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Diff for /OpenXM/src/k097/Doc/complex.texi between version 1.2 and 1.5

version 1.2, 2001/01/05 11:14:26 version 1.5, 2001/05/27 12:48:02
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 %% $OpenXM: OpenXM/src/k097/Doc/complex.texi,v 1.1 2001/01/04 12:29:32 takayama Exp $  %% $OpenXM: OpenXM/src/k097/Doc/complex.texi,v 1.4 2001/01/13 01:17:36 takayama Exp $
 /*&C  
 \input texinfo  
 @iftex  
 @catcode`@#=6  
 @def@b#1{{@bf@gt #1}}  
 @catcode`@#=@other  
 @end iftex  
 @overfullrule=0pt  
 @c -*-texinfo-*-  
 @comment %**start of header  
 @setfilename complex  
 @settitle complex  
 @comment %**end of header  
 @comment %@setchapternewpage odd  
   
 @iftex  
 @comment @finalout  
 @end iftex  
   
 @titlepage  
   
 */  
   
 //&C @title  Kan/k0   complex  
 //&ja @subtitle Kan/k0 complex $B%Q%C%1!<%8(B User's Manual ($BF|K\8lHG(B)  
 //&en @subtitle Kan/k0 complex Package User's Manual  
 /*&C  
 @subtitle Edition 1.1.3 for OpenXM/kan/k0  
 @subtitle December 31, 2000  
   
 @author  by Nobuki Takayama  
 @end titlepage  
   
 @synindex vr fn  
   
 @comment  node-name,  next,  previous,  up  
 @node Top,, (dir), (dir)  
   
 */  
   
 /*&ja  /*&ja
   
 @menu  
 * COMPLEX $BH!?t(B::  
 * $B4pK\(B $BH!?t(B::  
 * $B:w0z(B::  
 @end menu  
   
 */  
 /*&en  
   
 @menu  
 * COMPLEX function::  
 * Primitive function::  
 * index::  
 @end menu  
   
 */  
 /*&ja  
   
 @node COMPLEX $BH!?t(B,,, Top  @node COMPLEX $BH!?t(B,,, Top
 @chapter COMPLEX $BH!?t(B  @chapter COMPLEX $BH!?t(B
 @section $BH!?t0lMw(B  @section $BH!?t0lMw(B
Line 92 
Line 35 
 @findex Res_solv  @findex Res_solv
 @table @t  @table @t
 @item Res_solv(@var{m},@var{d})  @item Res_solv(@var{m},@var{d})
 ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B.  ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B.
 @item Res_solv(@var{m},@var{d},@var{r})  @item Res_solv(@var{m},@var{d},@var{r})
 ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B. @var{r} $B$O(B ring.  ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B. @var{r} $B$O(B ring.
 @end table  @end table
Line 218  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
Line 161  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{Res_solv_h}, @code{Kernel},  @code{GetRing}, @code{SetRing}.      @code{Res_solv_h}, @code{Kernel},  @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
     @code{Res_solv_h}, @code{Kernel},  @code{GetRing}, @code{SetRing}.      @code{Res_solv_h}, @code{Kernel},  @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 240  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
Line 187  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
 @findex Res_solv2  @findex Res_solv2
 @table @t  @table @t
 @item Res_solv2(@var{m},@var{v},@var{j})  @item Res_solv2(@var{m},@var{v},@var{j})
 ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.  ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.
 @item Res_solv2(@var{m},@var{v},@var{j},@var{r})  @item Res_solv2(@var{m},@var{v},@var{j},@var{r})
 ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.  ::  $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.
 @var{r} $B$O(B ring.  @var{r} $B$O(B ring.
Line 258  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
Line 205  In(5)= Res_solv([[1,2],[3,4]],[5,0],r):
 @table @t  @table @t
 @item Res_solv2(@var{m},@var{v},@var{j})  @item Res_solv2(@var{m},@var{v},@var{j})
 ::  Find a solution u of the linear indefinite equation u @var{m} =@var{v}  ::  Find a solution u of the linear indefinite equation u @var{m} =@var{v}
     mod @var{j}.      mod @var{j}.
 @item Res_solv2(@var{m},@var{v},@var{j},@var{r})  @item Res_solv2(@var{m},@var{v},@var{j},@var{r})
 ::  Find a solution u of the linear indefinite equation u @var{m} =@var{v}  ::  Find a solution u of the linear indefinite equation u @var{m} =@var{v}
 mod @var{j}.  mod @var{j}.
Line 363  The output implies that
Line 310  The output implies that
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{Res_solv2_h}, @code{Kernel2},  @code{GetRing}, @code{SetRing}.      @code{Res_solv2_h}, @code{Kernel2},  @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
     @code{Res_solv2_h}, @code{Kernel2},  @code{GetRing}, @code{SetRing}.      @code{Res_solv2_h}, @code{Kernel2},  @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 502  In(5)= k=Kernel([[1,2],[2,4]],r); k[0]:
Line 453  In(5)= k=Kernel([[1,2],[2,4]],r); k[0]:
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{Kernel_h}, @code{Res_solv}, @code{GetRing}, @code{SetRing}.      @code{Kernel_h}, @code{Res_solv}, @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
     @code{Kernel_h}, @code{Res_solv},  @code{GetRing}, @code{SetRing}.      @code{Kernel_h}, @code{Res_solv},  @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 614  In(43)=Kernel2([[0,0,0],[0,0,0]],[],r):
Line 569  In(43)=Kernel2([[0,0,0],[0,0,0]],[],r):
 @item $B;2>H(B  @item $B;2>H(B
     @code{Kernel2_h}, @code{Res_solv2}, @code{GetRing}, @code{SetRing},      @code{Kernel2_h}, @code{Res_solv2}, @code{GetRing}, @code{SetRing},
     @code{Kernel}.      @code{Kernel}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
     @code{Kernel2_h}, @code{Res_solv2},  @code{GetRing}, @code{SetRing},      @code{Kernel2_h}, @code{Res_solv2},  @code{GetRing}, @code{SetRing},
     @code{Kernel}      @code{Kernel}
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 743  In(13)= Gb(m,r):
Line 702  In(13)= Gb(m,r):
 @item $B;2>H(B  @item $B;2>H(B
     @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD},      @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD},
     @code{GetRing}, @code{SetRing}.      @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
     @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD},      @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD},
     @code{GetRing}, @code{SetRing}.      @code{GetRing}, @code{SetRing}.
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 865  In(19)=Pmat(Substitute(k2[0],t,1));
Line 828  In(19)=Pmat(Substitute(k2[0],t,1));
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{Gb}, (m,(u,v))-$B%0%l%V%J4pDl(B      @code{Gb}, (m,(u,v))-$B%0%l%V%J4pDl(B
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
    @code{Gb}, (m,(u,v))-Grobner basis     @code{Gb}, (m,(u,v))-Grobner basis
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 895  In(19)=Pmat(Substitute(k2[0],t,1));
Line 862  In(19)=Pmat(Substitute(k2[0],t,1));
 /*&C  /*&C
 @menu  @menu
 * ChangeRing::  * ChangeRing::
 * GetRing::  
 * SetRing::  
 * Intersection::  * Intersection::
 * Getxvars::  * Getxvars::
 * Firstn::  * Firstn::
Line 925  true $B$+(B false
Line 890  true $B$+(B false
    RingD("p,q,r");     RingD("p,q,r");
    ChangeRing(f);     ChangeRing(f);
 @end example  @end example
 @c  %%%%%%%%%%%%%%%%%%%%  end of ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 */  
   
 /*&ja  
 @c %%%%%%%%%%%%%%%%%%%%  start of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 @menu  
 * GetRing::  
 @end menu  
 @node GetRing,,, $B4pK\(B $BH!?t(B  
 @subsection @code{GetRing}  
 @findex GetRing  
 @table @t  @table @t
 @item GetRing(@var{f})  @item Files
 ::  @var{f} $B$NMWAG$NB0$9$k4D$rLa$9(B.      @code{lib/restriction/complex.k}
 @end table  @end table
   @c  %%%%%%%%%%%%%%%%%%%%  end of ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 @table @var  
 @item return  
 $B4D(B  
 @item f  
 $B%*%V%8%'%/%H(B  
 @end table  
   
 @itemize @bullet  
 @item  @var{f} $B$NMWAG$^$?$O(B @var{f} $B<+?H$NB0$9$k4D$rLa$9(B.  
 $B4D$,$J$$$H$-$O(B null $B$rLa$9(B.  
 @end itemize  
   
 @example  
 In(16)= RingD("x,y");  
 In(17)= r = GetRing([x^2,0,1]);  
 @end example  
   
 @table @t  
 @item $B;2>H(B  
     @code{SetRing},   @code{ChangeRing}.  
 @end table  
 @c  %%%%%%%%%%%%%%%%%%%%  end of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 */  */
   
 /*&ja  
 @c %%%%%%%%%%%%%%%%%%%%  start of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 @menu  
 * SetRing::  
 @end menu  
 @node SetRing,,, $B4pK\(B $BH!?t(B  
 @subsection @code{SetRing}  
 @findex SetRing  
 @table @t  
 @item SetRing(@var{r})  
 ::  Current ring $B$r(B @var{r} $B$KJQ99$9$k(B.  
 @end table  
   
 @table @var  
 @item return  
 $B$J$7(B  
 @item r  
 $B4D(B  
 @end table  
   
 @itemize @bullet  
 @item  Current ring $B$r(B @var{r} $B$KJQ99$9$k(B.  
 @end itemize  
   
 @example  
 In(16)= RingD("x,y");  
 In(17)= f=[x^2,0,1]; r = GetRing(f);  
 In(19)= RingD("p,q");  
 In(20)= SetRing(r);  
 In(21)= f = DC(f,"polynomial");  
 @end example  
   
 @table @t  
 @item $B;2>H(B  
     @code{GetRing},   @code{ChangeRing}, @code{DC}.  
 @end table  
 @c  %%%%%%%%%%%%%%%%%%%%  end of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 */  
   
 /*&ja  /*&ja
 @c %%%%%%%%%%%%%%%%%%%%  start of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c %%%%%%%%%%%%%%%%%%%%  start of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 @menu  @menu
Line 1043  In(33)=Intersection(mm,nn):
Line 938  In(33)=Intersection(mm,nn):
   
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 1108  In(5)=Getxvars():
Line 1004  In(5)=Getxvars():
   
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
Line 1197  In(17)= Firstn(mm,2):
Line 1095  In(17)= Firstn(mm,2):
   
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
   @item Files
       @code{lib/restriction/complex.k}
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  /*&en
   
 @table @t  @table @t
 @item Reference  @item See also
   @item Files
       @code{lib/restriction/complex.k}
   
   
 @end table  @end table
 @c  %%%%%%%%%%%%%%%%%%%%  end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  @c  %%%%%%%%%%%%%%%%%%%%  end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
   
 /*&ja  /*&ja
 @node $B:w0z(B,,, Top  @c %%%%%%%%%%%%%%%%%%%%  start of GKZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 @unnumbered $B:w0z(B  @menu
   * GKZ::
   @end menu
   @node GKZ,,, $B4pK\(B $BH!?t(B
   @subsection @code{GKZ}
   @findex GKZ
   @table @t
   @item GKZ(@var{a},@var{b})
   ::  $B9TNs(B @var{a} $B$H(B $B%Y%/%H%k(B @var{b} $B$GDj$^$k(B, GKZ hypergeometric system $B$rLa$9(B.
   @end table
   
   @table @var
   @item return
   D $B$N%$%G%"%k$N@8@.85(B
   @item a
   $B@0?t9TNs(B
   @item b
   $B@0?t%Y%/%H%k(B
   @end table
   
   @itemize @bullet
   @item   $B9TNs(B @var{a} $B$H(B $B%Y%/%H%k(B @var{b} $B$GDj$^$k(B, GKZ hypergeometric system $B$rLa$9(B.
   @item Gelfand, Kapranov, Zelevinski $B$ND64v2?HyJ,J}Dx<0$rLa$9(B.
   @end itemize
   
   @example
   In(3)= GKZ([[1,1,1,1],[0,1,2,3]],[-1,-2]):
   [    x1*Dx1+x2*Dx2+x3*Dx3+x4*Dx4+1 , x2*Dx2+2*x3*Dx3+3*x4*Dx4+2 , Dx2^2-Dx1*Dx3 , -Dx3^2+Dx2*Dx4 , Dx2*Dx3-Dx1*Dx4 ]
   @end example
   
   @table @t
   @item $B;2>H(B
   @item Files
       @code{lib/restriction/demo2.k}
   @end table
   @c  %%%%%%%%%%%%%%%%%%%%  end of GKZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&en  
 @node index,,, Top  /*&ja
 @unnumbered index  @c %%%%%%%%%%%%%%%%%%%%  start of Slope %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   @menu
   * Slope::
   @end menu
   @node Slope,,, $B4pK\(B $BH!?t(B
   @subsection @code{Slope}
   @findex Slope
   @table @t
   @item Slope(@var{i},@var{v},@var{f},@var{v})
   ::  $BHyJ,J}Dx<07O(B @var{i} $B$N(B slope $B$N=89g$r$b$H$a$k(B.
   @end table
   
   @table @var
   @item return
   Slope $B$N=89g$H$=$l$rM?$($k(B, weight vectors.
   @item i
   D $B$N%$%G%"%k$N@8@.85(B
   @item v
   $B6u4VJQ?t(B
   @item f
   F-filtration $B$rM?$($k(B weight vector (0,...,0,1,...,1).
   @item v
   V-filtration $B$rM?$($k(B weight vector.
   $B$?$H$($P(B (0,...,0,-1,0,...,0,1).
   @end table
   
   @itemize @bullet
   @item @var{i} $B$N(B x_i = 0 $B$K$=$C$?(B, $B86E@$G$N(B slope $B$NA4BN$r$b$H$a$k(B.
   @item $B7W;;$K$O(B Assi, Castro, Granger $B$N%"%k%4%j%:%`$rMQ$$$k(B.
   @item Geometric slope $B$r7W;;$9$k$?$a(B, radical $B$N7W;;$r$*$3$J$C$F$$$k(B.
   $B$3$l$K$O(B ox_asir $B$rMQ$$$F$$$k(B.
   @end itemize
   
   @example
   In(13)= a=GKZ([[1,3,7]],[-30]);
   In(14)= a:
   [    x1*Dx1+3*x2*Dx2+7*x3*Dx3+30 , -Dx1^3+Dx2 , -Dx1*Dx2^2+Dx3 , -Dx2^3+Dx1^2*Dx3 ]
   In(15)= Slope(a,[x1,x2,x3],[0,0,0,1,1,1],[0,0,-1,0,0,1]):
   [    [    (3)/(4) , [    0 , 0 , -4 , 3 , 3 , 7 ]  ]  ]
   
   
   @end example
   
   @table @t
   @item $B;2>H(B
   @item Files
       @code{lib/restriction/demo2.k}
   @end table
   @c  %%%%%%%%%%%%%%%%%%%%  end of Slope %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 */  */
 /*&C  
 @printindex fn  
 @printindex cp  
 @iftex  
 @vfill @eject  
 @end iftex  
 @summarycontents  
 @contents  
 @bye  
 */  

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