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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.28 and 1.31

version 1.28, 2008/11/19 03:25:38 version 1.31, 2009/02/23 05:51:23
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 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.27 2008/11/11 08:18:50 ohara Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.30 2009/02/23 04:00:53 takayama Exp $
 \input texinfo  \input texinfo
 @iftex  @iftex
 @catcode`@#=6  @catcode`@#=6
Line 148  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
Line 148  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
 * chdir::  * chdir::
 * pwd::  * pwd::
 * dcurrenttime::  * dcurrenttime::
   * node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module)::
   * node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option)::
   
   
 @end menu  @end menu
Line 2474  ChangeLog
Line 2476  ChangeLog
 $B$3$N4X?t$O(B 2008-9-12 $B$K%3%_%C%H$5$l$?(B.  $B$3$N4X?t$O(B 2008-9-12 $B$K%3%_%C%H$5$l$?(B.
 $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/time.c (1.6) $B$G$"$k(B.  $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/time.c (1.6) $B$G$"$k(B.
 @end itemize  @end itemize
   
   @node nk_restriction.restriction,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{nk_restriction.restriction}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.restriction
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9!#(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
   ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
   $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
   x,y $B$K$D$$$F@)8B$r9T$&!#(B
   @end itemize
   
   $B0J2<$O!"%$%G%"%k(B
   @tex
   $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $
   @end tex
   $B$N(B
   @tex $x$ @end tex
   $B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B
   @example
   [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
   -- generic_bfct_and_gr :0.001sec(0.001629sec)
   generic bfct : [[1,1],[s-1,1]]
   S0 : 1
   B_{S0} length : 2
   -- fctr(BF) + base :0.000999sec(0.0005109sec)
   [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]
   [1433]
   @end example
   
   @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
   @subsection @code{nk_restriction.restriction_ideal}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.restriction_ideal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9!#(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
   ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
   $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
   x,y $B$K$D$$$F@)8B$r9T$&!#(B
   @end itemize
   
   $B0J2<$O!"%$%G%"%k(B
   @tex
   $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $
   @end tex
   $B$N(B
   @tex $x$ @end tex
   $B$K$D$$$F$N@)8B%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B
   @example
   [1346] nk_restriction.restriction_ideal([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
   -- generic_bfct_and_gr :0.002sec(0.001652sec)
   generic bfct : [[1,1],[s-1,1]]
   S0 : 1
   B_{S0} length : 2
   -- fctr(BF) + base :0sec(0.000566sec)
   -- restriction_ideal_internal :0.001sec(0.0007441sec)
   [-1]
   [1347]
   @end example
   
   @node nk_restriction.integration,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{nk_restriction.integration}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.integration
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9!#(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
   ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
   $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
   x,y $B$K$D$$$F@QJ,$r9T$&!#(B
   @end itemize
   
   $B0J2<$O!"%$%G%"%k(B
   @tex
   $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $
   @end tex
   $B$N(B
   @tex $t$ @end tex
   $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])
   @example
   [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],
   [dt,dx],[1,0]);
   -- generic_bfct_and_gr :0.001sec(0.001796sec)
   generic bfct : [[1,1],[s,1],[s-1,1]]
   S0 : 1
   B_{S0} length : 2
   -- fctr(BF) + base :0.001sec(0.0006731sec)
   [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]]
   @end example
   
   @node nk_restriction.integration_ideal,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{nk_restriction.integration_ideal}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.integration_ideal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9!#(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
   ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
   $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
   x,y $B$K$D$$$F@QJ,$r9T$&!#(B
   @end itemize
   
   $B0J2<$O!"%$%G%"%k(B
   @tex
   $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $
   @end tex
   $B$N(B
   @tex $t$ @end tex
   $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])
   @example
   [1431]  nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x],
   [dt,dx],[1,0]);
   -- generic_bfct_and_gr :0.002999sec(0.002623sec)
   generic bfct : [[1,1],[s,1],[s-1,1]]
   S0 : 1
   B_{S0} length : 2
   -- fctr(BF) + base :0.001sec(0.001091sec)
   -- integration_ideal_internal :0.002sec(0.001879sec)
   [2*x*dx+1]
   [1432]
   @end example
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item  $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B.
   @end itemize
   
   @node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module),,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{nd_gr}, @code{nd_gr_trace} ($B2C72(B)
   @findex nd_gr (module)
   @findex nd_gr_trace (module)
   @findex nd_weyl_gr (module)
   @findex nd_weyl_gr_trace (module)
   
   @comment --- nd_gr, nd_gr_trace $B$K$*$1$k2C72$N%0%l%V%J!<4pDl7W;;(B ---
   @table @t
   @item  nd_gr(@var{gen},@var{vars},@var{char},@var{ord})
   @itemx  nd_gr_trace(@var{gen},@var{vars},@var{homo},@var{char},@var{ord})
   @item  nd_weyl_gr(@var{gen},@var{vars},@var{char},@var{ord})
   @itemx  nd_weyl_gr_trace(@var{gen},@var{vars},@var{homo},@var{char},@var{ord})
   :: $BItJ,2C72$N%0%l%V%J!<4pDl$N7W;;(B
   @end table
   
   @table @var
   @item gen
   $B%j%9%H$N%j%9%H(B
   @item ord
   @var{[IsPOT,Ord]} $B$J$k%j%9%H(B
   @item return
   $B%j%9%H$N%j%9%H(B
   @end table
   
   @itemize @bullet
   @item $BB?9`<04D$"$k$$$O%o%$%kBe?t>e$N<+M32C72$NItJ,2C72$N%0%l%V%J!<4pDl(B
   $B$r7W;;$9$k(B. $B7k2L$O%j%9%H$N%j%9%H$G$"$k(B. $B3FMWAG%j%9%H$O(B, $B<+M32C72$N(B
   $B85$G$"$k%Y%/%H%k$H$_$J$9(B.
   @item @var{ord} $B$H$7$F(B @var{[IsPOT,Ord]} $B$H$$$&(B2$BMWAG%j%9%H$,;XDj$5$l$?(B
   $B>l9g(B, $B2C72$N%0%l%V%J!<4pDl7W;;$r<B9T$9$k(B. $B$3$N>l9g(B, @var{gen} $B$O(B, $BB?9`<0(B
   $B$N%j%9%H$N%j%9%H$H$7$FM?$($kI,MW$,$"$k(B.
   @item @var{IsPOT} $B$,(B 1 $B$N>l9g(B, POT (position over term), 0 $B$N(B
   $B>l9g(B TOP (term over position) $B$GHf3S$9$k(B. $B4pAC4D$G$N9`Hf3S$O(B @var{Ord}
   $B$G9T$&(B.
   @item $B@bL@$5$l$F$$$J$$0z?t$O(B, $B%$%G%"%k$N>l9g$N2r@b$r;2>H$N$3$H(B.
   @end itemize
   
   @example
   [0] Gen=[[x,y,z],[y^2+x,x^2,z],[y^2,z^3+x,x+z]];
   [[x,y,z],[x+y^2,x^2,z],[y^2,x+z^3,x+z]]
   [1]  nd_gr(Gen,[x,y,z],0,[0,0]);
   [[x,y,z],[y^2,x^2-y,0],[y^2,x+z^3,x+z],[y^3+z^3*y^2,y^3*x-y^3,
   -x^3-z*x^2+(z*y^2+y)*x-z*y^2+z*y],[0,0,x^4+z*x^3+(-z*y^2-y)*x^2
   +(-y^3+z*y^2-z*y)*x+z^4*y^2]]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{nd_gr}, @ref{nd_gr_trace}
   @end table
   
   @node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option),,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{nd_gr}, @code{nd_gr_trace} (option)
   @findex nd_gr (option)
   @findex nd_gr_trace (option)
   @findex nd_weyl_gr (option)
   @findex nd_weyl_gr_trace (option)
   
   @comment --- nd_gr, nd_gr_trace $B$N%*%W%7%g%s(B ---
   
   @table @t
   @item  nd_gr(@var{...}[|@var{opt},@var{opt},@dots{}])
   @itemx  nd_gr_trace(@var{...}[|@var{opt},@var{opt},@dots{}])
   @itemx  nd_weyl_gr(@var{...}[|@var{opt},@var{opt},@dots{}])
   @itemx  nd_weyl_gr_trace(@var{...}[|@var{opt},@var{opt},@dots{}])
   :: $B%0%l%V%J!<4pDl7W;;$K4X$9$k<o!9$N%*%W%7%g%s$N@bL@(B
   @end table
   
   @table @var
   @item opt
   @var{key=value} $B$J$k%*%W%7%g%s@_Dj(B
   @item return
   $B%*%W%7%g%s$K$h$j0[$J$k(B
   @end table
   
   @itemize @bullet
   @item $B%0%l%V%J!<4pDl7W;;$r%*%W%7%g%s$K$h$j@)8f$9$k(B.
   @item $B8=>u$G$O<!$N(B 3 $B$D$N%*%W%7%g%s$r<u$1IU$1$k(B.
   
   @table @var
   @item gentrace
   @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.
   @item gentsyz
   @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.
   @item nora
   @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.
   @end table
   
   @item @var{gentrace} $B$,;XDj$5$l$?>l9g(B, $B=PNO$O(B,
   @var{[GB,Homo,Trace,IntRed,Ind,InputRed,SpairTrace]} $B$J$k%j%9%H$G$"$k(B. $B3FMWAG$N0UL#$O(B
   $B<!$NDL$j$G$"$k(B.
   @table @var
   @item GB
   $B%0%l%V%J!<4pDl(B
   @item Homo
   $BCf4V4pDl$,@F<!2=$5$l$F$$$k>l9g(B 1, $B$=$&$G$J$$>l9g(B 0.
   @item Trace
   $BA4Cf4V4pDl$KBP$9$k7W;;7P2a>pJs(B
   @item IntRed
   $BAj8_4JLs$KBP$9$k7W;;7P2a>pJs(B
   @item Ind
   $B4JLs%0%l%V%J!<4pDl$N3FMWAG$N(B, $BA4Cf4V4pDl$N$K$*$1$k%$%s%G%C%/%9(B
   @item InputRed
   $B3FF~NOB?9`<0$r%0%l%V%J!<4pDl$G4JLs$7$F>jM>(B 0 $B$rF@$k$^$G$N7W;;7P2a>pJs(B
   (@var{gensyz} $B$,;XDj$5$l$?>l9g(B)
   @item SpairTrace
   $B4JLs%0%l%V%J!<4pDl$KBP$9$k(B S $BB?9`<0$r4JLs$7$F>jM>(B 0 $B$rF@$k$^$G$N7W;;7P2a>pJs(B
   (syzygy $B2C72$N@8@.7O$NMWAG$N$_(B; @var{gensyz} $B$,;XDj$5$l$?>l9g(B)
   @end table
   @item $B>\:Y$O(B, $BF~NOB?9`<0=89g$H%0%l%V%J!<4pDl$NAj8_JQ499TNs(B, $B$*$h$S(B syzygy $B7W;;(B
   $B4X?t$N9`$G@bL@$9$kM=Dj(B.
   @end itemize
   
   @example
   [0] C=[c3*c2*c1*c0-1,((c2+c3)*c1+c3*c2)*c0+c3*c2*c1,...]
   [1] D=nd_gr_trace(C,[c0,c1,c2,c3,c4],0,1,0|gentrace=1,gensyz=1)$
   [2] D[0];
   [c0+c1+c2+c3,-c1^2-2*c3*c1-c3^2,...]
   [3] D[2];
   [[[0,0,1],[1,1,1],[2,2,1],[3,3,1]],[4,[[1,2,(1)*<<0,0,0,0>>,1],...]
   [4] D[6];
   [[-1,[[1,0,(1)*<<0,0,2,4>>,1],[1,6,(-1)*<<1,0,0,0>>,1],...]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{nd_gr}, @ref{nd_gr_trace}
   @end table
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.
 @comment ****************************************************************  @comment ****************************************************************
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  Added in v.1.31
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