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Annotation of OpenXM/src/asir-doc/int-parts/operation.texi, Revision 1.2

1.2     ! noro        1: @comment $OpenXM: OpenXM/src/asir-doc/int-parts/operation.texi,v 1.1 2001/04/23 05:45:35 noro Exp $
        !             2: \JP @chapter $B$=$NB>$N1i;;(B
        !             3: \EG @chapter Other operations
        !             4:
        !             5: \BJP
        !             6: $B0J2<$N=t1i;;$K$*$$$F(B, $B:G8e$N0z?t$O(B, $B8F$S=P$7B&$K$h$C$F3NJ]$5$l$?(B,
        !             7: $B7k2L$N%]%$%s%?$r=q$/>l=j$r<($9%]%$%s%?$G$"$k(B.
        !             8: \E
        !             9: \BEG
        !            10: \E
        !            11:
        !            12: \JP @section $B=|;;(B
        !            13: \EG @section Division
1.1       noro       14:
                     15: @example
                     16: #include "ca.h"
                     17:
1.2     ! noro       18: divsrp(vl,a,b,qp,rp)   *qp = a / b; *rp = a % b
1.1       noro       19: VL vl;
                     20: P a,b,*qp,*rp;
                     21:
1.2     ! noro       22: premp(vl,a,b,rp)       *rp = lc(b)^(deg(a)-deg(b)+1)*a % b
1.1       noro       23: VL vl;
                     24: P a,b,*rp;
                     25: @end example
1.2     ! noro       26:
1.1       noro       27: @noindent
1.2     ! noro       28: \BJP
1.1       noro       29: $B0lHL$KB?JQ?tB?9`<0$KBP$7$F$O(B, $BI,$:$7$b=|;;$,<B9T$G$-$k$H$O8B$i$J$$(B.
                     30: @code{divsrp()} $B$O(B, $B>&(B, $B>jM>$,B8:_$9$k$3$H$,J,$+$C$F$$$k>l9g$K$=$l$i$r5a(B
                     31: $B$a$kH!?t$G$"$k(B. $B$3$l$O(B, $BNc$($P=|?t$N<g78?t$,M-M}?t$G$"$k>l9g$J$I$KMQ$$$i(B
                     32: $B$l$k(B. $B0lHL$KB?9`<0>jM>$O5<>jM>$r7W;;$9$k$3$H$K$h$j5a$a$k(B.
1.2     ! noro       33: \E
        !            34: \BEG
        !            35: \E
1.1       noro       36: @section GCD
                     37: @example
                     38: #include "ca.h"
                     39:
1.2     ! noro       40: ezgcdp(vl,a,b,rp)     *rp = gcd(pp(a),pp(b))
1.1       noro       41: VL vl;
                     42: P a,b,*rp;
                     43:
1.2     ! noro       44: ezgcdpz(vl,a,b,rp)    *rp = gcd(a,b)
1.1       noro       45: VL vl;
                     46: P a,b,*rp;
                     47:
                     48: pcp(vl,a,pp,cp)       *pp = pp(a); *cp = cont(cp);
                     49: VL vl;
                     50: P a,*pp,*cp;
                     51: @end example
                     52: @noindent
1.2     ! noro       53: \BJP
1.1       noro       54: @code{pp(a)} $B$O(B @code{a} $B$N86;OE*ItJ,(B, @code{cont(a)} $B$OMFNL$r(B
                     55: $BI=$9(B. @code{ezgcdp()} $B$O@0?t0x;R$r=|$$$?(B gcd, @code{ezgcdpz()} $B$O@0?t0x(B
                     56: $B;R$r$3$a$?(B gcd $B$r7W;;$9$k(B.
1.2     ! noro       57: \E
        !            58: \BEG
        !            59: \E
        !            60:
        !            61: \JP @section $BBeF~(B
        !            62: \EG @section Substitution
1.1       noro       63:
                     64: @example
                     65: #include "ca.h"
                     66:
1.2     ! noro       67: substp(vl,a,v,b,rp)
1.1       noro       68: VL vl;
                     69: P a,b,*rp;
                     70: V v;
                     71:
1.2     ! noro       72: substr(vl,a,v,b,rp)
1.1       noro       73: VL vl;
                     74: R a,b,*rp;
                     75: V v;
                     76: @end example
1.2     ! noro       77:
        !            78: @JP @section $BHyJ,(B
        !            79: @EG @section Differentiation
        !            80:
1.1       noro       81: @example
                     82: #include "ca.h"
                     83:
1.2     ! noro       84: diffp(vl,a,v,rp)
1.1       noro       85: VL vl;
                     86: P a,*rp;
                     87: V v;
                     88:
1.2     ! noro       89: pderivr(vl,a,v,rp)
1.1       noro       90: VL vl;
                     91: R a,*rp;
                     92: V v;
                     93: @end example
1.2     ! noro       94: \BJP
        !            95: @code{diffp()} $B$OB?9`<0(B @code{a} $B$r(B @code{v} $B$GJPHyJ,$9$k(B.
        !            96: @code{pderivr()} $B$OM-M}<0(B @code{a} $B$r(B @code{v} $B$GJPHyJ,$9$k(B.
        !            97: \E
        !            98: \BEG
        !            99: \E
        !           100:
        !           101: \JP @section $B=*7k<0(B
        !           102: \EG @section Resultants
1.1       noro      103:
                    104: @example
                    105: #include "ca.h"
                    106:
1.2     ! noro      107: resultp(vl,v,a,b,rp)
1.1       noro      108: VL v;
                    109: P a,b,*rp;
                    110: @end example
1.2     ! noro      111: \BJP
        !           112: @code{resultp()} $B$OB?9`<0(B $a,b$ $B$N(B, @code{v} $B$K4X$9$k=*7k<0$r7W;;$9$k(B.
        !           113: \E
        !           114: \BEG
        !           115: \E
1.1       noro      116:
1.2     ! noro      117: \JP @section $B0x?tJ,2r(B
        !           118: \EG @section Polynomial factorization
1.1       noro      119: @example
                    120: #include "ca.h"
                    121:
1.2     ! noro      122: fctrp(vl,a,dcp)
1.1       noro      123: VL vl;
                    124: P a;
                    125: DCP *dcp;
                    126:
1.2     ! noro      127: sqfrp(vl,a,dcp)
1.1       noro      128: VL vl;
                    129: P a;
                    130: DCP *dcp;
                    131: @end example
                    132: @noindent
1.2     ! noro      133: \BJP
        !           134: @code{fctrp()}, @code{sqfrp()} $B$OB?9`<0(B @code{a} $B$NM-M}?tBN>e$G$N(B
        !           135: $B4{Ls0x;RJ,2r(B, $BL5J?J}0x;RJ,2r$r$=$l$>$l9T$&(B.
1.1       noro      136: $B0x?tJ,2r$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
                    137: $B<!?t78?t%j%9%HMQ$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
                    138: $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
                    139: $BF~NOB?9`<0(B @code{a} $B$r(B
                    140: @example
                    141: a = c * b   (c $B$OM-M}?t(B, b $B$O@0?t>e86;OE*$JB?9`<0(B)
                    142: @end example
                    143: @noindent
                    144: $B$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,
                    145: @code{[c, 1]} $B$J$kDj?t9`(B, $B0J2<(B @code{b} $B$N0x;R$,B3$/(B.
1.2     ! noro      146: \E
        !           147: \BEG
        !           148: \E
1.1       noro      149: