N$?$a$N%*%V%8%'%/%H$H$7$FMQ$$$i$l(B
 $B$k(B.  $B$k(B.
Line 338  This is used for basis conversion in finite fields of 
Line 338  This is used for basis conversion in finite fields of 
   
 \JP @item 13 @b{MATHCAP $B%*%V%8%'%/%H(B}  \JP @item 13 @b{MATHCAP $B%*%V%8%'%/%H(B}
 \EG @item 13 @b{MATHCAP object}  \EG @item 13 @b{MATHCAP object}
   @*
 \JP 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.  \JP 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.
 \EG This object is used to express available funcionalities for Open XM.  \EG This object is used to express available funcionalities for Open XM.
   
 @item 14 @b{first order formula}  @item 14 @b{first order formula}
   @*
 \JP quantifier elimination $B$GMQ$$$i$l$k0l3,=R8lO@M}<0(B.  \JP quantifier elimination $B$GMQ$$$i$l$k0l3,=R8lO@M}<0(B.
 \EG This expresses a first order formula used in quantifier elimination.  \EG This expresses a first order formula used in quantifier elimination.
   
 \JP @item -1 @b{VOID $B%*%V%8%'%/%H(B}  \JP @item -1 @b{VOID $B%*%V%8%'%/%H(B}
 \EG @item -1 @b{VOID object}  \EG @item -1 @b{VOID object}
   @*
 \JP $B7?<1JL;R(B -1 $B$r$b$D%*%V%8%'%/%H$O4X?t$NLa$jCM$J$I$,L58z$G$"$k$3$H$r<($9(B.  \JP $B7?<1JL;R(B -1 $B$r$b$D%*%V%8%'%/%H$O4X?t$NLa$jCM$J$I$,L58z$G$"$k$3$H$r<($9(B.
 \BEG  \BEG
 The object with the object identifier -1 indicates that a return value  The object with the object identifier -1 indicates that a return value
Line 370  of a function is void.
Line 370  of a function is void.
 @item 0  @item 0
 \JP @b{$BM-M}?t(B}  \JP @b{$BM-M}?t(B}
 \EG @b{rational number}  \EG @b{rational number}
   @*
 \BJP  \BJP
 $BM-M}?t$O(B, $BG$0UB?G\D9@0?t(B (@b{bignum}) $B$K$h$j<B8=$5$l$F$$$k(B. $BM-M}?t$O>o$K(B  $BM-M}?t$O(B, $BG$0UB?G\D9@0?t(B (@b{bignum}) $B$K$h$j<B8=$5$l$F$$$k(B. $BM-M}?t$O>o$K(B
 $B4{LsJ,?t$GI=8=$5$l$k(B.  $B4{LsJ,?t$GI=8=$5$l$k(B.
Line 384  lowest terms.
Line 384  lowest terms.
 @item 1  @item 1
 \JP @b{$BG\@:EYIbF0>.?t(B}  \JP @b{$BG\@:EYIbF0>.?t(B}
 \EG @b{double precision floating point number (double float)}  \EG @b{double precision floating point number (double float)}
   @*
 \BJP  \BJP
 $B%^%7%s$NDs6!$9$kG\@:EYIbF0>.?t$G$"$k(B. @b{Asir} $B$N5/F0;~$K$O(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,  $BDL>o$N7A<0$GF~NO$5$l$?IbF0>.?t$O$3$N7?$KJQ49$5$l$k(B. $B$?$@$7(B,
Line 424  result shall be computed as a double float number.
Line 424  result shall be computed as a double float number.
 @item 2  @item 2
 \JP @b{$BBe?tE*?t(B}  \JP @b{$BBe?tE*?t(B}
 \EG @b{algebraic number}  \EG @b{algebraic number}
   @*
 \JP @xref{$BBe?tE*?t$K4X$9$k1i;;(B}.  \JP @xref{$BBe?tE*?t$K4X$9$k1i;;(B}.
 \EG @xref{Algebraic numbers}.  \EG @xref{Algebraic numbers}.
   
 @item 3  @item 3
 @b{bigfloat}  @b{bigfloat}
   @*
 \BJP  \BJP
 @b{bigfloat} $B$O(B, @b{Asir} $B$G$O(B @b{PARI} $B%i%$%V%i%j$K$h$j(B  @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<B8=$5$l$F$$$k(B. @b{PARI} $B$K$*$$$F$O(B, @b{bigfloat} $B$O(B, $B2>?tIt(B
Line 479  operations of @b{PARI} are performed.
Line 479  operations of @b{PARI} are performed.
 @item 4  @item 4
 \JP @b{$BJ#AG?t(B}  \JP @b{$BJ#AG?t(B}
 \EG @b{complex number}  \EG @b{complex number}
   @*
 \BJP  \BJP
 $BJ#AG?t$O(B, $BM-M}?t(B, $BG\@:EYIbF0>.?t(B, @b{bigfloat} $B$r<BIt(B, $B5uIt$H$7$F(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  @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
Line 498  taken out by @code{real()} and @code{imag()} respectiv
Line 498  taken out by @code{real()} and @code{imag()} respectiv
 @item 5  @item 5
 \JP @b{$B>.I8?t$NM-8BAGBN$N85(B}  \JP @b{$B>.I8?t$NM-8BAGBN$N85(B}
 \EG @b{element of a small finite prime field}  \EG @b{element of a small finite prime field}
   @*
 \BJP  \BJP
 $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  $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  $BBN$O(B, $B8=:_$N$H$3$m%0%l%V%J4pDl7W;;$K$*$$$FFbItE*$KMQ$$$i$l(B, $BM-8BBN78?t$N(B
Line 521  field operations are executed by using a prime @var{p}
Line 521  field operations are executed by using a prime @var{p}
 @item 6  @item 6
 \JP @b{$BBgI8?t$NM-8BAGBN$N85(B}  \JP @b{$BBgI8?t$NM-8BAGBN$N85(B}
 \EG @b{element of large finite prime field}  \EG @b{element of large finite prime field}
   @*
 \BJP  \BJP
 $BI8?t$H$7$FG$0U$NAG?t$,$H$l$k(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.  $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.
Line 535  is an arbitrary prime. An object of this type is obtai
Line 535  is an arbitrary prime. An object of this type is obtai
 @item 7  @item 7
 \JP @b{$BI8?t(B 2 $B$NM-8BBN$N85(B}  \JP @b{$BI8?t(B 2 $B$NM-8BBN$N85(B}
 \EG @b{element of a finite field of characteristic 2}  \EG @b{element of a finite field of characteristic 2}
   @*
 \BJP  \BJP
 $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  $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)] $B$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
Line 560  representing @var{g} and @var{f} respectively.
Line 560  representing @var{g} and @var{f} respectively.
 @itemize @bullet  @itemize @bullet
 @item  @item
 @code{@@}  @code{@@}
   @*
 \BJP  \BJP
 @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,  @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.  $BC1FH$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.
Line 574 } one can input an element of @var{F}
Line 574 } one can input an element of @var{F}
   
 @item  @item
 @code{ptogf2n}  @code{ptogf2n}
   @*
 \JP $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.  \JP $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.
 \BEG  \BEG
 @code{ptogf2n} converts a univariate polynomial into an element of @var{F}.  @code{ptogf2n} converts a univariate polynomial into an element of @var{F}.
Line 582 } one can input an element of @var{F}
Line 582 } one can input an element of @var{F}
   
 @item  @item
 @code{ntogf2n}  @code{ntogf2n}
   @*
 \BJP  \BJP
 $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,  $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.  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.
Line 596  hexadecimal (@code{0x} prefix) and binary (@code{0b} p
Line 596  hexadecimal (@code{0x} prefix) and binary (@code{0b} p
 @item  @item
 \JP @code{$B$=$NB>(B}  \JP @code{$B$=$NB>(B}
 \EG @code{micellaneous}  \EG @code{micellaneous}
   @*
 \BJP  \BJP
 $BB?9`<0$N78?t$r4]$4$H(B F $B$N85$KJQ49$9$k$h$&$J>l9g(B, @code{simp_ff}  $BB?9`<0$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.  $B$K$h$jJQ49$G$-$k(B.
Line 660  and further are classified into sub-types of the type 
Line 660  and further are classified into sub-types of the type 
 @item 0  @item 0
 \JP @b{$B0lHLITDj85(B}  \JP @b{$B0lHLITDj85(B}
 \EG @b{ordinary indeterminate}  \EG @b{ordinary indeterminate}
   @*
 \JP $B1Q>.J8;z$G;O$^$kJ8;zNs(B. $BB?9`<0$NJQ?t$H$7$F:G$bIaDL$KMQ$$$i$l$k(B.  \JP $B1Q>.J8;z$G;O$^$kJ8;zNs(B. $BB?9`<0$NJQ?t$H$7$F:G$bIaDL$KMQ$$$i$l$k(B.
 \BEG  \BEG
 An object of this sub-type is denoted by a string that start with  An object of this sub-type is denoted by a string that start with
Line 678  polynomials.
Line 678  polynomials.
 @item 1  @item 1
 \JP @b{$BL$Dj78?t(B}  \JP @b{$BL$Dj78?t(B}
 \EG @b{undetermined coefficient}  \EG @b{undetermined coefficient}
   @*
 \BJP  \BJP
 @code{uc()} $B$O(B, @samp{_} $B$G;O$^$kJ8;zNs$rL>A0$H$9$kITDj85$r@8@.$9$k(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$$$,(B,  $B$3$l$i$O(B, $B%f!<%6$,F~NO$G$-$J$$$H$$$&$@$1$G(B, $B0lHLITDj85$HJQ$o$i$J$$$,(B,
Line 705  _0
Line 705  _0
 @item 2  @item 2
 \JP @b{$BH!?t7A<0(B}  \JP @b{$BH!?t7A<0(B}
 \EG @b{function form}  \EG @b{function form}
   @*
 \BJP  \BJP
 $BAH$_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  $BAH$_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  $BFbIt7A<0$KJQ49$5$l$k$,(B, @code{sin(x)}, @code{cos(x+1)} $B$J$I$O(B, $BI>2A8e(B
Line 737  sin(x)
Line 737  sin(x)
 @item 3  @item 3
 \JP @b{$BH!?t;R(B}  \JP @b{$BH!?t;R(B}
 \EG @b{functor}  \EG @b{functor}
   @*
 \BJP  \BJP
 $BH!?t8F$S=P$7$O(B, @var{fname(args)} $B$H$$$&7A$G9T$J$o$l$k$,(B, @var{fname} $B$N(B  $BH!?t8F$S=P$7$O(B, @var{fname(args)} $B$H$$$&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,  $BItJ,$rH!?t;R$H8F$V(B. $BH!?t;R$K$O(B, $BH!?t$N<oN`$K$h$jAH$_9~$_H!?t;R(B,
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