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