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version 1.1, 2001/04/23 05:45:35 version 1.2, 2003/04/19 10:36:29
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 @comment $OpenXM$  @comment $OpenXM: OpenXM/src/asir-doc/int-parts/operation.texi,v 1.1 2001/04/23 05:45:35 noro Exp $
 @chapter $B$=$NB>$N1i;;(B  \JP @chapter $B$=$NB>$N1i;;(B
   \EG @chapter Other operations
   
 @section $B=|;;(B  \BJP
   $B0J2<$N=t1i;;$K$*$$$F(B, $B:G8e$N0z?t$O(B, $B8F$S=P$7B&$K$h$C$F3NJ]$5$l$?(B,
   $B7k2L$N%]%$%s%?$r=q$/>l=j$r<($9%]%$%s%?$G$"$k(B.
   \E
   \BEG
   \E
   
   \JP @section $B=|;;(B
   \EG @section Division
   
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 divsrp(vl,a,b,qp,rp)   *qp = a / b; *rp = a % b; ($BB?9`<0$H$7$F$N>&(B, $B>jM>(B)  divsrp(vl,a,b,qp,rp)   *qp = a / b; *rp = a % b
 VL vl;  VL vl;
 P a,b,*qp,*rp;  P a,b,*qp,*rp;
   
 premp(vl,a,b,rp)       *rp = lc(b)^(deg(a)-deg(b)+1)*a % b ($B5<>jM>(B)  premp(vl,a,b,rp)       *rp = lc(b)^(deg(a)-deg(b)+1)*a % b
 VL vl;  VL vl;
 P a,b,*rp;  P a,b,*rp;
 @end example  @end example
   
 @noindent  @noindent
   \BJP
 $B0lHL$KB?JQ?tB?9`<0$KBP$7$F$O(B, $BI,$:$7$b=|;;$,<B9T$G$-$k$H$O8B$i$J$$(B.  $B0lHL$KB?JQ?tB?9`<0$KBP$7$F$O(B, $BI,$:$7$b=|;;$,<B9T$G$-$k$H$O8B$i$J$$(B.
 @code{divsrp()} $B$O(B, $B>&(B, $B>jM>$,B8:_$9$k$3$H$,J,$+$C$F$$$k>l9g$K$=$l$i$r5a(B  @code{divsrp()} $B$O(B, $B>&(B, $B>jM>$,B8:_$9$k$3$H$,J,$+$C$F$$$k>l9g$K$=$l$i$r5a(B
 $B$a$kH!?t$G$"$k(B. $B$3$l$O(B, $BNc$($P=|?t$N<g78?t$,M-M}?t$G$"$k>l9g$J$I$KMQ$$$i(B  $B$a$kH!?t$G$"$k(B. $B$3$l$O(B, $BNc$($P=|?t$N<g78?t$,M-M}?t$G$"$k>l9g$J$I$KMQ$$$i(B
 $B$l$k(B. $B0lHL$KB?9`<0>jM>$O5<>jM>$r7W;;$9$k$3$H$K$h$j5a$a$k(B.  $B$l$k(B. $B0lHL$KB?9`<0>jM>$O5<>jM>$r7W;;$9$k$3$H$K$h$j5a$a$k(B.
   \E
   \BEG
   \E
 @section GCD  @section GCD
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 ezgcdp(vl,a,b,rp)     *rp = gcd(pp(a),pp(b));  ezgcdp(vl,a,b,rp)     *rp = gcd(pp(a),pp(b))
 VL vl;  VL vl;
 P a,b,*rp;  P a,b,*rp;
   
 ezgcdpz(vl,a,b,rp)    *rp = gcd(a,b);  ezgcdpz(vl,a,b,rp)    *rp = gcd(a,b)
 VL vl;  VL vl;
 P a,b,*rp;  P a,b,*rp;
   
Line 36  VL vl;
Line 50  VL vl;
 P a,*pp,*cp;  P a,*pp,*cp;
 @end example  @end example
 @noindent  @noindent
   \BJP
 @code{pp(a)} $B$O(B @code{a} $B$N86;OE*ItJ,(B, @code{cont(a)} $B$OMFNL$r(B  @code{pp(a)} $B$O(B @code{a} $B$N86;OE*ItJ,(B, @code{cont(a)} $B$OMFNL$r(B
 $BI=$9(B. @code{ezgcdp()} $B$O@0?t0x;R$r=|$$$?(B gcd, @code{ezgcdpz()} $B$O@0?t0x(B  $BI=$9(B. @code{ezgcdp()} $B$O@0?t0x;R$r=|$$$?(B gcd, @code{ezgcdpz()} $B$O@0?t0x(B
 $B;R$r$3$a$?(B gcd $B$r7W;;$9$k(B.  $B;R$r$3$a$?(B gcd $B$r7W;;$9$k(B.
   \E
   \BEG
   \E
   
 @section $BBeF~(B  \JP @section $BBeF~(B
   \EG @section Substitution
   
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 substp(vl,a,v,b,rp)   *rp = a $B$N(B v $B$K(B b $B$rBeF~(B  substp(vl,a,v,b,rp)
 VL vl;  VL vl;
 P a,b,*rp;  P a,b,*rp;
 V v;  V v;
   
 substr(vl,a,v,b,rp)   *rp = a $B$N(B v $B$K(B b $B$rBeF~(B  substr(vl,a,v,b,rp)
 VL vl;  VL vl;
 R a,b,*rp;  R a,b,*rp;
 V v;  V v;
 @end example  @end example
 @section $BHyJ,(B  
   @JP @section $BHyJ,(B
   @EG @section Differentiation
   
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 diffp(vl,a,v,rp)      *rp = a $B$r(B v $B$GJPHyJ,(B  diffp(vl,a,v,rp)
 VL vl;  VL vl;
 P a,*rp;  P a,*rp;
 V v;  V v;
   
 pderivr(vl,a,v,rp)    *rp = a $B$r(B v $B$GJPHyJ,(B  pderivr(vl,a,v,rp)
 VL vl;  VL vl;
 R a,*rp;  R a,*rp;
 V v;  V v;
 @end example  @end example
   \BJP
   @code{diffp()} $B$OB?9`<0(B @code{a} $B$r(B @code{v} $B$GJPHyJ,$9$k(B.
   @code{pderivr()} $B$OM-M}<0(B @code{a} $B$r(B @code{v} $B$GJPHyJ,$9$k(B.
   \E
   \BEG
   \E
   
 @section $B=*7k<0(B  \JP @section $B=*7k<0(B
   \EG @section Resultants
   
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 resultp(vl,v,a,b,rp)  *rp = a $B$H(B b $B$N=*7k<0(B ($BId9f$O=|$/(B)  resultp(vl,v,a,b,rp)
 VL v;  VL v;
 P a,b,*rp;  P a,b,*rp;
 @end example  @end example
   \BJP
   @code{resultp()} $B$OB?9`<0(B $a,b$ $B$N(B, @code{v} $B$K4X$9$k=*7k<0$r7W;;$9$k(B.
   \E
   \BEG
   \E
   
 @section $B0x?tJ,2r(B  \JP @section $B0x?tJ,2r(B
   \EG @section Polynomial factorization
 @example  @example
 #include "ca.h"  #include "ca.h"
   
 fctrp(vl,a,dcp)       *dcp = a $B$rM-M}?t>e$G0x?tJ,2r$7$?$b$N(B  fctrp(vl,a,dcp)
 VL vl;  VL vl;
 P a;  P a;
 DCP *dcp;  DCP *dcp;
   
 sqfrp(vl,a,dcp)       *dcp = a $B$NM-M}?t>e$GL5J?J}J,2r$7$?$b$N(B  sqfrp(vl,a,dcp)
 VL vl;  VL vl;
 P a;  P a;
 DCP *dcp;  DCP *dcp;
 @end example  @end example
 @noindent  @noindent
   \BJP
   @code{fctrp()}, @code{sqfrp()} $B$OB?9`<0(B @code{a} $B$NM-M}?tBN>e$G$N(B
   $B4{Ls0x;RJ,2r(B, $BL5J?J}0x;RJ,2r$r$=$l$>$l9T$&(B.
 $B0x?tJ,2r$N7k2L$O(B @code{[$B0x;R(B, $B=EJ#EY(B]} $B$N%j%9%H$H$7$FI=8=$G$-$k(B. $B$3$l$r(B  $B0x?tJ,2r$N7k2L$O(B @code{[$B0x;R(B, $B=EJ#EY(B]} $B$N%j%9%H$H$7$FI=8=$G$-$k(B. $B$3$l$r(B
 $B<!?t78?t%j%9%HMQ$N%G!<%?9=B$(B @code{DCP} $B$rN.MQ$7$FI=8=$9$k(B. $B$9$J$o$A(B, $B%a(B  $B<!?t78?t%j%9%HMQ$N%G!<%?9=B$(B @code{DCP} $B$rN.MQ$7$FI=8=$9$k(B. $B$9$J$o$A(B, $B%a(B
 $B%s%P(B @code{d} $B$K=EJ#EY(B, $B%a%s%P(B @code{c} $B$K0x;R$rBeF~$9$k(B. $BJ,2r$O(B, $B$^$:(B  $B%s%P(B @code{d} $B$K=EJ#EY(B, $B%a%s%P(B @code{c} $B$K0x;R$rBeF~$9$k(B. $BJ,2r$O(B, $B$^$:(B
Line 103  a = c * b   (c $B$OM-M}?t(B, b $B$O@0?t>e86;OE*$JB?
Line 143  a = c * b   (c $B$OM-M}?t(B, b $B$O@0?t>e86;OE*$JB?
 @noindent  @noindent
 $B$HJ,2r$7$?8e(B, @code{b} $B$r<B:]$KJ,2r$9$k(B. $B7k2L$O(B, $B%j%9%H$N@hF,$K(B,  $B$HJ,2r$7$?8e(B, @code{b} $B$r<B:]$KJ,2r$9$k(B. $B7k2L$O(B, $B%j%9%H$N@hF,$K(B,
 @code{[c, 1]} $B$J$kDj?t9`(B, $B0J2<(B @code{b} $B$N0x;R$,B3$/(B.  @code{[c, 1]} $B$J$kDj?t9`(B, $B0J2<(B @code{b} $B$N0x;R$,B3$/(B.
   \E
   \BEG
   \E
   
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