[BACK]Return to exp-ja.texi CVS log [TXT][DIR] Up to [local] / OpenXM / src / asir-doc / exp

Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.48 and 1.51

version 1.48, 2014/05/29 13:18:18 version 1.51, 2016/05/14 07:55:16
Line 1 
Line 1 
 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.47 2013/02/18 07:18:32 takayama Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.50 2015/08/08 06:28:38 takayama Exp $
 \input texinfo  \input texinfo
 @iftex  @iftex
 @catcode`@#=6  @catcode`@#=6
Line 38 
Line 38 
 @title $B<B83E*;EMM$N4X?t(B  @title $B<B83E*;EMM$N4X?t(B
 @subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B  @subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B
 @subtitle 1.0 $BHG(B  @subtitle 1.0 $BHG(B
 @subtitle 2013 $BG/(B 2 $B7n(B  @subtitle 2014 $BG/(B 12 $B7n(B
   
 @author  by Risa/Asir committers  @author  by Risa/Asir committers
 @page  @page
Line 2777  B_@{S0@} length : 2
Line 2777  B_@{S0@} length : 2
 -- fctr(BF) + base :0.000999sec(0.0005109sec)  -- fctr(BF) + base :0.000999sec(0.0005109sec)
 [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]  [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]
 @end example  @end example
   $BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B,
   $B@)8B2C72$N4pDl(B
   @tex $\partial_x^1, \partial_x^0$ @end tex
   $B$r0UL#$7(B,
   $BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B
   @tex $(y \partial_y - 1, 0), (0, y\partial_y-1), (-1,0)$ @end tex
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
   
 @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B  @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
Line 2886  $t$
Line 2893  $t$
 @ifinfo  @ifinfo
 I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t  I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t
 @end ifinfo  @end ifinfo
 $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])  $B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])
 @example  @example
 [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],  [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],
 [dt,dx],[1,0]);  [dt,dx],[1,0]);
Line 2897  B_@{S0@} length : 2
Line 2904  B_@{S0@} length : 2
 -- fctr(BF) + base :0.001sec(0.0006731sec)  -- 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]]]  [[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  @end example
   $BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B,
   $B@QJ,2C72$N4pDl(B
   @tex $t^1, t^0$ @end tex
   $B$r0UL#$7(B,
   $BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@QJ,2C72$O(B
   @tex $(4 x \partial_x^2 + 6 \partial_x, 0), (0, -4 x \partial_x^2 - 6 \partial_x),
   (0, -2 x \partial_x), (0, 2 \partial_x)$ @end tex
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
 @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B  @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
 @subsection @code{nk_restriction.integration_ideal}  @subsection @code{nk_restriction.integration_ideal}
Line 3317  B_{S0} length : 1
Line 3332  B_{S0} length : 1
 [[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]]  [[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]]
 @end example  @end example
   
   @subsection @code{nk_restriction.module_restriction}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.module_restriction
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.module_restriction(@var{M}, @var{VL}, @var{DVL}, @var{W})
   :: D $B2C72(B @var{M} $B$N=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
   D $B2C72$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(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
   @comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)}
   $B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@)8B$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B,
   @var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B.
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B.
   $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B
   x $B$K$D$$$F@)8B$r9T$&(B.
   @end itemize
   
   $B0J2<$O(B, D $B2C72(B
   @iftex
   @tex
   $M = D \cdot \{(\partial_x, \partial_y), (\partial_y, \partial_x), (x,y) \}$
   @end tex
   $B$N(B
   @tex
   $x$
   @end tex
   @ifinfo
   I = D . @{ (dx, dy), (dy, dx), (x, y) @} $B$N(B x
   @end ifinfo
   $B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B
   @example
   [2691] nk_restriction.module_restriction([[dx,dy],[dy,dx],[x,y]], [x,y], [dx,dy], [1,0]);
   ....
   bfunction :
   s
   [[1,1],[s,1]]
   integer roots :
   [0,0]
   Generators:
   [e1,e2]
   Relations:
   [-8*e2*dy,4*e2*dy^2,-4*e2*dy^3,4*e1*y*dy-4*e1,-4*e1*dy^2,-4*e2,-e2*y*dy^2+2*e2*dy,-e1*y*dy+e1,e1*y*dy-e1]
   [[0,-1],[-dy^2,0],[y*dy-1,0]]
   @end example
   $B@)8B2C72$O(B
   @tex $(0, -1), (-\partial_y^2, 0), (y \partial_y -1 , 0)$ @end tex
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
   @subsection @code{nk_restriction.module_integration}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.module_integration
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.module_integration(@var{M}, @var{VL}, @var{DVL}, @var{W})
   :: D $B2C72(B @var{M} $B$N=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
   D $B2C72$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(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
   @comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)}
   $B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@QJ,$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B,
   @var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B.
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B.
   $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B
   x $B$K$D$$$F@QJ,$r9T$&(B.
   @end itemize
   
   $B0J2<$O(B, D $B2C72(B
   @iftex
   @tex
   $M = D \cdot \{(x, y), (y, x), (\partial_x, \partial_y) \}$
   @end tex
   $B$N(B
   @tex
   $x$
   @end tex
   @ifinfo
   I = D . @{ (x, y), (y, x), (dx, dy) @} $B$N(B x
   @end ifinfo
   $B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k!#(B
   @example
   [2702] nk_restriction.module_integration([[x,y],[y,x],[dx,dy]], [x,y], [dx,dy], [1,0]);
   ...
   bfunction :
   s
   [[1,1],[s,1]]
   integer roots :
   [0,0]
   Generators:
   [e1,e2]
   Relations:
   [-8*e2*y,-4*e2*y^2,-4*e2*y^3,-4*e1*y*dy-8*e1,-4*e1*y^2,-4*e2,-e2*y^2*dy-4*e2*y,e1*y*dy+2*e1,e1*y*dy+2*e1]
   [[0,-1],[y*dy+2,0],[-y^2,0]]
   @end example
   $B@QJ,2C72$O(B
   @tex $(0, -1), (y \partial_y + 2, 0), (-y^2, 0)$ @end tex
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
 @noindent  @noindent
 ChangeLog  ChangeLog
 @itemize @bullet  @itemize @bullet
Line 3326  ChangeLog
Line 3470  ChangeLog
 @item 2010-05 $B$+$i(B 2010-07 $B$K$+$1$F(B 2 $B$D$N(B option (@code{ht}, @code{ord}) $B$H(B  @item 2010-05 $B$+$i(B 2010-07 $B$K$+$1$F(B 2 $B$D$N(B option (@code{ht}, @code{ord}) $B$H(B
 $B?7$?$J4X?t(B trans_inhomo() $B$,DI2C$5$l$?(B. 1.10--1.13 $B$r8+$h(B.  $B?7$?$J4X?t(B trans_inhomo() $B$,DI2C$5$l$?(B. 1.10--1.13 $B$r8+$h(B.
 @item 2011-08 $B$K(B ost_sum() $B$,DI2C$5$l$?(B. 1.20 $B$r8+$h(B.  @item 2011-08 $B$K(B ost_sum() $B$,DI2C$5$l$?(B. 1.20 $B$r8+$h(B.
   @item 2016-05 $B$K(B module_integration(), module_restriction() $B$,DI2C$5$l$?(B.
 @end itemize  @end itemize
   
 @node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B  @node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B
Line 3680  holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7
Line 3825  holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7
 @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.  @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.
 @end itemize  @end itemize
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  template  @node ot_hgm_ahg.cbase,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.cbase}
   @findex ot_hgm_ahg.cbase
   
   @table @t
   @item cbase(@var{A})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(B Pfaffian $B$N4pDl$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   Pfaffian$B$N4pDl(B($BHyJ,:nMQAG$N%b%N%_%"%k(B)$B$N%j%9%H(B
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item A-$BD64v2?%$%G%"%k$N(B Q(x)[dx] $B$K$*$1$kI8=`4pDl$O(B Pfaffian $B$N4pDl$H$J$k$,(B, $B5U$O$+$J$i$:$7$b??$G$O$J$$(B.  $B8D?t$O$b$A$m$sF1$8$G$"$k(B.
   @item
   $B%"%k%4%j%:%`$O(B
   T.Hibi, K.Nishiyama, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103
   $B$K$h$k(B.
   $B$5$i$K%Q%i%a!<%?(B b $B$r?t$KFC<l2=$9$k3NN(;;K!$rMQ$$$F$$$k(B.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] ot_hgm_ahg.cbase([[1,1,1,1],[0,1,2,3]]);
   We use a probabilistic algorithm to determine the base.[dx2^2,dx3*dx2,dx3^2]
   
   [dx3,dx4,1]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{get_mat2}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2012  $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B.
   @item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog  ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B.
   @end itemize
   
   @node ot_hgm_ahg.get_mat2,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.get_mat2}
   @findex ot_hgm_ahg.get_mat2
   @comment get_mat2
   @table @t
   @item get_mat2(@var{A},@var{W},@var{Std},@var{Mset})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O(B H_A $B$N(B Pfaffian $B$N4pDl$r5a$a$k$?$a$N(B Sylvester $BK!(B $B$rE,MQ$9$k$?$a$N9TNs$r@8@.$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item W
   $B%j%9%H(B. toric ideal $B$N%0%l%V%J!<4pDl$r7W;;$9$k$?$a$N(B weight vector.
   $BB?J,$J$s$G$b$$$$$O$:(B.
   @item Std
   $B%j%9%H(B. Pfaffian $B$N4pDl(B.  cbase(A) $B$N=PNO$rMQ$$$k(B.
   @item Mset
   Sylvester $B7?9TNs$r:n$k$?$a$NHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item $B=PNO$r(B @var{P} $B$KBeF~$9$k$H(B,
   @var{P}[0]*@var{P}[2] - @var{P}[1]*@var{Std} $B$,(B modulo  H_A $B$G(B 0 $B$H$J$k(B.
   @var{P}[0] $B$H(B @var{P}[2] $B$r7k9g$7$?9TNs$,(B, sylvester $B9TNs(B ($BO@J8$N5-9f$G$N(B F').
   @var{P}[2], @var{Std} $B$,(B index $B%b%N%_%"%k$G$"$k(B.
   $BO@J8$G$N5-9f$G$O(B @var{P}[2] $B$O(B M_t,  @var{Std} $B$O(B S.
   @item
   $B%"%k%4%j%:%`$O(B
   K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method
   $B$K$h$k(B.  $BO@J8$N9TNs(B F'.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] A=[[1,1,1,1],[0,1,2,3]]$
   Std=ot_hgm_ahg.cbase(A)$
   W=[[dx1,1,dx2,1,dx3,1,dx4,1]]$
   Mset=[1,dx1,dx2,dx3,dx4]$
   [2192] ot_hgm_ahg.get_mat2(A,W,Std,Mset);
   
   $B>JN,(B
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{cbase}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2012  $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B.
   @item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog  ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B.
   @item
   $B%=!<%9(B ot_hgm_ahg.rr $B$N(B test3(), test3b(), test4(), test5(), test6(), test6c() $BEy$KMxMQNc$,$"$k(B.
   @item
   test3b() $B$G(B @var{Mset} $B$r0l<!<0A4It$K$7$?$b$N$,(B, $BO@J8$NNc(B.
   @end itemize
   
   @comment -------------------
   @comment  hgm_ahg_contiguity
   @comment -------------------
   @node ot_hgm_ahg.hgm_ahg_contiguity,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.hgm_ahg_contiguity}
   @findex ot_hgm_ahg.hgm_ahg_contiguity
   
   @table @t
   @item hgm_ahg_contiguity(@var{A},@var{StdMon},@var{Line},@var{X0},@var{InitVal},@var{Start},@var{End})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(Bcontiguity relation
   $B$r(B Sylvester matrix $B$rMQ$$$F7W;;$7(B, $B$=$l$rMQ$$$FD64v2?4X?t$NCM$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   $B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$NCM(B F(End;X0) ??
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B.
   @item StdMon
   $B%j%9%H(B.  Pfaffian $B$N4pDl$rM?$($kHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B.
   @item Line
   $B%j%9%H(B  [ContiDir,Beta,Z].
   @item X0
   $B%j%9%H(B. x $BJQ?t$NCM(B.
   @item InitVal
   $B%j%9%H(B. $B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$N=i4|CM(B F(Start;X0)
   @item Start
   $B%j%9%H(B.   Z $B%Q%i%a!<%?$N=i4|CM(B??
   @item End
   $B%j%9%H(B.   Z $B%Q%i%a!<%?$N=*C<CM(B??
   @end table
   
   @itemize @bullet
   @item Todo, $B$3$N4X?t$N%$%s%?%U%'!<%9$OJQ99$5$l$kM=Dj(B.
   @item  X0 $B$OM-M}?t$N%j%9%H(B.
   @item ContiDir $B$O(B End-Start $B$HF1$8J}8~(B.
   @item Beta.  A$BD64v2?4X?t$N(B B $B%Q%i%a!<%?$N=i4|CM(B ??
   @item Z.  ContiDir $B$G$N0l<!85(B contiguity $B$rI=8=$9$k$?$a$NITDj85$NL>A0(B.
   @item $B%=!<%9Cf$NMxMQNc(B. test_fd_conti(), test_c111_conti()
   @item
   $B%"%k%4%j%:%`$*$h$SMxE@$O(B
   K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method
   $B;2>H(B.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] ot_hgm_ahg.test_fd_conti();
   (Todo, $B0z?t$,$I$&$J$k$+$NNc$r2C$($k(B.)
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{get_mat2}
   @ref{hgm_ahg_expected_value_contiguity}
   @ref{hgm_ahg}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2014-07-11 $B$K:G=i$NHG$,(B 1.10$BHG(B ot_hgm_ahg.rr $B$K(B commit $B$5$l$?(B.
   @item $B%$%s%?%U%'!<%9$,99?7$5$l$?HG$O(B, 1.??$BHG(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_hgpoly.optip
   @comment -------------------
   @node tk_hgpoly.optip,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_hgpoly.optip}
   @findex tk_hgpoly.optip
   
   @table @t
   @item hgpoly.optip(@var{A},@var{B},@var{W})
   ::  $B@0?t7W2hLdBj$r%0%l%V%J!<4pDl$rMQ$$$F2r$/(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $BHsIi@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item B
   $BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B
   @item W
   $BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item  @var{A} U = @var{B} $B$rK~$?$9HsIi$N@0?t%Y%/%H%k(B U $B$NCf$G(B,
   $BFb@Q(B @var{W} U $B$r:G>.2=$9$k(B U $B$rLa$9(B.
   @end itemize
   
   @example
   [0] import("tk_hgpoly.rr");
   [2191] tk_hgpoly.optip([[1,1,1,1],[0,1,2,3]],[20,40],[1,1,1,0]);
   [6,1,0,13]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{feasible}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-12 $B$K(B commit $B$5$l$?(B.
   $B85HG$O(B h-mle/A-hg/Prog
   @end itemize
   
   @comment -------------------
   @comment  tk_hgpoly.hgpoly
   @comment -------------------
   @node tk_hgpoly.hgpoly,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_hgpoly.hgpoly}
   @findex tk_hgpoly.hgpoly
   @table @t
   @item hgpoly.hgpoly(@var{A},@var{B})
   ::  @var{A}, @var{B} $B$GDj5A$5$l$kD64v2?B?9`<0$r7W;;$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $BHsIi@0?t(B(todo, $B:FEY3NG'(B)$B$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item B
   $BHsIi@0?t$r@.J,$H$9$k%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item  $BLa$jCM$r(B F $B$H$9$k$H$-(B, F[0] $B$,D64v2?B?9`<0(B. $BJQ?t$O(B x_1, x_2, ...
   F[1] $B$O(B F[0] $B$NJ,;6I=8=B?9`<0(B.
   @end itemize
   
   @example
   [0] import("tk_hgpoly.rr");
   [2191] tk_hgpoly.hgpoly([[1,1,1,1],[0,1,2,3]],[2,2]);
   [x_3*x_1+1/2*x_2^2,(1/2)*<<0,2,0,0>>+(1)*<<1,0,1,0>>]
   @end example
   
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-12 $B$K(B commit $B$5$l$?(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_fd.abc2ahg
   @comment -------------------
   @node tk_fd.abc2ahg,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_fd.abc2ahg}
   @findex tk_fd.abc2ahg
   @table @t
   @item tk_fd.abc2ahg(@var{A},@var{B},@var{C})
   ::  F_D(@var{A}, @var{B},@var{C}) $B$r2r$K$b$D(B A-$BD64v2?J}Dx<07O$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $B?t(B
   @item B
   $B?t$N%j%9%H(B
   @item C
   $B?t(B
   @end table
   
   @itemize @bullet
   @item $BLa$jCM%j%9%H$NBh#0@.J,$O(B A-$BD64v2?J}Dx<07O$rDj5A$9$k9TNs(B.
   $BBh#1@.J,$O(BA-$BD64v2?J}Dx<07O$N%Q%i%a!<%?&B(B.
   @end itemize
   
   @example
   [2191] tk_fd.abc2ahg(-3,[-4,-5],3);
   
   [[[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],[11,5,4,5]]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{abc2marginal}
   @ref{marginal2abc}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-13 $B$K(B tk_fd.rr $B$KDI2C$5$l$?(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_fd.ahvec_abc
   @comment -------------------
   @node tk_fd.ahvec_abc,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_fd.ahvec_abc}
   @findex tk_fd.ahvec_abc
   @table @t
   @item tk_fd.ahvec_abc(@var{A},@var{B},@var{C},@var{Y} | all=1)
   ::   abc2marginal(@var{A}, @var{B},@var{C})  $B$r<~JUOB$K$b$D(B (2,m+1) $BJ,3dI=A4BN$K$D$$$F$N@55,2=Dj?t(B Z, $B$*$h$S(B Z $B$NJQ?t(B Y[1][0], ..., Y[1][m]
   (2$BHVL\$N9T(B)$B$K$D$$$F$NJPHyJ,$r7W;;$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B @var{Ans}
   @item A
   $B?t(B
   @item B
   $B?t$N%j%9%H(B. $BD9$5$O(B m.
   @item C
   $B?t(B
   @item Y
   (2,m+1) $BJQ?tCM$r$"$i$o$9%j%9%H$N%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item
   @var{A}, @var{B}, @var{C}, $B$K8=$l$k?t$O@0?t$rM?$($k(B.
   @var{Y} $B$N@.J,$OM-M}?t$rM?$($k(B.
   @item
   @var{Ans}[2]*@var{Ans}[1] $B$,(B Z.
   @var{Ans}[2]*@var{Ans}[0][I] $B$,(B Z $B$N(B Y[1][I] $B$K$D$$$F$NJPHyJ,(B.
   @item
   $BO@J8(B
   1.Y.Goto, Contiguity relations of Lauricella's F_D revisited,  arxiv:1412.3256
   $B$GF3=P$5$l$F$$$k(B
   contiguity relation $B$rMQ$$$F7W;;$9$k(B.
   @end itemize
   
   @example
   [2449] marginal2abc([3,12],[6,3,3,3]);
   [-3,[-3,-3,-3],4]
   
   [2450] tk_fd.ahvec_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]);
   [[ 24041/1152 143551/11520 16973/1280 78827/5760 ],1/7776]
   
   [2451] expectation_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]);
   [721230/173593,430653/173593,458271/173593,67566/24799]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{expectation_abc}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-$B2F$K3+H/$5$l$?(B.
   @end itemize
   
   
   @node pari,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{pari}, @code{setbprec},@code{setround},@code{todouble},@code{mpfr_gamma},@code{mpfr_floor},@code{mpfr_round},
   @findex pari
   @findex setbprec
   @findex setround
   @findex todouble
   @findex mpfr_gamma
   @findex mpfr_floor
   @findex mpfr_round
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item pari(@var{arg1},@var{arg2},...)
   ::  MPFR $B$G(B pari $B$N4X?t$r(B emulate $B$9$k$+(B ox_pari $B%5!<%P!<$r8F$S=P$9(B.
   @itemx setbprec(@var{arg1})
   @itemx setround(@var{arg1})
      $B4]$a$NJ}K!$N;XDj(B. mpfr $B=`5r(B.
   @itemx todouble(@var{arg1})
   :: bigfloat $B7?$r(B double $B$KJQ49$9$k(B.
   @itemx mpfr_gamma(@var{arg1})
   :: gamma $B4X?t$N7W;;(B.
   @itemx mpfr_floor(@var{arg1})
   ::  floor $B$N7W;;(B.
   @itemx mpfr_round(@var{arg1})
   :: $B4]$a$N7W;;(B.
   @end table
   
   @table @var
   @item return
   $B8e=R(B.
   @item arg1, arg2
   $B8e=R(B.
   @end table
   
   @itemize @bullet
   @item 20150807 $B0J9_$N(B asir $B$G$O(B, bigfloat $B$,(B pari $B$G$O$J$/(B mpfr $B$rMQ$$$F7W;;$5$l$k(B.
   Todo, pari $B$O(B ox_pari $B$r8F$S=P$9$,(B, $B$^$@(B ox_pari $B$KL$<BAu$N5!G=$,B?$/$"$k(B.
   $B6h4V1i;;$X$NBP1~$O9T$C$F$$$J$$(B.
   @item
   pari(floor,@var{arg1}),
   pari(round,@var{arg1}),
   pari(gamma,@var{arg1})
   $B$O(B mpfr $B$G(B pari $B$r(B emulate $B$7$F$$$k$N$G(B, $BF0:n$,0[$J$k(B.
   $BFC$K(B gamma $B$OJ#AG?t$N0z?t$r<u$1<h$i$J$$(B.
   pari $B$N(B floor $B$O7e?t$,B-$j$J$/$J$k$H%(%i!<$G=*N;$7$?$,(B,
   $B$3$N(B floor $B$G$O(B setprec $B$G;XDj$7$?7e?t0JFb$J$i@5$7$/(B floor $B$rLa$9(B.
   Todo, ox_pari  $B$r;XDj$7$F8F$S=P$9J}K!(B.
   @end itemize
   
   @example
   [219] ctrl("bigfloat",1)$
   [220] setprec(100)$
   [221] pari(floor,1111111111111.1+1/10);
   1111111111111
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{pari}
   @end table
   
   @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
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$l$i$NBgJQ99$O(B 2015-08-03 $B$h$j(B 08-07 $B$N(B asir $B9g=I$G$*$3$J$o$l$?(B.
   $B$^$@:n6HCf(B.  Todo, asirgui $B$X$NBP1~(B. debug, ...
   @item $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B asir2000/builtin/bfaux.c,
   asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB??t(B.
   @end itemize
   
 @comment ****************************************************************  @comment ****************************************************************
 @comment --- $B"~"~"~"~(B  $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B  @comment --- $B"~"~"~"~(B  $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B
 @comment $B?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.  @comment $B?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.
Legend:
Removed from v.1.48  
changed lines
  Added in v.1.51
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>