Annotation of OpenXM/src/asir-contrib/packages/doc/todo_parametrize_ja.tex, Revision 1.1
1.1 ! takayama 1: @comment $OpenXM$
! 2: @comment Copyright (c) 2005, Shuhei Todo,
! 3: @comment Permission is granted to copy, distribute and/or modify this document
! 4: @comment under the terms of the GNU Free Documentation License, Version 1.1
! 5: @comment or any later version published by the Free Software Foundation;
! 6: @comment with the Invariant Sections being LIST THEIR TITLES, with the
! 7: @comment Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.
! 8: @comment A copy of the license is included in the section entitled "GNU
! 9: @comment Free Documentation License".
! 10: @comment
! 11: \input texinfo
! 12: @comment \input jtexinfo
! 13: @iftex
! 14: @catcode`@#=6
! 15: @def@fref#1{@xrefX[#1,,@code{#1},,,]}
! 16: @def@b#1{{@bf@gt #1}}
! 17: @catcode`@#=@other
! 18: @end iftex
! 19: @overfullrule=0pt
! 20: @c -*-texinfo-*-
! 21: @comment %**start of header
! 22: @comment --- $B$*$^$8$J$$=*$j(B ---
! 23:
! 24: @comment --- GNU info $B%U%!%$%k$NL>A0(B ---
! 25: @setfilename parametrize
! 26:
! 27: @comment --- $B%?%$%H%k(B ---
! 28: @settitle Risa/Asir $BBe?t6J@~O@MQ%Q%C%1!<%8(B
! 29:
! 30: @comment %**end of header
! 31: @comment %@setchapternewpage odd
! 32:
! 33: @comment --- $B$*$^$8$J$$(B ---
! 34: @ifinfo
! 35: @macro fref{name}
! 36: @ref{\name\,,@code{\name\}}
! 37: @end macro
! 38: @end ifinfo
! 39:
! 40: @iftex
! 41: @comment @finalout
! 42: @end iftex
! 43:
! 44: @titlepage
! 45: @comment --- $B$*$^$8$J$$=*$j(B ---
! 46:
! 47: @comment --- $B%?%$%H%k(B, $B%P!<%8%g%s(B, $BCx<TL>(B, $BCx:n8"I=<((B ---
! 48: @title Risa/Asir $BBe?t6J@~O@MQ%Q%C%1!<%8@bL@=q(B
! 49: @subtitle $BMxMQ@bL@=q(B
! 50: @subtitle 1.0 $BHG(B
! 51: @subtitle 2004 $BG/(B 8 $B7n(B
! 52:
! 53: @author by Shuhei Todo
! 54: @page
! 55: @vskip 0pt plus 1filll
! 56: Copyright @copyright{} Risa/Asir committers
! 57: 2001. All rights reserved.
! 58: @end titlepage
! 59:
! 60: @comment --- $B$*$^$8$J$$(B ---
! 61: @synindex vr fn
! 62: @comment --- $B$*$^$8$J$$=*$j(B ---
! 63:
! 64: @comment --- @node $B$O(B GNU info, HTML $BMQ(B ---
! 65: @comment --- @node $B$N0z?t$O(B node-name, next, previous, up ---
! 66: @node Top,, (dir), (dir)
! 67:
! 68: @menu
! 69: * $B4X?t4J0W%^%K%e%"%k(B::
! 70: * Index::
! 71: @end menu
! 72:
! 73: @node $B4X?t4J0W%^%K%e%"%k(B,,, Top
! 74: @chapter $B4X?t4J0W%^%K%e%"%k(B
! 75:
! 76: @menu
! 77: * $B35MW(B::
! 78: * Notation::
! 79: * $B<g$J4X?t(B::
! 80: * $B$=$NB>$N4X?t(B::
! 81: @end menu
! 82:
! 83: @node $B35MW(B,,, $B4X?t4J0W%^%K%e%"%k(B
! 84: @section $B35MW(B
! 85:
! 86: @comment --- $B=qBN;XDj$K$D$$$F(B ---
! 87: @comment --- @code{} $B$O%?%$%W%i%$%?BNI=<((B ---
! 88: @comment --- @var{} $B$O<P;zBNI=<((B ---
! 89: @comment --- @b{} $B$O%\!<%k%II=<((B ---
! 90: @comment --- @samp{} $B$O%U%!%$%kL>$J$I$NI=<((B ---
! 91:
! 92: $B$3$N%Q%C%1!<%8$K$O!"Be?t6J@~$N=t@-<A$rD4$Y$k$?$a$N4X?t$,(B
! 93: $B=8$a$i$l$F$$$k!#<g$J5!G=$O!"Be?t6J@~$KBP$7$FDj5A$5$l$k0J2<(B
! 94: $B$NBP>]$r7W;;$G$-$k$3$H$G$"$k!'(B
! 95: @itemize @bullet
! 96: @item 2$B6J@~$N8rE@$N:BI8(B
! 97: @item $BFC0[E@$N:BI8(B
! 98: @item neighborhood graph$B!JFs<!JQ49$K$h$C$FFC0[E@$,$I$N$h$&$K(B
! 99: $BJ,2r$5$l$k$+$rI=$9(Btree$B!K(B
! 100: @item $B4{Ls6J@~$N<o?t(B
! 101: @item $B?oH<6J@~(B(adjoint curves)
! 102: @item $BFs<!6J@~>e$NM-M}E@(B
! 103: @item $BM-M}6J@~!J<o?t#0$N6J@~!K$r%Q%i%a%H%i%$%:$9$kM-M}4X?t(B
! 104: @end itemize
! 105: $B$=$NB>!"B?9`<0$NA4<!?t$r7W;;$9$k$H$$$C$?$h$&$JM=HwE*$J4X?t72(B
! 106: $B$,MQ0U$5$l$F$$$k!#%f!<%6!<$NF~NO$9$kBe?t6J@~$NDj5AB?9`<0$OI,$:(B
! 107: $BM-M}?tBN>e$NJQ?t(B@var{x,y,z} $B$N(B@b{$B@F<!(B}$BB?9`<0$G$J$1$l$P$J$i$J$$!#(B
! 108:
! 109: @node Notation,,,$B4X?t4J0W%^%K%e%"%k(B
! 110: @section Notation
! 111:
! 112: $BK\=q$GMQ$$$i$l$k5-9f$K$D$$$F!"<!$N$h$&$JLsB+$r$7$F$*$/!#(B
! 113: @itemize @bullet
! 114: @item $BE@(B@code{[x,y,z]} $B$H$O<M1FJ?LL$NE@$N@F<!:BI8(B
! 115: @var{(x:y:z)}$B$r0UL#$7!"FC$KCG$j$,$J$1$l$P!"(B@var{z=0}$B$G$J$$(B
! 116: $B$H$-$OI,$:(B@var{z=1}$B$H$J$k$h$&$K@55,2=$5$l$F$$$k!#(B
! 117: @item Q $B$OM-M}?tBN!"(B
! 118: @tex $\overline{Q}$ @end tex
! 119: $B$OBe?tE*?tA4BN$N$J$9BN$r0UL#$9$k!#(B
! 120: @end itemize
! 121:
! 122: @node $B<g$J4X?t(B,,, $B4X?t4J0W%^%K%e%"%k(B
! 123: @section $B<g$J4X?t(B
! 124:
! 125: @menu
! 126: * intersect::
! 127: * sing::
! 128: * nbh::
! 129: * genus::
! 130: * adjoint1,adjoint2::
! 131: * intpt::
! 132: * parametrize::
! 133: @end menu
! 134:
! 135: @node intersect,,, $B<g$J4X?t(B
! 136: @subsection @code{intersect}
! 137: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 138: @findex intersect
! 139:
! 140: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 141: @table @t
! 142: @item intersect(@var{F},@var{G})
! 143: :: 2$B6J@~(B@var{F=0},@var{G=0} $B$N8rE@$N:BI8$+$i$J$k%j%9%H$rJV$9(B.
! 144: @end table
! 145:
! 146: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 147: @table @var
! 148: @item return
! 149: $B%j%9%H(B
! 150: @item F G
! 151: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 152: @end table
! 153:
! 154: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 155: @itemize @bullet
! 156: @item 2$B6J@~(B@var{F=0},@var{G=0} $B$N8rE@(B@code{[x,y,z]}$B$+$i$J$k(B
! 157: $B%j%9%H$rJV$9!#(B
! 158: @item @var{F},@var{G}$B$O6&DL0x;R$r;}$C$F$$$F$O$$$1$J$$!#(B
! 159: @end itemize
! 160:
! 161: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 162: @example
! 163: [1] intersect(y^2-x*z,(x^2+y^2)^3-4*x^2*y^2*z^2);
! 164: [[0,0,1],[(#4),(#5),1]]
! 165: [2] defpoly(alg(4));
! 166: t#4^3+3*t#4^2+3*t#4-3
! 167: [3] defpoly(alg(5));
! 168: t#5^2-t#4
! 169: [4] intersect(x^2-y^2,x^3+y*x^2+(y^2-z^2)*x+y^3-z^2*y);
! 170: ***two curve have common components***
! 171: @end example
! 172:
! 173:
! 174: @node sing,,, $B<g$J4X?t(B
! 175: @subsection @code{sing}
! 176: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 177: @findex sing
! 178:
! 179: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 180: @table @t
! 181: @item sing(@var{F})
! 182: :: $B6J@~(B@var{F=0} $B$NFC0[E@$N:BI8$+$i$J$k%j%9%H$rJV$9(B.
! 183: @end table
! 184:
! 185: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 186: @table @var
! 187: @item return
! 188: $B%j%9%H(B
! 189: @item F
! 190: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 191: @end table
! 192:
! 193: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 194: @itemize @bullet
! 195: @item $B6J@~(B@var{F=0} $B$NFC0[E@(B@code{[x,y,z]}$B!J(B
! 196: @tex
! 197: $F_x(x,y,z)=F_y(x,y,z)=F_z(x,y,z)=0$
! 198: @end tex
! 199: $B$rK~$?$9E@!K$+$i$J$k%j%9%H(B
! 200: $B$rJV$9!#(B
! 201: @item @var{F}$B$O=EJ#0x;R$r;}$C$F$$$F$O$$$1$J$$!JDj5A$h$j(B
! 202: $B=EJ#0x;R$NNmE@$O$9$Y$FFC0[E@$G$"$k!K!#(B
! 203: @end itemize
! 204:
! 205: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 206: @example
! 207: [1] sing(16*x^6-24*z^2*x^4+9*z^4*x^2+4*z^2*y^4-4*z^4*y^2);
! 208: [[0,0,1],[(#4),0,1],[1/2,(#3),1],[-1/2,(#3),1],[0,1,0]]
! 209: [2] defpoly(alg(3));
! 210: 2*t#3^2-1
! 211: [3] defpoly(alg(4));
! 212: 4*t#4^2-3
! 213: [4] sing((x-y)*(y^2-x*z));
! 214: [[1,1,1],[0,0,1]]
! 215: [5] sing((x-y)^2*(y^2-x*z));
! 216: ***Argument has multiple divisor***
! 217: @end example
! 218:
! 219: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 220: @table @t
! 221: @item $B;2>H(B
! 222: @ref{nbh}
! 223: @ref{multia}
! 224: @end table
! 225:
! 226:
! 227: @node nbh,,, $B<g$J4X?t(B
! 228: @subsection @code{nbh}
! 229: @findex nbh
! 230:
! 231: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 232:
! 233: @table @t
! 234: @item nbh(@var{F})
! 235: :: $B6J@~(B@var{F}=0 $B$N(Bneighborhood graph $B$rJV$9!#(B
! 236: @end table
! 237:
! 238: @table @var
! 239: @item return
! 240: $B%j%9%H(B
! 241: @item F
! 242: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 243: @end table
! 244:
! 245: @itemize @bullet
! 246: @item $B6J@~(B@var{F=0} $B$N(Bneigborhood graph $B$rI=$9%j%9%H$rJV$9!#(B
! 247: neighborhood graph $B$H$OFs<!JQ49$K$h$C$FFC0[E@$,$I$N$h$&$K(B
! 248: $BJ,2r$5$l$k$+$rI=$9(Btree$B$G$"$k!#J,2r$K$h$C$F8=$l$kE@$N$3$H$r(B
! 249: $BNY@\E@$H8F$V!#FC0[E@!"NY@\E@$N>pJs$O!"$=$l$>$l<!$N$h$&$J(B
! 250: @b{$B%Y%/%H%k(B}$B$K$h$C$FI=$5$l$k!#(B
! 251:
! 252: @table @code
! 253: @item $BFC0[E@(B
! 254: [ $BE@$N8D?t(B, $BE@$N:BI8(B, [$B=EJ#EY(B, $BDL>oFC0[E@(B(=1)$B$+$=$&$G$J$$(B(=-1)$B$+(B], [$B$3$N!J$3$l$i$N!KFC0[E@$+$i=P$F$/$kNY@\E@$N>pJs(B($B$3$l0J>eNY@\E@$,8=$l$J$$>l9g$O(B''terminal'')] ]
! 255: @item $BNY@\E@(B
! 256: [ $BE@$N8D?t(B, [$B=EJ#EY(B, $BDL>oFC0[E@(B(=1)$B$+$=$&$G$J$$$+(B(=-1)$B$+(B], [$B$3$N!J$3$l$i$N!KNY@\E@$+$i=P$F$/$kNY@\E@$N>pJs(B($B$3$l0J>eNY@\E@$,8=$l$J$$>l9g$O(B''terminal'')] ]
! 257: @item $B0lHL$K!"FC0[E@$N:BI8$OBe?tE*?t$K$J$k!#$3$N>l9g!"Be?tE*?t$r6&Lr$JBe?tE*?t$GCV$-49$($FF@$i$l$kE@$b$^$?!"FC0[E@$K$J$k!#$3$N@-<A$rMxMQ$7$FJ#?t$NFC0[E@$r0lEY$KI=<($9$k$N$G$"$k$,!"FC0[E@%Y%/%H%k$N:G=i$N0z?t!VE@$N8D?t!W$O$3$N$h$&$JI=<($K$h$C$F!"$$$/$D$NFC0[E@$,I=$5$l$F$$$k$+$r<($7$F$$$k!#$7$?$,$C$F!"FC0[E@$,M-M}E@$J$i$P!"E@$N8D?t(B=1 $B$G$"$k!#NY@\E@%Y%/%H%k$N:G=i$N0z?t$G$"$k!VE@$N8D?t!W$O?F%Y%/%H%k$NI=$93FE@$+$i!"$3$N?t$@$1F1$8%?%$%W$NNY@\E@$,=P$F$/$k$3$H$r0UL#$9$k!#(B
! 258: @end table
! 259:
! 260: @item neighborhood graph $B$O$3$l$i$N%Y%/%H%k$rF~$l;R$K$7$?%j%9%H$K$h$C$FI=8=$5$l$F$$$k!#(B
! 261:
! 262: @example
! 263: [1] F=x^6+3*y^2*x^4+(3*y^4-4*z^2*y^2)*x^2+y^6;
! 264: x^6+3*y^2*x^4+(3*y^4-4*z^2*y^2)*x^2+y^6
! 265: [2] sing(F);
! 266: [[0,0,1],[(#0),1,0]]
! 267: [3] nbh(F);
! 268: [ 1 [0,0,1] [4,-1] [[ 1 [2,1] [terminal] ],[ 1 [2,1] [terminal] ]] ]
! 269: [ 2 [(#0),1,0] [2,-1] [[ 1 [1,1] [terminal] ]] ]
! 270: @end example
! 271: $BFC0[E@(B@code{[0,0,1]} $B$O=EJ#EY(B4 $B$NDL>o$G$J$$FC0[E@$G$"$j!"(B
! 272: 2$B$D$NNY@\E@$r$b$D!#$=$l$i$O$I$A$i$H$b=EJ#EY(B2 $B$NDL>oFC0[E@(B
! 273: $B$G$"$k!#FC0[E@(B@code{[(#0),1,0]}$B$NNY@\E@$OC1=cE@$G$"$k!#(B
! 274: @item @var{F}$B$O=EJ#0x;R$r;}$C$F$$$F$O$$$1$J$$!#(B
! 275: @end itemize
! 276:
! 277: @table @t
! 278: @item $B;2>H(B
! 279: @ref{sing}
! 280: @end table
! 281:
! 282:
! 283: @node genus,,, $B<g$J4X?t(B
! 284: @subsection @code{genus}
! 285: @findex genus
! 286:
! 287: @table @t
! 288: @item genus(@var{F})
! 289: :: $B6J@~(B@var{F=0} $B$NFC0[E@$N:BI8$+$i$J$k%j%9%H$rJV$9(B.
! 290: @end table
! 291:
! 292: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 293: @table @var
! 294: @item return
! 295: 0$B0J>e$N@0?t(B
! 296: @item F
! 297: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 298: @end table
! 299:
! 300: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 301: @itemize @bullet
! 302: @item $B6J@~(B@var{F=0} $B$N<o?t$rJV$9!#(B
! 303: @item @var{F} $B$O(B@tex $\overline{Q}[x,y,z]$ @end tex
! 304: $B$K$*$$$F4{Ls$G$J$1$l$P$J$i$J$$!#$3$N>r7o$N2<$G$7$+@53N$JCM$,JV$5$l$kJ]>Z$,$J$$!#(BQ[x,y,z] $B$K$*$$$F4{Ls$G$"$C$?$H$7$F$b!"(B
! 305: @tex $\overline{Q}[x,y,z]$ @end tex
! 306: $B$G4{Ls$H$O8B$i$J$$$N$GCm0U$rMW$9$k!#F~NO$,$3$N>r7o$rK~$?$7$F(B
! 307: $B$$$k$+$I$&$+$O%A%'%C%/$5$l$J$$!#(B
! 308: @end itemize
! 309:
! 310: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 311: @example
! 312: [1] genus(x^6+3*y^2*x^4+(3*y^4-4*z^2*y^2)*x^2+y^6);
! 313: 0
! 314: [2] genus(y^2*z-x^3-z^3);
! 315: 1
! 316: [3] genus(x^2+y^2+z^2-x*y-y*z-z*x);
! 317: -1
! 318: [4] fctr(x^2+y^2+z^2-x*y-y*z-z*x);
! 319: [[1,1],[x^2+(-y-z)*x+y^2-z*y+z^2,1]]
! 320: [5] irr_conic(x^2+y^2+z^2-x*y-y*z-z*x);
! 321: reducible
! 322: @end example
! 323:
! 324: @table @t
! 325: @item $B;2>H(B
! 326: @ref{irr_conic}
! 327: @end table
! 328:
! 329: @node adjoint1 adjoint2,,, $B<g$J4X?t(B
! 330: @subsection @code{adjoint1},@code{adjoint2}
! 331: @findex adjoint1
! 332: @findex adjoint2
! 333:
! 334: @table @t
! 335: @item adjoint1(@var{F})
! 336: @itemx adjoint2(@var{F})
! 337: :: $B$=$l$>$l6J@~(B@var{F=0}$B$N(Bn-1$B<!(B,n-2$B<!$N?oH<6J@~(B(adjoint
! 338: curve)$B$rJV$9(B(n=deg(F))$B!#(B
! 339: @end table
! 340:
! 341: @table @var
! 342: @item return
! 343: $B@~7A$N%Q%i%a!<%?!<$r4^$`JQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 344: @item F
! 345: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 346: @end table
! 347:
! 348: @itemize @bullet
! 349: @item n-2 $B<!$N6J@~(B@var{G=0}$B$,6J@~(B@var{F=0} $B$N=EJ#EY(Br $B$NE@$r>/$J$/$H$b=EJ#EY(Br-1 $B$K$b$D$H$-!"6J@~(B@var{G=0}$B$r6J@~(B@var{F=0} $B$N(Bn-2 $B<!$N?oH<6J@~(B(adjoint curve)$B$H8F$V!#(Bn-1 $B8D$N?oH<6J@~(B
! 350: @tex
! 351: $G_0=0,G_1=0, \ldots ,G_{n-2}=0$
! 352: @end tex
! 353: $B$,B8:_$7$F!"(Bn-2 $B<!$N?oH<6J@~$NDj5AB?9`<0A4BN$O(B
! 354: @tex
! 355: $c_0G_0+c_1G_1+ \ldots +c_{n-2}G_{n-2}$ ($c_{i}$ $B$O78?tBN$N85(B)
! 356: @end tex
! 357: $B$HI=$5$l$k!#(B@code{adjoint2}(@var{F}) $B$O!"$3$N(Bn-1 $B8D$N@~7A$N%Q%i%a!<%?!<$r4^$s$@@F<!B?9`<0$rJV$9!#(Bn-1 $B<!$N?oH<6J@~$bF1MM$KDj5A$5$l$k!#(Bn-1 $B<!$N?oH<6J@~$NDj5AB?9`<0A4BN$b>e$HF1MM$K!"(B2n-1 $B8D$N@~7A%Q%i%a!<%?!<$r4^$s$@(Bn-1 $B<!$N@F<!B?9`<0$GI=$5$l$k!#(B@code{adjoint1}(@var{F}) $B$O$3$NB?9`<0$rJV$9!#(B
! 358: @item $B:G=i$K%Q%i%a!<%?!<$N%j%9%H$H!"$=$ND9$5$,I=<($5$l$k!#(B
! 359: @item @var{F}$B$O=EJ#0x;R$r;}$C$F$$$F$O$$$1$J$$!#(B
! 360: @end itemize
! 361:
! 362: @example
! 363: [1] adjoint2(x^6+3*y^2*x^4+(3*y^4-4*z^2*y^2)*x^2+y^6);
! 364: [c2,c3,c4,c6,c7] 5
! 365: (c2-c4)*x^4+c3*y*x^3+(c2*y^2+c6*z*y)*x^2+(c3*y^3+c7*z*y^2)*x+c4*y^4
! 366: [2] adjoint1(F);
! 367: [c1,c7,c11,c12,c13,c15,c16,c17,c18,c19,c20] 11
! 368: (c1*y+(c11-c15+c18-c20)*z)*x^4+(c13*y^2+c7*z*y+c11*z^2)*x^3+(c17*z*y^2+c12*z^2*y
! 369: +c15*z^3)*x^2+(c13*z^2*y^2+c16*z^3*y+c18*z^4)*x+c17*z^3*y^2+c19*z^4*y+c20*z^5
! 370: @end example
! 371:
! 372: @table @t
! 373: @item $B;2>H(B
! 374: @ref{restriction}
! 375: @end table
! 376:
! 377:
! 378: @node intpt,,, $B<g$J4X?t(B
! 379: @subsection @code{intpt}
! 380: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 381: @findex intpt
! 382:
! 383: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 384: @table @t
! 385: @item intpt(@var{F})
! 386: :: $BFs<!6J@~(B@var{F=0} $B>e$N@0?tE@(B@code{[x,y,z]} $B$r$R$H$D8+$D$1$FJV$9!#@0?tE@$,B8:_$7$J$1$l$P!"J8;zNs(B@code{no integer solution}$B$rJV$9!#(B
! 387: @end table
! 388:
! 389: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 390: @table @var
! 391: @item return
! 392: $B%j%9%H!"$"$k$$$OJ8;zNs(B@code{no integer solution}.
! 393: @item F
! 394: $BJQ?t(Bx,y,z $B$NFs<!$N@F<!B?9`<0(B
! 395: @end table
! 396:
! 397: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 398: @itemize @bullet
! 399: @item $BFs<!6J@~(B@var{F=0} $B>e$K@0?tE@(B(affine$B$G$$$&M-M}E@(B)$B$,(B
! 400: $B$"$l$P!"$=$N:BI8(B@code{[x,y,z]}$B$rJV$9!#(B@code{x},@code{y},
! 401: @code{z} $B$O$9$Y$F@0?t$G$"$k!#@0?tE@$,B8:_$7$J$$$H$-$O(B
! 402: $BJ8;zNs(B@code{no integer solution} $B$rJV$9!#(B
! 403: @item $B;085Fs<!7A<0$N@0?t2r$r5a$a$k8EE5E*$J(BLegendre$B$NJ}K!$rMQ$$$F$$$k!#%5%V%k!<%A%s$GFs<!$N9gF1J}Dx<0$r2r$/:]!"C1$KAmEv$jK!$rMQ$$$F$$$k$@$1$N$G!"(B@var{F} $B$N78?t$,Bg$-$/$J$k$HHs>o$K;~4V$,$+$+$k!#(B
! 404: @end itemize
! 405:
! 406: @example
! 407: [1] intpt(22*x^2-10*y^2+z^2+5*x*y+13*y*x-z*x);
! 408: [71,-121,473]
! 409: [2] intpt(22*x^2-10*y^2+z^2+5*x*y+12*y*x-z*x);
! 410: no integer solution
! 411: @end example
! 412:
! 413:
! 414: @node parametrize,,, $B<g$J4X?t(B
! 415: @subsection @code{parametrize}
! 416: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 417: @findex parametrize
! 418:
! 419: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 420: @table @t
! 421: @item parametrize(@var{F})
! 422: :: $BM-M}6J@~(B@var{F=0} $B$r%Q%i%a%H%i%$%:$9$kB?9`<0$NAH$rJV$9!#(B
! 423: @end table
! 424:
! 425: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 426: @table @var
! 427: @item return
! 428: $B%j%9%H(B
! 429: @item F
! 430: $BM-M}6J@~$NDj5AB?9`<0!JJQ?t(Bx,y,z $B$N@F<!B?9`<0!K(B
! 431: @end table
! 432:
! 433: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 434: @itemize @bullet
! 435: @item $BM-M}6J@~(B@var{F=0}$B!J<o?t$,(B0$B$N6J@~!K$O!"JQ?t(Bt $B$NB?9`<0(BP(t),Q(t),R(t) $B$*$h$S(Bx,y,z$B$N@F<!B?9`<0(BS(x,y,z),T(x,y,z)$B$rMQ$$$F(B(x:y:z)=(P(t):Q(t):R(t)), t=T(x,y,z)/S(x,y,z) $B$H%Q%i%a!<%?!<I=<($5$l$k!#(B@code{parametrize}(@var{F}) $B$O$3$l$i$NB?9`<0$+$i$J$k%j%9%H(B@code{[P(t),Q(t),R(t),T(x,y,z)/S(x,y,z)]} $B$rJV$9!J(BGCD(@code{P(t)},@code{Q(t)},@code{R(t)})=1 $B$G$"$k!K!#0lHL$K$O(BP(t),Q(t),R(t) $B$O78?t$KM-M}?t$NJ?J}:,$r4^$`B?9`<0$H$J$k$,!"M-M}?t78?t$NB?9`<0$G6J@~$r%Q%i%a%H%i%$%:$G$-$k>l9g$O!"(B@b{$B>o$K(B}$BM-M}?t78?t$NB?9`<0$NAH$rJV$9!JNc$($P6J@~$N<!?t$,4q?t$N>l9g!K!#(B
! 436: @item @var{F} $B$O(B@tex $\overline{Q}[x,y,z]$ @end tex
! 437: $B$K$*$$$F4{Ls$G!"$+$D<o?t$,(B0$B$G$J$1$l$P$J$i$J$$$,!"$3$l$i$N>r7o$,K~$?$5$l$F$$$k$+$I$&$+$N%A%'%C%/$O$J$5$l$J$$!#(B
! 438: @end itemize
! 439:
! 440: @example
! 441: [1] parametrize(x^4+(2*y^2-z^2)*x^2+y^4+z^2*y^2);
! 442: [-t^3-t,t^3-t,t^4+1,(-x^2-y^2)/(z*x+z*y)]
! 443: [2] parametrize((x^2+y^2)^3-4*x^2*y^2*z^2);
! 444: heuristic2 failed...
! 445: heuristic3 succeed
! 446: [32256*t^6-133120*t^5-129024*t^4+1064960*t^3-516096*t^2
! 447: -2129920*t+2064384,-127008*t^6+1048320*t^5-2671232*t^4
! 448: +10684928*t^2-16773120*t+8128512,274625*t^6-3194100*t^5
! 449: +15678780*t^4-41555808*t^3+62715120*t^2-51105600*t+17576000,
! 450: (-126*x^4+1040*y*x^3-382*y^2*x^2+1040*y^3*x-256*y^4)
! 451: /(-65*x^4+520*y*x^3+(-65*y^2-32*z*y)*x^2+(520*y^3+256*z*y^2)*x)]
! 452: [3] parametrize(22*x^2-10*y^2+z^2+5*x*y+12*y*x-z*x);
! 453: [(220*#6-10)*t^2+(-22*#6+1),(374*#6-17)*t^2+(-22*#6-43)*t,
! 454: (220*#6+210)*t^2+(-374*#6+17)*t+22,(-y)/((22*#6-1)*x+z)]
! 455: @end example
! 456:
! 457: @table @t
! 458: @item $B;2>H(B
! 459: @ref{genus}
! 460: @end table
! 461:
! 462:
! 463: @node $B$=$NB>$N4X?t(B,,, $B4X?t4J0W%^%K%e%"%k(B
! 464: @section $B$=$NB>$N4X?t(B
! 465:
! 466: @menu
! 467: * tdeg::
! 468: * homzation::
! 469: * random_line::
! 470: * multia::
! 471: * irr_conic::
! 472: * lissajou::
! 473: * restriction::
! 474: @end menu
! 475:
! 476: @node tdeg,,, $B$=$NB>$N4X?t(B
! 477: @subsection @code{tdeg}
! 478: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 479: @findex tdeg
! 480:
! 481: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 482: @table @t
! 483: @item tdeg(Poly)
! 484: :: $BB?9`<0(B@var{Poly}$B$NA4<!?t$rJV$9!#(B
! 485: @end table
! 486:
! 487: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 488: @table @var
! 489: @item return
! 490: 0$B0J>e$N@0?t(B
! 491: @item Poly
! 492: $BB?9`<0(B
! 493: @end table
! 494:
! 495: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 496: @itemize @bullet
! 497: @item $BB?9`<0(B@var{Poly}$B$NA4<!?t$rJV$9!#(B
! 498: @end itemize
! 499:
! 500: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 501: @example
! 502: [1] tdeg(u^3+v^3-x*y*z*w);
! 503: 4
! 504: [956] tdeg((x^3+y^2+z)*(a^2+b+1));
! 505: 5
! 506: @end example
! 507:
! 508:
! 509: @node homzation,,, $B$=$NB>$N4X?t(B
! 510: @subsection @code{homzation}
! 511: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 512: @findex homzation
! 513:
! 514: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 515: @table @t
! 516: @item homzation(AF)
! 517: :: $BJQ?t(Bx,y$B$NB?9`<0$r@F<!2=$7$F(Bx,y,z$B$N@F<!B?9`<0$K$9$k!#(B
! 518: @end table
! 519:
! 520: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 521: @table @var
! 522: @item return
! 523: $BJQ?t(Bx,y,z$B$N@F<!B?9`<0(B
! 524: @item F
! 525: $BJQ?t(Bx,y$B$NB?9`<0(B
! 526: @end table
! 527:
! 528: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 529: @itemize @bullet
! 530: @item $BJQ?t(Bx,y$B$NB?9`<0$r@F<!2=$7$F(Bx,y,z$B$N@F<!B?9`<0$K$9$k!#F~NO$9$kB?9`<0$NJQ?t$O(Bx,y$B$G$J$1$l$P$J$i$J$$!#(B
! 531: @end itemize
! 532:
! 533: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 534: @example
! 535: [1] homzation((x^2+4*x^3+6*x^4)-4*x^4*y
! 536: +(-2*x-4*x^2-2*x^3)*y^2+y^4);
! 537: (-4*y+6*z)*x^4+(-2*y^2+4*z^2)*x^3
! 538: +(-4*z*y^2+z^3)*x^2-2*z^2*y^2*x+z*y^4
! 539: [958] homzation(u*v+1);
! 540: Input must be polynomial of variable x,y
! 541: @end example
! 542:
! 543:
! 544: @node random_line,,, $B$=$NB>$N4X?t(B
! 545: @subsection @code{random_line}
! 546: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 547: @findex random_line
! 548:
! 549: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 550: @table @t
! 551: @item random_line(@var{Pt},B[,@var{Seed}])
! 552: :: $BE@(B@var{Pt}(=@code{[x,y,z]})$B$rDL$kD>@~$r$R$H$D%i%s%@%`$K(B
! 553: $BJV$9!#(B
! 554: @end table
! 555:
! 556: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 557: @table @var
! 558: @item return
! 559: $BJQ?t(Bx,y,z$B$N0l<!<0(B
! 560: @item Pt
! 561: $BE@$rI=$9%j%9%H(B
! 562: @item B
! 563: $B<+A3?t(B
! 564: @item Seed
! 565: $B<+A3?t(B
! 566: @end table
! 567:
! 568: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 569: @itemize @bullet
! 570: @item $BE@(B@var{Pt}(=@code{[x,y,z]})$B$rDL$kD>@~$NJ}Dx<0$G(B
! 571: $B3F78?t$NCM$,(B-B$B0J>e(BB$BL$K~$N$b$N$r!"$R$H$D%i%s%@%`$KJV$9!#(B
! 572: @item Seed$B$O%5%V%k!<%A%s$G(Brandom([Seed])$B$rMQ$$$k:]$K;HMQ(B
! 573: $B$5$l$k!#(B
! 574: @end itemize
! 575:
! 576: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 577: @example
! 578: [1] random_line([0,0,1],1);
! 579: x-8*y
! 580: @end example
! 581:
! 582:
! 583: @node multia,,, $B$=$NB>$N4X?t(B
! 584: @subsection @code{multia}
! 585: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 586: @findex multia
! 587:
! 588: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 589: @table @t
! 590: @item multia(F,Pt)
! 591: :: $B6J@~(B@var{F=0} $B$NE@(B@var{Pt}(=@code{[x,y,z]})$B$K$*$1$k(B
! 592: $B=EJ#EY$rJV$9!#(B
! 593: @end table
! 594:
! 595: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 596: @table @var
! 597: @item return
! 598: 0$B0J>e$N<+A3?t(B
! 599: @item F
! 600: $BJQ?t(Bx,y,z $B$N@F<!B?9`<0(B
! 601: @item Pt
! 602: $BE@$rI=$9%j%9%H(B
! 603: @end table
! 604:
! 605: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 606: @itemize @bullet
! 607: @item $B6J@~(B@var{F=0} $B$NE@(B@var{Pt}(=@code{[x,y,z]})$B$K$*$1$k(B
! 608: $B=EJ#EY$rJV$9!#(BF$B$r(BN $B3,JPHyJ,$7$FF@$i$l$kB?9`<0$,=i$a$FE@(BPt$B$G(B
! 609: 0$B$K$J$i$J$$$H$-!"@0?t(BN$B$r6J@~(B@var{F=0}$B$NE@(BPt$B$K$*$1$k=EJ#EY(B
! 610: $B$H$$$&!#(B
! 611: @end itemize
! 612:
! 613: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 614: @example
! 615: [1] multia((4*y^2+4*z^2)*x^4+8*z^3*x^3+8*z^2*y^2*x^2-8*z^5*x+
! 616: 4*z^4*y^2-4*z^6,[0,0,1]);
! 617: 0
! 618: [2] multia((4*y^2+4*z^2)*x^4+8*z^3*x^3+8*z^2*y^2*x^2-8*z^5*x+
! 619: 4*z^4*y^2-4*z^6,[0,1,0]);
! 620: 4
! 621: [3] multia((4*y^2+4*z^2)*x^4+8*z^3*x^3+8*z^2*y^2*x^2-8*z^5*x+
! 622: 4*z^4*y^2-4*z^6,[1,0,0]);
! 623: 2
! 624: @end example
! 625:
! 626: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 627: @table @t
! 628: @item $B;2>H(B
! 629: @ref{sing}
! 630: @ref{nbh}
! 631: @end table
! 632:
! 633:
! 634: @node irr_conic,,, $B$=$NB>$N4X?t(B
! 635: @subsection @code{irr_conic}
! 636: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 637: @findex irr_conic
! 638:
! 639: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 640: @table @t
! 641: @item irr_conic(@var{F})
! 642: :: $B;085Fs<!7A<0(B@var{F}$B$,(B
! 643: @tex
! 644: $\overline{Q}[x,y,z]$
! 645: @end tex
! 646: $B$G4{Ls$+$I$&$+$rH=Dj$9$k!#(B
! 647: @end table
! 648:
! 649: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 650: @table @var
! 651: @item return
! 652: $BJ8;zNs(B
! 653: @item F
! 654: $BJQ?t(Bx,y,z $B$NFs<!$N@F<!B?9`<0(B
! 655: @end table
! 656:
! 657: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 658: @itemize @bullet
! 659: @item $B;085Fs<!7A<0(B@var{F}$B$,(B
! 660: @tex
! 661: $\overline{Q}[x,y,z]$
! 662: @end tex
! 663: $B$G4{Ls$J$i$P(B@code{irreducible}$B$r!"2DLs$J$i$P(B@code{reducible}
! 664: $B$rJV$9!#(B
! 665: @end itemize
! 666:
! 667: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 668: @example
! 669: [1] irr_conic(x^2+y^2+z^2-x*y-y*z-z*x);
! 670: reducible
! 671: [2] fctr(x^2+y^2+z^2-x*y-y*z-z*x);
! 672: [[1,1],[x^2+(-y-z)*x+y^2-z*y+z^2,1]]
! 673: @end example
! 674:
! 675:
! 676: @node lissajou,,, $B$=$NB>$N4X?t(B
! 677: @subsection @code{lissajou}
! 678: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 679: @findex lissajou
! 680:
! 681: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 682: @table @t
! 683: @item lissajou(M,N)
! 684: :: @tex
! 685: $x=\sin(M\theta),y=\cos(N\theta)$
! 686: @end tex
! 687: $B$K$h$C$FDj5A$5$l$k%j%5!<%8%e6J@~$N1"4X?tI=<((B
! 688: @end table
! 689:
! 690: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 691: @table @var
! 692: @item return
! 693: $BJQ?t(Bx,y,z$B$N@F<!B?9`<0(B
! 694: @item M N
! 695: $B8_$$$KAG$J<+A3?t(B
! 696: @end table
! 697:
! 698: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 699: @itemize @bullet
! 700: @item @tex
! 701: $x=\sin(M\theta),y=\cos(N\theta)$
! 702: @end tex
! 703: $B$K$h$C$FDj5A$5$l$k%j%5!<%8%e6J@~$N1"4X?tI=<(!JJQ?t(Bx,y,z$B$N(B
! 704: $B@F<!B?9`<0!K$rJV$9!#(B
! 705: @end itemize
! 706:
! 707: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 708: @example
! 709: [984] lissajou(3,4);
! 710: 64*x^8-128*z^2*x^6+80*z^4*x^4-16*z^6*x^2+16*z^2*y^6
! 711: -24*z^4*y^4+9*z^6*y^2
! 712: [985] lissajou(2,7);
! 713: 4096*x^14-14336*z^2*x^12+19712*z^4*x^10-13440*z^6*x^8
! 714: +4704*z^8*x^6-784*z^10*x^4+49*z^12*x^2+4*z^10*y^4-4*z^12*y^2
! 715: @end example
! 716:
! 717:
! 718: @node restriction,,, $B$=$NB>$N4X?t(B
! 719: @subsection @code{restriction}
! 720: @comment --- $B:w0zMQ%-!<%o!<%I(B---
! 721: @findex restriction
! 722:
! 723: @comment --- $B4X?t$N4JC1$J@bL@(B ---
! 724: @table @t
! 725: @item restriction(@var{A},@var{List})
! 726: :: $BFCDj$NE@$rDL$k?oH<6J@~$NDj5AB?9`<0$r7W;;$7$?$$$H$-$KMQ$$$k!#(B
! 727: @end table
! 728:
! 729: @comment --- $B0z?t$N4JC1$J@bL@(B ---
! 730: @table @var
! 731: @item return
! 732: $B@~7A$N%Q%i%a!<%?!<$r4^$`(Bx,y,z$B$N@F<!B?9`<0(B
! 733: @item A
! 734: @code{adjoint1,adjoint2}$B$+$iJV$5$l$k7A$HF1MM$N!"@~7A%Q%i%a!<%?!<(B
! 735: $B$D$-$NJQ?t(Bx,y,z$B$N@F<!B?9`<0(B
! 736: @item List
! 737: $BE@(B@code{[x,y,z]}$B$+$i$J$k%j%9%H(B
! 738: @end table
! 739:
! 740: @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
! 741: @itemize @bullet
! 742: @item @code{adjoint1,adjoint2}$B$+$iJV$5$l$k@~7A%Q%i%a!<%?!<IU$N(B
! 743: $B@F<!B?9`<0$,!"(B@var{List}$B$K4^$^$l$k3FE@$rNmE@$K$b$D$?$a$K$O!"(B
! 744: $B@~7A%Q%i%a!<%?!<$N4V$K$$$/$D$+$N!J(BQ$B>e$N!K0l<!4X78<0$,@.$jN)$F(B
! 745: $B$P$h$$!#$3$N>r7o$r2CL#$7$F!"?7$?$J@~7A%Q%i%a!<%?!<IU$N@F<!(B
! 746: $BB?9`<0$r:n$k!#(B
! 747: @item @var{List}$B$K4^$^$l$kE@$O!"(B@code{intersect}$B$d(B@code{sing}
! 748: $B$+$iJV$5$l$kE@$r;H$&$3$H$rA[Dj$7$F$$$k!#(B
! 749: @end itemize
! 750:
! 751: @comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
! 752: @example
! 753: @end example
! 754:
! 755: @comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
! 756: @table @t
! 757: @item $B;2>H(B
! 758: @ref{adjoint1,adjoint2}
! 759: @end table
! 760:
! 761:
! 762: @comment --- $B"~"~"~"~(B $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B
! 763:
! 764:
! 765: @comment --- $B$*$^$8$J$$(B ---
! 766: @node Index,,, Top
! 767: @unnumbered Index
! 768: @printindex fn
! 769: @printindex cp
! 770: @iftex
! 771: @vfill @eject
! 772: @end iftex
! 773: @summarycontents
! 774: @contents
! 775: @bye
! 776: @comment --- $B$*$^$8$J$$=*$j(B ---
! 777:
! 778:
! 779:
! 780:
! 781:
! 782:
! 783:
! 784:
! 785:
! 786:
! 787:
! 788:
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