Annotation of OpenXM/src/asir-doc/int-parts/operation.texi, Revision 1.3
1.3 ! saito 1: @comment $OpenXM: OpenXM/src/asir-doc/int-parts/operation.texi,v 1.2 2003/04/19 10:36:29 noro Exp $
1.2 noro 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:
1.3 ! saito 78: \JP @section $BHyJ,(B
! 79: \EG @section Differentiation
1.2 noro 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:
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