Annotation of OpenXM/src/asir-contrib/packages/doc/taji_alc/taji_alc_manual.texi, Revision 1.1
1.1 ! takayama 1: \input texinfo
! 2: @iftex
! 3: @catcode`@#=6
! 4: @def@fref#1{@xrefX[#1,,@code{#1},,,]}
! 5: @def@b#1{{@bf@gt #1}}
! 6: @catcode`@#=@other
! 7: @end iftex
! 8: @overfullrule=0pt
! 9: @c -*-texinfo-*-
! 10: @comment %**start of header
! 11: @comment --- $B$*$^$8$J$$=*$j(B ---
! 12:
! 13: @comment --- GNU info $B%U%!%$%k$NL>A0(B ---
! 14: @setfilename xyzman
! 15:
! 16: @comment --- $B%?%$%H%k(B ---
! 17: @settitle 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc
! 18:
! 19: @comment %**end of header
! 20: @comment %@setchapternewpage odd
! 21:
! 22: @comment --- $B$*$^$8$J$$(B ---
! 23: @ifinfo
! 24: @macro fref{name}
! 25: @ref{\name\,,@code{\name\}}
! 26: @end macro
! 27: @end ifinfo
! 28:
! 29: @iftex
! 30: @comment @finalout
! 31: @end iftex
! 32:
! 33: @titlepage
! 34: @comment --- $B$*$^$8$J$$=*$j(B ---
! 35:
! 36: @comment --- $B%?%$%H%k(B, $B%P!<%8%g%s(B, $BCx<TL>(B, $BCx:n8"I=<((B ---
! 37: @title 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc
! 38: @subtitle 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc
! 39: @subtitle 1.0 $BHG(B
! 40: @subtitle 2007 $BG/(B 11 $B7n(B
! 41:
! 42: @author $B>1;JBnL4(B, $BEDEg?50l(B
! 43: @page
! 44: @vskip 0pt plus 1filll
! 45: Copyright @copyright{} Takumu Shoji, Shinichi Tajima.
! 46: 2007. All rights reserved. Licensed by GPL.
! 47: @end titlepage
! 48:
! 49: @comment --- $B$*$^$8$J$$(B ---
! 50: @synindex vr fn
! 51: @comment --- $B$*$^$8$J$$=*$j(B ---
! 52:
! 53: @comment --- @node $B$O(B GNU info, HTML $BMQ(B ---
! 54: @comment --- @node $B$N0z?t$O(B node-name, next, previous, up ---
! 55: @node Top,, (dir), (dir)
! 56:
! 57: @comment --- @menu $B$O(B GNU info, HTML $BMQ(B ---
! 58: @comment --- chapter $BL>$r@53N$KJB$Y$k(B ---
! 59: @comment --- $B$3$NJ8=q$G$O(B chapter XYZ, Chapter Index $B$,$"$k(B.
! 60: @comment --- Chapter XYZ $B$K$O(B section XYZ$B$K$D$$$F(B, section XYZ$B$K4X$9$k4X?t$,$"$k(B.
! 61: @menu
! 62: * Experimental Functions::
! 63: * Index::
! 64: @end menu
! 65:
! 66: @comment --- chapter $B$N3+;O(B ---
! 67: @comment --- $B?F(B chapter $BL>$r@53N$K(B. $B?F$,$J$$>l9g$O(B Top ---
! 68: @node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B,,, Top
! 69: @chapter 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B
! 70:
! 71: @comment --- section $BL>$r@53N$KJB$Y$k(B. ---
! 72: @menu
! 73: * 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B::
! 74: * 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B::
! 75: @end menu
! 76:
! 77: @comment --- section ``XYZ$B$K$D$$$F(B'' $B$N3+;O(B --- section XYZ$B$K$D$$$F$N?F$O(B chapter XYZ
! 78: @node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B
! 79: @section 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B
! 80:
! 81: @comment --- $B=qBN;XDj$K$D$$$F(B ---
! 82: @comment --- @code{} $B$O%?%$%W%i%$%?BNI=<((B ---
! 83: @comment --- @var{} $B$O<P;zBNI=<((B ---
! 84: @comment --- @b{} $B$O%\!<%k%II=<((B ---
! 85: @comment --- @samp{} $B$O%U%!%$%kL>$J$I$NI=<((B ---
! 86:
! 87: $B$3$N@bL@=q$G$O(B
! 88: 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F@bL@$9$k(B.
! 89: $B?t3XE*2r@b$dGX7J$K$D$$$F$O(B, $B2r@b5-;v(B
! 90: ``1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$KBP$9$k(B Risa/Asir $BMQ%Q%C%1!<%8(B taji_alc''
! 91: (Risa/Asir Journal (2007))
! 92: $B$*$h$S$=$N;29MJ88%$r;2>H(B.
! 93:
! 94:
! 95: @comment --- section ``$B<B83E*4X?t(B'' $B$N3+;O(B ---
! 96: @node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B
! 97: @section 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 98:
! 99: @comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc
! 100: @comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B.
! 101: @menu
! 102: * taji_alc.cpfd::
! 103: * taji_alc.snoether::
! 104: * taji_alc.laurent_expansion::
! 105: * taji_alc.residue::
! 106: * taji_alc.invpow::
! 107: * taji_alc.rem_formula::
! 108: * taji_alc.solve_ode_cp::
! 109: * taji_alc.solve_ode_cp_ps::
! 110: * taji_alc.fbt::
! 111: * taji_alc.inv::
! 112: @end menu
! 113:
! 114: $BK\%;%/%7%g%s$N4X?t$r8F$S=P$9$K$O(B,
! 115: @example
! 116: import("taji_alc.rr")$
! 117: @end example
! 118: $B$r<B9T$7$F%W%m%0%i%`$r%m!<%I$9$k(B.
! 119:
! 120:
! 121: @comment ****************************************************************
! 122: @node taji_alc.cpfd,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 123: @subsection @code{taji_alc.cpfd}
! 124: @findex taji_alc.cpfd
! 125:
! 126: @table @t
! 127: @item taji_alc.cpfd(@var{num},@var{den})
! 128: :: $BM-M}4X?t(B@var{num}/@var{den}$B$NItJ,J,?tJ,2r$r5a$a$k(B.
! 129: @end table
! 130:
! 131: @table @var
! 132: @item return
! 133: @var{switch}$B$,(B0$B$+(B1$B$J$i$P(B, [[[$BJ,;R(B,[$BJ,Jl$N0x;R(B,$B=EJ#EY(B]],...],...] $B$J$k%j%9%H(B.
! 134:
! 135: @var{switch}$B$,(B10$B$+(B11$B$J$i$P(B, [[$BJ,;R(B,[$BJ,Jl$N0x;R(B,$B=EJ#EY(B]],...] $B$J$k%j%9%H(B.
! 136:
! 137: @item num
! 138: ($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
! 139: @item den
! 140: ($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B
! 141:
! 142: $B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 143: @item switch
! 144: $B%*%W%7%g%s;XDj(B
! 145:
! 146: case 0 : complete$B$JItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$OM-M}?t78?tB?9`<0(B)
! 147:
! 148: case 1 : complete$B$JItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$O@0?t78?t2=%j%9%H(B)
! 149:
! 150: case 10 : $BJ,Jl$rQQE83+$7$J$$ItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$OM-M}?t78?tB?9`<0(B)
! 151:
! 152: case 11 : $BJ,Jl$rQQE83+$7$J$$ItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$O@0?t78?t2=%j%9%H(B)
! 153:
! 154: default : case 0
! 155: @end table
! 156:
! 157: @itemize @bullet
! 158: @item taji_alc.cpfd()$B$O(B, proper$B$JM-M}4X?t$rBP>]$H$9$k(B.
! 159: $BF~NOCM$,(Bproper$B$G$J$$>l9g$G$b@5>o$KF0:n$9$k$,(B, $BB?9`<0$H$7$F=P$F$/$kItJ,$OI=<($7$J$$(B.
! 160: @item $BItJ,J,?tJ,2r$O(B, $BQQE83+$r$9$k(Bcomplete$B$J%?%$%W$H(B, $BQQE83+$r$7$J$$%?%$%W$N(B2$B$D$N%?%$%W$,$"$k(B.
! 161: taji_alc.cpfd()$B$G:NMQ$7$F$$$k%"%k%4%j%:%`$G$O(B, $BA0<T$,@h$K5a$^$k(B.
! 162: $B8e<T$O(B, $BA0<T$N%G!<%?$r%[!<%J!<K!$GB-$7>e$2$F5a$a$k(B.
! 163: @item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
! 164: ($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
! 165: $B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
! 166: $BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
! 167: @end itemize
! 168:
! 169: @example
! 170: [235] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1);
! 171: [[[1/2*x-1,[x^2+1,1]]],[[-1/2,[x+1,2]],[1/2,[x+1,1]]]]
! 172: [236] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=1);
! 173: [[[[x-2,2],[x^2+1,1]]],[[[-1,2],[x+1,2]],[[1,2],[x+1,1]]]]
! 174: [237] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=10);
! 175: [[1/2*x-1,[x^2+1,1]],[1/2*x,[x+1,2]]]
! 176: [238] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=11);
! 177: [[[x-2,2],[x^2+1,1]],[[x,2],[x+1,2]]]
! 178: @end example
! 179:
! 180: @table @t
! 181: @item $B;2>H(B
! 182: @end table
! 183:
! 184: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 185: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 186: @noindent
! 187: ChangeLog
! 188: @itemize @bullet
! 189: @end itemize
! 190: @comment ****************************************************************
! 191:
! 192:
! 193: @page
! 194: @comment ****************************************************************
! 195: @node taji_alc.snoether,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 196: @subsection @code{taji_alc.snoether}
! 197: @findex taji_alc.snoether
! 198:
! 199: @table @t
! 200: @item taji_alc.snoether(@var{num},@var{den})
! 201: :: $BM-M}4X?t(B@var{num}/@var{den}$B$,Dj$a$kBe?tE*6I=j%3%[%b%m%8!<N`$N%M!<%?!<:nMQAG$r5a$a$k(B.
! 202: @end table
! 203:
! 204: @table @var
! 205: @item return
! 206: [[$B0x;R(B,$B%M!<%?!<:nMQAG(B],...] $B$J$k%j%9%H(B.
! 207:
! 208: $B%M!<%?!<:nMQAG$O(B, $B78?t$r9b3,$NItJ,$+$i9_=g$KJB$Y$?%j%9%H(B
! 209:
! 210: @item num
! 211: ($BM-M}4X?t$NJ,;R$N(B)$BB?9`<0(B
! 212: @item den
! 213: ($BM-M}4X?t$NJ,Jl$N(B)$BB?9`<0(B
! 214:
! 215: $B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B.
! 216: @item switch
! 217: $B%*%W%7%g%s;XDj(B
! 218:
! 219: case 0 : $B%M!<%?!<:nMQAG$r(B [$BM-M}?t78?tB?9`<0(B,...] $B$J$k%j%9%H$GJV$9(B.
! 220:
! 221: case 1 : $B%M!<%?!<:nMQAG$r(B [$B@0?t78?t2=%j%9%H(B,...] $B$J$k%j%9%H$GJV$9(B.
! 222:
! 223: case 10 : $B%M!<%?!<:nMQAG$r(B [[$B@0?t78?tB?9`<0(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.
! 224:
! 225: case 20 : $B%M!<%?!<:nMQAG$r(B [[$B@0?t78?t2=%j%9%H(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.
! 226:
! 227: default : case 0
! 228: @end table
! 229:
! 230: @itemize @bullet
! 231: @item taji_alc.snoether()$B$O(B, @var{den}$B$r(BQ$B>e$G4{LsJ,2r$7(B,
! 232: $B3F0x;R$KBP1~$9$k%M!<%?!<:nMQAG$rJV$9(B.
! 233: @item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
! 234: ($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
! 235: $B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
! 236: $BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
! 237: @item $BLa$jCM$N7?$O(B@var{switch}$B$GA*Br$G$-$k(B.
! 238:
! 239: case 10$B$O(B, $B%M!<%?!<:nMQAG$N3F78?tA4BN$rDLJ,$7(B, $B$=$NJ,JlItJ,$H3,>h$N@Q$r%j%9%H$GJ,$1$?I=8=$G$"$k(B.
! 240: $B$o$+$j$d$9$$$,(B, $BDLJ,CM$H78?tItJ,$H$GLsJ,$G$-$kItJ,$,$"$k(B($BFC$K9b3,$NItJ,$KB?$$(B)$B$N$G(B, $B>iD9@-$r$b$C$F$$$k(B.
! 241:
! 242: case 20$B$O(B, $B3,>h$NItJ,$GA4BN$r$/$/$j(B($B%j%9%H$GJ,$1(B), $B%M!<%?!<:nMQAG$N3F78?t$r8DJL$KDLJ,$7%j%9%H2=$9$k(B.
! 243: $B3,>h$NItJ,$H78?tItJ,$H$GLsJ,$G$-$kItJ,$,$"$k(B($BFC$KDc3,$NItJ,$KB?$$(B)$B$N$G(B,
! 244: $B>iD9$H8@$($J$/$b$J$$(B(case 10$B$h$j$O$^$7(B)$B$,(B, $B?t3XE*$J9=B$$,e:No$K8+$($kI=8=$G$"$k(B.
! 245: @end itemize
! 246:
! 247: @example
! 248: [296] taji_alc.snoether(1,[[x^3-x-1,3]]);
! 249: [[x^3-x-1,[9/529*x^2-27/1058*x+11/1058,-81/529*x^2-9/529*x+135/529,-49
! 250: 05/12167*x^2+4563/12167*x+3270/12167]]]
! 251: [299] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=1);
! 252: [[x^3-x-1,[[18*x^2-27*x+11,1058],[-81*x^2-9*x+135,529],[-4905*x^2+4563
! 253: *x+3270,12167]]]]
! 254: [297] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=10);
! 255: [[x^3-x-1,[[414*x^2-621*x+253,-3726*x^2-414*x+6210,-9810*x^2+9126*x+65
! 256: 40],24334]]]
! 257: [298] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=20);
! 258: [[x^3-x-1,[[[18*x^2-27*x+11,529],[-162*x^2-18*x+270,529],[-9810*x^2+91
! 259: 26*x+6540,12167]],2]]]
! 260:
! 261: [241] taji_alc.snoether(x^3+1,x^18-2*x^14+x^10-x^8+2*x^4-1|switch=10);
! 262: [[x^4+x^3+x^2+x+1,[[-2*x^2-x-2],50]],[x^4-x^3+x^2-x+1,[[-2*x^3+4*x^2-x
! 263: -2],50]],[x^2+1,[[-x+1,8*x+5],32]],[x+1,[[-6,-39],320]],[x-1,[[2,-24,6
! 264: 7],320]]]
! 265: @end example
! 266:
! 267: @table @t
! 268: @item $B;2>H(B
! 269: @end table
! 270:
! 271: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 272: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 273: @noindent
! 274: ChangeLog
! 275: @itemize @bullet
! 276: @end itemize
! 277: @comment ****************************************************************
! 278:
! 279:
! 280: @page
! 281: @comment ****************************************************************
! 282: @node taji_alc.laurent_expansion,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 283: @subsection @code{taji_alc.laurent_expansion}
! 284: @findex taji_alc.laurent_expansion
! 285:
! 286: @table @t
! 287: @item taji_alc.laurent_expansion(@var{num},@var{den})
! 288: :: $BM-M}4X?t(B@var{num}/@var{den}$B$N6K$K$*$1$k%m!<%i%sE83+$N<gMWIt$N78?t$r5a$a$k(B.
! 289: @end table
! 290:
! 291: @table @var
! 292: @item return
! 293: [[$B0x;R(B,$B%m!<%i%sE83+$N78?t(B],...] $B$J$k%j%9%H(B.
! 294:
! 295: $B%m!<%i%sE83+$N78?t$O(B, $B9b0L$N78?t$+$i=g$KJB$Y$?%j%9%H(B.
! 296:
! 297: @item num
! 298: ($BM-M}4X?t$NJ,;R$N(B)$BB?9`<0(B
! 299: @item den
! 300: ($BM-M}4X?t$NJ,Jl$N(B)$BB?9`<0(B
! 301:
! 302: $B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 303:
! 304: @item switch
! 305: $B%*%W%7%g%s;XDj(B
! 306:
! 307: case 0 : $B%m!<%i%sE83+$N78?t$r(B [$BM-M}?t78?tB?9`<0(B,...] $B$J$k%j%9%H$GJV$9(B.
! 308:
! 309: case 1 : $B%m!<%i%sE83+$N78?t$r(B [$B@0?t78?t2=%j%9%H(B,...] $B$J$k%j%9%H$GJV$9(B.
! 310:
! 311: case 10 : $B%m!<%i%sE83+$N78?t$r(B [[$B@0?t78?tB?9`<0(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.
! 312:
! 313: case 20 : $B%m!<%i%sE83+$N78?t$r(B [[$B@0?t78?t2=%j%9%H(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.
! 314:
! 315: default : case 0
! 316: @end table
! 317:
! 318: @itemize @bullet
! 319: @item taji_alc.laurent_expansion()$B$O(B, taji_alc.snoether()$B$r;H$C$F(B, $B%m!<%i%sE83+$N78?t$r5a$a$k(B.
! 320: @item taji_alc.laurent_expansion()$B$G$O(B,
! 321: C$B>e$N(B1$BE@$KCmL\$9$k$N$G$O$J$/(B, Q$B>e$G$N4{Ls0x;R<+BN$KCmL\$7$F%m!<%i%sE83+$N78?t$r5a$a$k(B.
! 322: $BLa$jCM$N78?t%j%9%H$N3F@.J,$O(B, $B$=$N0x;R$NA4$F$NNmE@$,6&DL$KK~$?$9%m!<%i%sE83+$N78?tB?9`<0$G$"$k(B.
! 323: $B=>$C$F(B, 1$BE@$4$H$N%m!<%i%sE83+$N78?t$r$5$i$K5a$a$?$$>l9g$K$O(B,
! 324: $B5a$a$?%m!<%i%sE83+$N78?tB?9`<0$K0x;R$NNmE@(B($BB($AFC0[E@(B)$B$NCM$rBeF~$9$kI,MW$,$"$k(B.
! 325: @end itemize
! 326:
! 327: @example
! 328: [354] taji_alc.laurent_expansion(x,(x-1)^3);
! 329: [[x-1,[1,1,0]]]
! 330: [356] taji_alc.laurent_expansion(x^5+x^4+x^3+x^2+x+1,(x^4+1)^3);
! 331: [[x^4+1,[1/64*x^2+1/64*x,1/16*x^3+1/16*x^2-3/128*x-5/128,-5/128*x^3-1/
! 332: 8*x^2-3/16*x]]]
! 333: @end example
! 334:
! 335: @table @t
! 336: @item $B;2>H(B
! 337: @ref{taji_alc.snoether}
! 338: @end table
! 339:
! 340: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 341: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 342: @noindent
! 343: ChangeLog
! 344: @itemize @bullet
! 345: @end itemize
! 346: @comment ****************************************************************
! 347:
! 348:
! 349: @page
! 350: @comment ****************************************************************
! 351: @node taji_alc.residue,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 352: @subsection @code{taji_alc.residue}
! 353: @findex taji_alc.residue
! 354:
! 355: @table @t
! 356: @item taji_alc.residue(@var{num},@var{den})
! 357: :: $BM-M}4X?t(B@var{num}/@var{den}$B$N6K$K$*$1$kN1?t$r5a$a$k(B.
! 358: @end table
! 359:
! 360: @table @var
! 361: @item return
! 362: [[$B0x;R(B,$BN1?t(B],...] $B$J$k%j%9%H(B
! 363:
! 364: @item num
! 365: ($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
! 366: @item den
! 367: ($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B
! 368:
! 369: $B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 370: @item switch
! 371: $B%*%W%7%g%s;XDj(B
! 372:
! 373: case 0 : $BN1?t$rM-M}?t78?tB?9`<0$GJV$9(B.
! 374:
! 375: case 1 : $BN1?t$r@0?t78?t2=%j%9%H$GJV$9(B.
! 376:
! 377: default : case 0
! 378:
! 379: @item pole
! 380: $B%*%W%7%g%s;XDj(B
! 381:
! 382: [$B0x;R(B,...] $B$J$k%*%W%7%g%s%j%9%H(B
! 383: @end table
! 384:
! 385: @itemize @bullet
! 386: @item taji_alc.residue()$B$O(B, @var{den}$B$r(BQ$B>e$G4{LsJ,2r$7(B, $B3F0x;R$NNmE@(B($BB($AM-M}4X?t$N6K(B)$B$K$*$1$kN1?t$rJV$9(B.
! 387: @item $B%*%W%7%g%s$G(B@var{pole}$B$r;XDj$9$l$P$=$N0x;R$N$_$NN1?t$rJV$9(B. $B;XDj$,ITE,Ev$@$H(B0$B$rJV$9(B.
! 388: @item taji_alc.residue()$B$G:NMQ$7$F$$$k%"%k%4%j%:%`$G$O(B,
! 389: C$B>e$N(B1$BE@$KCmL\$9$k$N$G$O$J$/(B, Q$B>e$G$N4{Ls0x;R<+BN$KCmL\$7$FN1?t$r5a$a$k(B.
! 390: $BLa$jCM$NN1?t$O(B, $B$=$N0x;R$NA4$F$NNmE@$,6&DL$KK~$?$9N1?tB?9`<0$G$"$k(B.
! 391: $B=>$C$F(B, 1$BE@$4$H$NN1?tCM$r$5$i$K5a$a$?$$>l9g$K$O(B,
! 392: $B5a$a$?N1?tB?9`<0$K0x;R$NNmE@(B($BB($AFC0[E@(B)$B$NCM$rBeF~$9$kI,MW$,$"$k(B.
! 393:
! 394: @example
! 395: [219] taji_alc.residue(1,x^4+1);
! 396: [[x^4+1,-1/4*x]]
! 397: @end example
! 398:
! 399: $B$3$NNc$G8@$&$H(B, $B5a$a$?N1?tB?9`<0(B-1/4*x$B$K(B, x^4+1$B$N(B(4$B$D$"$k(B)$BNmE@$r$=$l$>$lBeF~$7$?$b$N$,8DJL$NN1?tCM$G$"$k(B.
! 400: @item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
! 401: ($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
! 402: $B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
! 403: $BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
! 404: @end itemize
! 405:
! 406: @example
! 407: [221] taji_alc.residue(x^8,[[x^3-x-1,3]]);
! 408: [[x^3-x-1,-2243/12167*x^2+2801/12167*x+5551/12167]]
! 409: [222] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]);
! 410: [[x^2+3*x-1,-284/4563*x-311/1521],[x-1,89/432],[x+1,7/432]]
! 411: [223] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]|switch=1)
! 412: ;
! 413: [[x^2+3*x-1,[-284*x-933,4563]],[x-1,[89,432]],[x+1,[7,432]]]
! 414: [234] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]|switch=1,
! 415: pole=[x+1]);
! 416: [[x+1,[7,432]]]
! 417: [225] taji_alc.residue(x^3+1,x^18-2*x^14+x^10-x^8+2*x^4-1);
! 418: [[x^4+x^3+x^2+x+1,-1/25*x^2-1/50*x-1/25],[x^4-x^3+x^2-x+1,-1/25*x^3+2/
! 419: 25*x^2-1/50*x-1/25],[x^2+1,1/4*x+5/32],[x+1,-39/320],[x-1,67/320]]
! 420: @end example
! 421:
! 422: @table @t
! 423: @item $B;2>H(B
! 424: @end table
! 425:
! 426: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 427: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 428: @noindent
! 429: ChangeLog
! 430: @itemize @bullet
! 431: @end itemize
! 432: @comment ****************************************************************
! 433:
! 434:
! 435: @page
! 436: @comment ****************************************************************
! 437: @node taji_alc.invpow,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 438: @subsection @code{taji_alc.invpow}
! 439: @findex taji_alc.invpow
! 440:
! 441: @table @t
! 442: @item taji_alc.invpow(@var{poly},@var{f},@var{m})
! 443: :: $B>jM>BN(BQ[x]/<@var{f}>$B>e$G$N(B@var{poly}$B$N5U85$N(B@var{m}$B>h$r5a$a$k(B.
! 444: @end table
! 445:
! 446: @table @var
! 447: @item return
! 448: $B5UQQ(B
! 449:
! 450: @item poly
! 451: $BB?9`<0(B
! 452: @item f
! 453: Q$B>e$G4{Ls$JB?9`<0(B
! 454: @item m
! 455: $B<+A3?t(B
! 456: @item switch
! 457: $B%*%W%7%g%s;XDj(B
! 458:
! 459: case 0 : $B5UQQ$rM-M}?t78?tB?9`<0$GJV$9(B.
! 460:
! 461: case 1 : $B5UQQ$r@0?t78?t2=%j%9%H$GJV$9(B.
! 462:
! 463: default : case 0
! 464: @end table
! 465:
! 466: @itemize @bullet
! 467: @item @var{poly}$B$H(B@var{f}$B$O8_$$$KAG$G$J$1$l$P$J$i$J$$(B.
! 468: @item $B%"%k%4%j%:%`$N9|3J$O7+$jJV$7(B2$B>hK!$G$"$k(B. $B$=$3$K:G>.B?9`<0$NM}O@$r1~MQ$7$F9bB.2=$7$F$$$k(B.
! 469: @end itemize
! 470:
! 471: @example
! 472: [236] taji_alc.invpow(3*x^2-1,x^3-x-1,1);
! 473: -6/23*x^2+9/23*x+4/23
! 474: [237] taji_alc.invpow(3*x^2-1,x^3-x-1,1|switch=1);
! 475: [-6*x^2+9*x+4,23]
! 476: [238] taji_alc.invpow(3*x^2-1,x^3-x-1,30|switch=1);
! 477: [1857324483*x^2-2100154824*x-477264412,266635235464391245607]
! 478: @end example
! 479:
! 480: @table @t
! 481: @item $B;2>H(B
! 482: @end table
! 483:
! 484: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 485: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 486: @noindent
! 487: ChangeLog
! 488: @itemize @bullet
! 489: @end itemize
! 490: @comment ****************************************************************
! 491:
! 492:
! 493: @page
! 494: @comment ****************************************************************
! 495: @node taji_alc.rem_formula,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 496: @subsection @code{taji_alc.rem_formula}
! 497: @findex taji_alc.rem_formula
! 498:
! 499: @table @t
! 500: @item taji_alc.rem_formula(@var{polylist})
! 501: :: $BB?9`<0(Bf(x)$B$rM?$($?$H$-$N>jM>8x<0$r5a$a$k(B.
! 502: @end table
! 503:
! 504: @table @var
! 505: @item return
! 506: @var{switch} $B$*$h$S(B $B@bL@J8$r;2>H(B
! 507:
! 508: @item polylist
! 509: f(x)$B$r(BQ$B>e$G4{LsJ,2r$7$?(B [[$B0x;R(B,$B=EJ#EY(B,$BNmE@$N5-9f(B],...] $B$J$k%j%9%H(B
! 510:
! 511: @item switch
! 512: $B%*%W%7%g%s;XDj(B
! 513:
! 514: case 0 : x$B$NQQ$G@0M}$7(B, $B%j%9%H$GJV$9(B.
! 515:
! 516: case 10 : f(x)$B$NQQ$G@0M}$7(B, $B%j%9%H$GJV$9(B. ($B0l0x;R$N>l9g$N$_BP1~(B)
! 517:
! 518: case 20 : x$B$NQQ$G@0M}$7(B, symbolic$B$JI=8=$GJV$9(B.
! 519:
! 520: default : case 0
! 521: @end table
! 522:
! 523: @itemize @bullet
! 524: @item $B%"%k%4%j%:%`$O(B, $B%(%k%_!<%H$NJd4V>jM>$rMQ$$$F$$$k(B.
! 525: @item $B>jM>8x<0$NI=8=J}K!$O$$$/$D$+9M$($i$l$k$?$a(B, @var{switch}$B$GA*Br<0$H$7$?(B.
! 526: @item @var{switch}=0 $B$NLa$jCM$N8+J}$r=R$Y$k(B. $BNc$H$7$F(B, f(x)=f1(x)^m1*f2(x)^m2$B$r9M$($k(B.
! 527: $BF~NO$O(B [[f1(x),m1,z1],[f2(x),m2,z2]] $B$H$J$k(B. $B$=$N$H$-La$jCM$O(B,
! 528:
! 529: [r_{f1}(x,z1),r_{f2}(x,z2)]
! 530:
! 531: $B$J$k%j%9%H$GJV$5$l$k(B. $B$3$l$O(B, $B>jM>8x<0$,(B
! 532:
! 533: @tex
! 534: $r(x)=r_{f1}(x,z1)+r_{f2}(x,z2)$
! 535: @end tex
! 536:
! 537: $B$J$k7A$GM?$($i$l$k$3$H$r0UL#$7$F$$$k(B.
! 538: $B3F@.J,$N(Br_{fi}(x,zi)$B$O(B,
! 539:
! 540: [p^(mi-1)(zi)$B$N78?t$H$J$k(Bx$B$H(Bzi$B$NB?9`<0(B,...,p^(0)(zi)$B$N78?t$H$J$k(Bx$B$H(Bzi$B$NB?9`<0(B]
! 541:
! 542: $B$J$k%j%9%H$G$"$k(B.
! 543: @item @var{switch}=10 $B$NLa$jCM$N8+J}$r=R$Y$k(B. $BNc$H$7$F(B, f(x)=f1(x)^m$B$r9M$($k(B.
! 544: $BF~NO$O(B [[f1(x),m,z]] $B$H$J$k(B. $B$=$N$H$-La$jCM$O(B,
! 545:
! 546: [r_(m-1)(x,z),...,r_0(x,z)]
! 547:
! 548: $B$J$k%j%9%H$GJV$5$l$k(B. $B3F@.J,$O(B, $B>jM>8x<0$r(B
! 549:
! 550: @tex
! 551: $r(x)=r_{m-1}(x,z)f_1(x)^{m-1}+\cdots+r_0(x,z)$
! 552: @end tex
! 553:
! 554: $B$N$h$&$K(Bf1(x)$B$NQQ$GE83+$7$?$H$-$N3F78?t$r0UL#$7$F$$$k(B.
! 555: $B3F@.J,$N(Br_{i}(x,z)$B$O(B,
! 556:
! 557: [p^(m-1)(z)$B$N78?t$H$J$k(Bx$B$H(Bz$B$NB?9`<0(B,...,p^(0)(z)$B$N78?t$H$J$k(Bx$B$H(Bz$B$NB?9`<0(B]
! 558:
! 559: $B$J$k%j%9%H$G$"$k(B.
! 560: @item @var{switch}=20 $B$NLa$jCM$N8+J}$r=R$Y$k(B.
! 561: symbolic$B$J=PNO$N(Bp^(m)(z)$B$O(B, p(x)$B$N(Bm$B3,$NF34X?t$K(Bz$B$rBeF~$7$?CM$H$$$&0UL#$G$"$k(B.
! 562: @item $BLa$jCM$O(B, $BM?$($?0x;R$NA4$F$NNmE@$rBeF~$7$?$b$N$NOB$H$7$F8+$k(B.
! 563: $B$3$l$O0x;R$,(B2$B<!0J>e$NB?9`<0$N>l9g$K4X78$7$F$/$k(B. $BNc$($P(B,
! 564:
! 565: @example
! 566: [228] taji_alc.rem_formula([[x^2+1,1,z]]);
! 567: [[-1/2*z*x+1/2]]
! 568: @end example
! 569:
! 570: $B$N@5$7$$8+J}$O(B, x^2+1$B$NNmE@$r(Ba1,a2$B$H$*$$$?$H$-$K(B, z$B$K(Ba1$B$H(Ba2$B$rBeF~$7$?(B,
! 571:
! 572: r(x)=(-1/2*a1*x+1/2)+(-1/2*a2*x+1/2)
! 573: $B$G$"$k(B. $B$7$+$7=PNO$G$O(B, $BNmE@$NOB$NItJ,$rJX59>e>JN,$7$FJV$9(B.
! 574: @end itemize
! 575:
! 576: @example
! 577: [583] taji_alc.rem_formula([[x-1,1,z1],[x-2,1,z2]]);
! 578: [[-x+2],[x-1]]
! 579: [584] taji_alc.rem_formula([[x-1,1,z1],[x-2,1,z2]]|switch=20);
! 580: (-p^(0)(z1)+p^(0)(z2))*x+2*p^(0)(z1)-p^(0)(z2)
! 581:
! 582: [587] taji_alc.rem_formula([[x-1,2,z1]]);
! 583: [[x-1,1]]
! 584: [588] taji_alc.rem_formula([[x-1,2,z1]]|switch=20);
! 585: p^(1)(z1)*x-p^(1)(z1)+p^(0)(z1)
! 586:
! 587: [494] taji_alc.rem_formula([[x-1,3,z1]]|switch=20);
! 588: 1/2*p^(2)(z1)*x^2+(-p^(2)(z1)+p^(1)(z1))*x+1/2*p^(2)(z1)-p^(1)(z1)+p^(
! 589: 0)(z1)
! 590:
! 591: [229] taji_alc.rem_formula([[x+1,2,z1],[x^3-x-1,1,z2]]);
! 592: [[-x^4-x^3+x^2+2*x+1,-2*x^4-3*x^3+2*x^2+5*x+3],[(-1/23*z2^2-10/23*z2+1
! 593: 6/23)*x^4+(-12/23*z2^2-5/23*z2+31/23)*x^3+(-5/23*z2^2+19/23*z2-12/23)*
! 594: x^2+(22/23*z2^2+13/23*z2-53/23)*x+16/23*z2^2-1/23*z2-26/23]]
! 595: [230] taji_alc.rem_formula([[x+1,2,z1],[x^3-x-1,1,z2]]|switch=20);
! 596: (-1/23*p^(0)(z2)*z2^2-10/23*p^(0)(z2)*z2-2*p^(0)(z1)+16/23*p^(0)(z2)-p
! 597: ^(1)(z1))*x^4+(-12/23*p^(0)(z2)*z2^2-5/23*p^(0)(z2)*z2-3*p^(0)(z1)+31/
! 598: 23*p^(0)(z2)-p^(1)(z1))*x^3+(-5/23*p^(0)(z2)*z2^2+19/23*p^(0)(z2)*z2+2
! 599: *p^(0)(z1)-12/23*p^(0)(z2)+p^(1)(z1))*x^2+(22/23*p^(0)(z2)*z2^2+13/23*
! 600: p^(0)(z2)*z2+5*p^(0)(z1)-53/23*p^(0)(z2)+2*p^(1)(z1))*x+16/23*p^(0)(z2
! 601: )*z2^2-1/23*p^(0)(z2)*z2+3*p^(0)(z1)-26/23*p^(0)(z2)+p^(1)(z1)
! 602:
! 603: [231] taji_alc.rem_formula([[x^3-x-1,2,z]]|switch=10);
! 604: [[[(3/23*z^2-4/23)*x^2+(-1/23*z+3/23)*x-4/23*z^2+3/23*z+4/23,(162/529*
! 605: z^2-174/529*z-108/529)*x^2+(-105/529*z^2+54/529*z+70/529)*x-108/529*z^
! 606: 2+116/529*z+72/529],[(-6/23*z^2+9/23*z+4/23)*x^2+(9/23*z^2-2/23*z-6/23
! 607: )*x+4/23*z^2-6/23*z+5/23]]]
! 608: @end example
! 609:
! 610: @table @t
! 611: @item $B;2>H(B
! 612: @end table
! 613:
! 614: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 615: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 616: @noindent
! 617: ChangeLog
! 618: @itemize @bullet
! 619: @end itemize
! 620: @comment ****************************************************************
! 621:
! 622:
! 623: @page
! 624: @comment ****************************************************************
! 625: @node taji_alc.solve_ode_cp,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 626: @subsection @code{taji_alc.solve_ode_cp}
! 627: @findex taji_alc.solve_ode_cp
! 628:
! 629: @table @t
! 630: @item taji_alc.solve_ode_cp(@var{poly},@var{var},@var{exppoly})
! 631: :: $BM-M}?t78?t$N@~7A>oHyJ,J}Dx<0$N%3!<%7!<LdBj(B
! 632:
! 633: @tex
! 634: $Pu(z)=f(z)$, $u^{(0)}(0)=c_0,\ldots,u^{(n-1)}(0)=c_{n-1}$
! 635: @end tex
! 636:
! 637: $B$N2r$r5a$a$k(B.
! 638:
! 639: $B$?$@$7(B, P$B$O(Bn$B3,$NM-M}?t78?t$N@~7A>oHyJ,:nMQAG(B, f(z)$B$O;X?tB?9`<0$H$9$k(B.
! 640: @end table
! 641:
! 642: @table @var
! 643: @item return
! 644: 2$BDL$j$NI=8=$,$"$k(B.
! 645:
! 646: $B!&I=8=(B1 ($B%3!<%7!<%G!<%?$G@0M}$7$?7A(B)
! 647:
! 648: $B%3!<%7!<LdBj$N0lHL2r(Bu(z)$B$O(B,
! 649:
! 650: @tex$u(z)=c_0u_0(z)+\cdots+c_{n-1}u_{n-1}(z)+v(z)$@end tex
! 651:
! 652: $B$J$k@~7A7k9g$N7A$GM?$($i$l$k(B.
! 653: @tex$u_0(z),\ldots,u_{n-1}(z)$@end tex
! 654: $B$r%3!<%7!<LdBj$N4pK\2r(B,
! 655: @tex$v(z)$@end tex
! 656: $B$r%3!<%7!<LdBj$NFC<l2r$H$$$$(B,
! 657:
! 658: [u_0(z),...,u_(n-1)(z),v(z)]
! 659:
! 660: $B$J$k%j%9%H$GJV$9(B.
! 661: $B4pK\2r$HFC<l2r$O(B, $B;X?tB?9`<0%j%9%H$G$"$k(B.
! 662:
! 663: $B!&I=8=(B2 ($B;X?t4X?t$G@0M}$7$?7A(B)
! 664:
! 665: @var{data}$B$K%3!<%7!<%G!<%?$rM?$($k$H(B,
! 666: $B%3!<%7!<LdBj$N0lHL2r(Bu(z)$B$N(B
! 667: @tex$c_0,\ldots,c_{n-1}$@end tex
! 668: $B$N$H$3$m$K%G!<%?$rBeF~$7(B,
! 669: $B$=$l$r;X?t4X?t$G@0M}$7D>$7$?;X?tB?9`<0%j%9%H$rJV$9(B.
! 670:
! 671: @item poly
! 672: $BB?9`<0(B (P$B$NFC@-B?9`<0(B)
! 673:
! 674: $B$^$?$O(B (P$B$NFC@-B?9`<0$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 675:
! 676: @item var
! 677: $BITDj85(B ($B4X?t$NFHN)JQ?t(B)
! 678:
! 679: @item exppoly
! 680: $B@F<!7A$N$H$-(B0, $BHs@F<!7A$N$H$-(Bf(z)$B$N;X?tB?9`<0%j%9%H(B.
! 681:
! 682: @item switch
! 683: $B%*%W%7%g%s;XDj(B
! 684:
! 685: case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.
! 686:
! 687: case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.
! 688:
! 689: default : case 0
! 690: @item data
! 691: $B%*%W%7%g%s;XDj(B
! 692:
! 693: $B%3!<%7!<%G!<%?$r(B [c_0,...,c_(n-1)] $B$N=g$KJB$Y$?%j%9%H(B.
! 694: @end table
! 695:
! 696: @itemize @bullet
! 697: @item $B2rK!$O%(%k%_!<%H$NJ}K!(B($BN1?t7W;;$K5"Ce$5$;$kJ}K!(B)$B$r:NMQ$7$F$$$k(B.
! 698: @item $BJQ?t$O(B2$B<oN`I,MW(B($BFC@-B?9`<0$NJQ?t$H4X?t$NFHN)JQ?t(B).
! 699: @var{poly}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
! 700: @item $BLa$jCM$NFC<l2r(B
! 701: @tex
! 702: $v(z)$
! 703: @end tex
! 704: $B$O(B, $B%3!<%7!<>r7o(B
! 705: @tex
! 706: $v(0)=0,\ldots,v^{(n-1)}(0)=0$
! 707: @end tex
! 708: $B$rK~$?$9%3!<%7!<LdBj$NFC<l2r$G$"$k(B.
! 709: @end itemize
! 710:
! 711: @example
! 712: [287] taji_alc.solve_ode_cp(x*(x-3)^2,z,0);
! 713: [[[x-3,0],[x,1]],[[x-3,-z+2/3],[x,-2/3]],[[x-3,1/3*z-1/9],[x,1/9]]]
! 714:
! 715: [289] taji_alc.solve_ode_cp((x^3-x-1)^2,z,0|switch=1);
! 716: [[[x^3-x-1,[(92*z+200)*x^2+(-69*z-254)*x-92*z+43,529]]],[[x^3-x-1,[(92
! 717: *z+420)*x^2+(-46*z-216)*x-161*z-280,529]]],[[x^3-x-1,[(-69*z-195)*x^2+
! 718: (23*z+327)*x+23*z+130,529]]],[[x^3-x-1,[(-161*z-270)*x^2+(69*z+290)*x+
! 719: 184*z+180,529]]],[[x^3-x-1,[-105*x^2+(-23*z+54)*x+69*z+70,529]]],[[x^3
! 720: -x-1,[(69*z+162)*x^2-174*x-92*z-108,529]]]]
! 721:
! 722: [277] taji_alc.solve_ode_cp(x^2-4,z,0);
! 723: [[[x+2,1/2],[x-2,1/2]],[[x+2,-1/4],[x-2,1/4]]]
! 724: [278] taji_alc.solve_ode_cp(x^2-4,z,0|data=[1,-1]);
! 725: [[x+2,3/4],[x-2,1/4]]
! 726: [279] taji_alc.solve_ode_cp(x^2-4,z,0|data=[c0,c1]);
! 727: [[x+2,1/2*c0-1/4*c1],[x-2,1/2*c0+1/4*c1]]
! 728: @end example
! 729:
! 730: @table @t
! 731: @item $B;2>H(B
! 732: @end table
! 733:
! 734: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 735: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 736: @noindent
! 737: ChangeLog
! 738: @itemize @bullet
! 739: @end itemize
! 740: @comment ****************************************************************
! 741:
! 742:
! 743: @page
! 744: @comment ****************************************************************
! 745: @node taji_alc.solve_ode_cp_ps,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 746: @subsection @code{taji_alc.solve_ode_cp_ps}
! 747: @findex taji_alc.solve_ode_cp_ps
! 748:
! 749: @table @t
! 750: @item taji_alc.solve_ode_cp_ps(@var{poly},@var{var},@var{exppoly})
! 751: :: $BM-M}?t78?t$N@~7A>oHyJ,J}Dx<0$N%3!<%7!<LdBj(B
! 752:
! 753: @tex
! 754: $Pu(z)=f(z)$, $u^{(0)}(0)=c_0,\ldots,u^{(n-1)}(0)=c_{n-1}$
! 755: @end tex
! 756:
! 757: $B$NFC<l2r$r5a$a$k(B.
! 758:
! 759: $B$?$@$7(B, $BHs@F<!7A$N$_$rBP>]$H$7$F$$$k$N$G(B,
! 760: @tex
! 761: $f(z)\neq0$
! 762: @end tex
! 763: $B$H$9$k(B.
! 764:
! 765: @end table
! 766:
! 767: @table @var
! 768: @item return
! 769: $B;X?tB?9`<0%j%9%H(B
! 770:
! 771: @item poly
! 772: $BB?9`<0(B (P$B$NFC@-B?9`<0(B)
! 773:
! 774: $B$^$?$O(B (P$B$NFC@-B?9`<0$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 775:
! 776: @item var
! 777: $BITDj85(B ($B4X?t$NFHN)JQ?t(B)
! 778:
! 779: @item exppoly
! 780: f(z)$B$N;X?tB?9`<0%j%9%H(B
! 781:
! 782: @item switch
! 783: $B%*%W%7%g%s;XDj(B
! 784:
! 785: case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.
! 786:
! 787: case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.
! 788:
! 789: default : case 0
! 790:
! 791: @item switch2
! 792: $B%*%W%7%g%s;XDj(B
! 793:
! 794: case 0 : $B%3!<%7!<LdBj$NFC<l2r$rJV$9(B.
! 795:
! 796: case 1 : $B4JC1$J7A$NFC<l2r$rJV$9(B.
! 797:
! 798: default : case 0
! 799: @end table
! 800:
! 801: @itemize @bullet
! 802: @item $BJQ?t$O(B2$B<oN`I,MW(B($BFC@-B?9`<0$NJQ?t$H4X?t$NFHN)JQ?t(B).
! 803: @var{poly}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
! 804: @end itemize
! 805:
! 806: @example
! 807: [345] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-1,1]]);
! 808: [[x+3,1/20],[x-1,-1/4],[x-2,1/5]]
! 809: [346] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-1,1]]|switch2=1);
! 810: [[x-1,-1/4]]
! 811: [347] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-2,1]]);
! 812: [[x+3,1/25],[x-2,1/5*z-1/25]]
! 813: [348] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-2,1]]|switch2=1);
! 814: [[x-2,1/5*z-1/25]]
! 815: [349] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x+1,1],[x-2,1]]|switch2
! 816: =1);
! 817: [[x+1,-1/6],[x-2,1/5*z+2/75]]
! 818:
! 819: [350] taji_alc.solve_ode_cp_ps((x^3-x-1)*(x-3)^2,z,[[x-3,2],[x-1,3*z^2
! 820: +1]]);
! 821: [[x-1,[-6*z^2-36*z-119,8]],[x^3-x-1,[42291*x^2+55504*x+32313,12167]],[
! 822: x-3,[4232*z^2-4278*z-4295,97336]]]
! 823: @end example
! 824:
! 825: @table @t
! 826: @item $B;2>H(B
! 827: @end table
! 828:
! 829: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 830: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 831: @noindent
! 832: ChangeLog
! 833: @itemize @bullet
! 834: @end itemize
! 835: @comment ****************************************************************
! 836:
! 837:
! 838: @page
! 839: @comment ****************************************************************
! 840: @node taji_alc.fbt,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 841: @subsection @code{taji_alc.fbt}
! 842: @findex taji_alc.fbt
! 843:
! 844: @table @t
! 845: @item taji_alc.fbt(@var{num},@var{den},@var{var})
! 846: :: $BM-M}4X?t(B@var{num}/@var{den}$B$,Dj$a$kBe?tE*6I=j%3%[%b%m%8!<N`$N%U!<%j%(!&%\%l%kJQ49$r9T$&(B.
! 847: @end table
! 848:
! 849: @table @var
! 850: @item return
! 851: [$B;X?tB?9`<0%j%9%H(B,...] $B$J$k%j%9%H(B
! 852:
! 853: @item num
! 854: ($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
! 855: @item den
! 856: ($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B
! 857:
! 858: $B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
! 859: @item var
! 860: $BITDj85(B ($BA|$NFHN)JQ?t(B)
! 861: @item switch
! 862: $B%*%W%7%g%s;XDj(B
! 863:
! 864: case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.
! 865:
! 866: case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.
! 867:
! 868: default : case 0
! 869: @end table
! 870:
! 871: @itemize @bullet
! 872: @item $BJQ?t$O(B2$B<oN`I,MW(B($BBe?tE*6I=j%3%[%b%m%8!<N`$NJQ?t$HA|$NFHN)JQ?t(B).
! 873: @var{num/den}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
! 874: @item taji_alc.fbt()$B$O(B, Res(Rat*exp(z*x))$B$J$k7A$NM-M}7A4X?t$NN1?t$r5a$a$k(B.
! 875: $B$3$NM-M}7A4X?t$NN1?t$O;X?tB?9`<0$H$J$k$?$a(B, $B;X?tB?9`<0%j%9%H$GJV$9(B.
! 876: @item $BFbIt$N%"%k%4%j%:%`$O(Btaji_alc.residue()$B$H$[$\F1$8$G$"$j(B, $B<B:]$K(Btaji_alc.residue()$B$r8F$S=P$7$F7W;;$r9T$C$F$$$k(B.
! 877: @end itemize
! 878:
! 879: @example
! 880: [235] taji_alc.fbt(1,(x^3-x-1)^3,z);
! 881: [[x^3-x-1,(9/529*z^2-81/529*z-4905/12167)*x^2+(-27/1058*z^2-9/529*z+45
! 882: 63/12167)*x+11/1058*z^2+135/529*z+3270/12167]]
! 883: @end example
! 884:
! 885: @table @t
! 886: @item $B;2>H(B
! 887: @ref{taji_alc.residue, taji_alc.invfbt}
! 888: @end table
! 889:
! 890: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 891: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 892: @noindent
! 893: ChangeLog
! 894: @itemize @bullet
! 895: @end itemize
! 896: @comment ****************************************************************
! 897:
! 898:
! 899: @page
! 900: @comment ****************************************************************
! 901: @node taji_alc.inv,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
! 902: @subsection @code{taji_alc.invfbt}
! 903: @findex taji_alc.invfbt
! 904:
! 905: @table @t
! 906: @item taji_alc.invfbt(@var{exppoly},@var{var})
! 907: :: $B;X?tB?9`<0$N5U%U!<%j%(!&%\%l%kJQ49$r9T$&(B.
! 908: @end table
! 909:
! 910: @table @var
! 911: @item return
! 912: $BM-M}4X?t(B
! 913:
! 914: @item exppoly
! 915: $B;X?tB?9`<0%j%9%H(B
! 916: @item var
! 917: $BITDj85(B ($B;X?tB?9`<0$NFHN)JQ?t(B)
! 918:
! 919: @item switch
! 920: $B%*%W%7%g%s;XDj(B
! 921:
! 922: case 0 : $BM-M}4X?t$GJV$9(B.
! 923:
! 924: case 1 : $BM-M}4X?t$r(B[$BJ,;R(B,$BJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?%j%9%H(B]$B$J$k%j%9%H$GJV$9(B.
! 925:
! 926: default : case 0
! 927: @end table
! 928:
! 929: @itemize @bullet
! 930: @item $BJQ?t$O(B2$B<oN`I,MW(B($BBe?tE*?t$N:G>.B?9`<0$NJQ?t$H;X?tB?9`<0$NFHN)JQ?t(B).
! 931: $B>WFM$7$J$$$h$&Cm0U(B.
! 932: @item taji_alc.invfbt()$B$O(B, exppoly$B$r(B, Res(Rat*exp(z*x))$B$J$k7A$NN1?tI=<($KJQ49$7(B, Rat$BItJ,$rJV$9(B.
! 933: @item taji_alc.fbt()$B$N5U1i;;$G$"$k(B.
! 934: @end itemize
! 935:
! 936: @example
! 937: [8] taji_alc.invfbt([[x^3-x-1,2*x^2*z^2+x*z+1],[x^2+1,z*x+z^2]],z|swit
! 938: ch=1);
! 939: [3*x^14+14*x^12+39*x^11+33*x^10+179*x^9+206*x^8+350*x^7+223*x^6+126*x^
! 940: 5+176*x^4+107*x^3+101*x^2+15*x-4,[[x^2+1,3],[x^3-x-1,3]]]
! 941:
! 942: [9] taji_alc.fbt(3*x^14+14*x^12+39*x^11+33*x^10+179*x^9+206*x^8+350*x^
! 943: 7+223*x^6+126*x^5+176*x^4+107*x^3+101*x^2+15*x-4,[[x^2+1,3],[x^3-x-1,3
! 944: ]],z);
! 945: [[x^3-x-1,2*z^2*x^2+z*x+1],[x^2+1,z*x+z^2]]
! 946: @end example
! 947:
! 948: @table @t
! 949: @item $B;2>H(B
! 950: @ref{taji_alc.fbt}
! 951: @end table
! 952:
! 953: @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
! 954: @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
! 955: @noindent
! 956: ChangeLog
! 957: @itemize @bullet
! 958: @end itemize
! 959: @comment ****************************************************************
! 960:
! 961:
! 962:
! 963:
! 964:
! 965:
! 966: @comment --- $B$*$^$8$J$$(B ---
! 967: @node Index,,, Top
! 968: @unnumbered Index
! 969: @printindex fn
! 970: @printindex cp
! 971: @iftex
! 972: @vfill @eject
! 973: @end iftex
! 974: @summarycontents
! 975: @contents
! 976: @bye
! 977: @comment --- $B$*$^$8$J$$=*$j(B ---
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