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Diff for /OpenXM/src/k097/Doc/complex.texi between version 1.2 and 1.3

version 1.2, 2001/01/05 11:14:26 version 1.3, 2001/01/08 05:26:50
Line 1 
Line 1 
 %% $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 1.2 2001/01/05 11:14:26 takayama Exp $
 /*&C  /*&C
 \input texinfo  \input texinfo
 @iftex  @iftex
Line 92 
Line 92 
 @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 218  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 244  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 262  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 367  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 510  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 626  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 759  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 885  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 919  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 947  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 995  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 1061  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 1152  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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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