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Diff for /OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave between version 1.2 and 1.5

version 1.2, 2001/07/11 06:23:16 version 1.5, 2002/08/11 08:39:47
Line 1 
Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.1 2001/07/11 01:00:23 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.4 2002/07/14 13:14:37 takayama Exp $ */
   
 /*&C-texi  /*&C-texi
 @c DO NOT EDIT THIS FILE   oxphc.texi  @c DO NOT EDIT THIS FILE   oxphc.texi
Line 69  cohomology groups.
Line 69  cohomology groups.
 /*&C-texi  /*&C-texi
 @example  @example
   
 This is Risa/Asir, Version 20000126.  @include opening.texi
 Copyright (C) FUJITSU LABORATORIES LIMITED.  
 1994-1999. All rights reserved.  
 xm version 20000202. Copyright (C) OpenXM Developing Team. 2000.  
 ox_help(0); ox_help("keyword"); ox_grep("keyword"); for help message  
 Loading ~/.asirrc  
   
 [283] sm1_deRham([x*(x-1),[x]]);  [283] sm1_deRham([x*(x-1),[x]]);
 [1,2]  [1,2]
Line 407  def sm1(P,F) {
Line 402  def sm1(P,F) {
 /*&jp-texi  /*&jp-texi
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}.      @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}.
 @end table  @end table
 */  */
 /*&eg-texi  /*&eg-texi
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}.      @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}.
 @end table  @end table
 */  */
   
Line 768  def sm1_isListOfVar(A) {
Line 763  def sm1_isListOfVar(A) {
 @findex sm1_gb  @findex sm1_gb
 @findex sm1_gb_d  @findex sm1_gb_d
 @table @t  @table @t
 @item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q})  @item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r})
 ::  computes the Grobner basis of @var{f} in the ring of differential  ::  computes the Grobner basis of @var{f} in the ring of differential
 operators with the variable @var{v}.  operators with the variable @var{v}.
 @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})  @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})
Line 780  The result will be returned as a list of distributed p
Line 775  The result will be returned as a list of distributed p
 @table @var  @table @var
 @item return  @item return
 List  List
 @item p, q  @item p, q, r
 Number  Number
 @item f, v, w  @item f, v, w
 List  List
Line 814  List
Line 809  List
    the Grobner basis and the initial ideal     the Grobner basis and the initial ideal
    with sums of monomials sorted by the given order.     with sums of monomials sorted by the given order.
    Each polynomial is expressed as a string temporally for now.     Each polynomial is expressed as a string temporally for now.
      When the optional variable @var{r} is set to one,
      the polynomials are dehomogenized (,i.e., h is set to 1).
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&jp-texi
Line 827  List
Line 824  List
 @findex sm1_gb  @findex sm1_gb
 @findex sm1_gb_d  @findex sm1_gb_d
 @table @t  @table @t
 @item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q})  @item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r})
 ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B.  ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B.
 @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})  @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})
 ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B. $B7k2L$rJ,;6B?9`<0$N%j%9%H$GLa$9(B.  ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B. $B7k2L$rJ,;6B?9`<0$N%j%9%H$GLa$9(B.
Line 836  List
Line 833  List
 @table @var  @table @var
 @item return  @item return
 $B%j%9%H(B  $B%j%9%H(B
 @item p, q  @item p, q, r
 $B?t(B  $B?t(B
 @item f, v, w  @item f, v, w
 $B%j%9%H(B  $B%j%9%H(B
Line 866  List
Line 863  List
     3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(B      3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(B
     $BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B.      $BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B.
     $B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B.      $B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B.
       $B%*%W%7%g%J%kJQ?t(B @var{r} $B$,%;%C%H$5$l$F$$$k$H$-$O(B,
       $BLa$jB?9`<0$O(B dehomogenize $B$5$l$k(B ($B$9$J$o$A(B h $B$K(B 1 $B$,BeF~$5$l$k(B).
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C-texi
Line 1119  mode. So, it is strongly recommended to execute the co
Line 1118  mode. So, it is strongly recommended to execute the co
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1_start}, @code{deRham} (sm1 command)      @code{sm1_start}, @code{deRham} (sm1 command)
 @item Reference paper  @item Algorithm:
     Oaku, Takayama, An algorithm for de Rham cohomology groups of the      Oaku, Takayama, An algorithm for de Rham cohomology groups of the
     complement of an affine variety via D-module computation,      complement of an affine variety via D-module computation,
     Journal of pure and applied algebra 139 (1999), 201--233.      Journal of pure and applied algebra 139 (1999), 201--233.
Line 1129  mode. So, it is strongly recommended to execute the co
Line 1128  mode. So, it is strongly recommended to execute the co
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1_start}, @code{deRham} (sm1 command)      @code{sm1_start}, @code{deRham} (sm1 command)
 @item $B;29MO@J8(B  @item Algorithm:
     Oaku, Takayama, An algorithm for de Rham cohomology groups of the      Oaku, Takayama, An algorithm for de Rham cohomology groups of the
     complement of an affine variety via D-module computation,      complement of an affine variety via D-module computation,
     Journal of pure and applied algebra 139 (1999), 201--233.      Journal of pure and applied algebra 139 (1999), 201--233.
Line 2906  of the system of differential equations @var{ii}
Line 2905  of the system of differential equations @var{ii}
 along the hyperplane specified by  along the hyperplane specified by
 the V filtration @var{v_filtration}.  the V filtration @var{v_filtration}.
 @item @var{v} is a list of variables.  @item @var{v} is a list of variables.
 @item As to the algorithm,  
 see "A.Assi, F.J.Castro-Jimenez and J.M.Granger,  
 How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"  
 Note that the signs of the slopes are negative, but the absolute values  
 of the slopes are returned.  
 @item The return value is a list of lists.  @item The return value is a list of lists.
 The first entry of each list is the slope and the second entry  The first entry of each list is the slope and the second entry
 is the weight vector for which the microcharacteristic variety is  is the weight vector for which the microcharacteristic variety is
 not bihomogeneous.  not bihomogeneous.
 @end itemize  @end itemize
   
   @noindent
   Algorithm:
   see "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
   How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
   Note that the signs of the slopes are negative, but the absolute values
   of the slopes are returned.
   
 */  */
   
 /*&jp-texi  /*&jp-texi
Line 2950  not bihomogeneous.
Line 2952  not bihomogeneous.
 $BHyJ,J}Dx<07O(B @var{ii} $B$N(B V filtration  @var{v_filtration}  $BHyJ,J}Dx<07O(B @var{ii} $B$N(B V filtration  @var{v_filtration}
 $B$G;XDj$9$kD6J?LL$K1h$C$F$N(B (geomeric) slope $B$r7W;;$9$k(B.  $B$G;XDj$9$kD6J?LL$K1h$C$F$N(B (geomeric) slope $B$r7W;;$9$k(B.
 @item @var{v} $B$OJQ?t$N%j%9%H(B.  @item @var{v} $B$OJQ?t$N%j%9%H(B.
 @item $B;HMQ$7$F$$$k%"%k%4%j%:%`$K$D$$$F$O(B,  @item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B.
   $B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B
   microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B.
   @end itemize
   
   @noindent
   Algorithm:
 "A.Assi, F.J.Castro-Jimenez and J.M.Granger,  "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
 How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"  How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
 $B$r$_$h(B.  $B$r$_$h(B.
 Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B,  Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B,
 Slope $B$N@dBPCM$rLa$9(B.  Slope $B$N@dBPCM$rLa$9(B.
 @item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B.  
 $B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B  
 microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B.  
 @end itemize  
 */  */
   
 /*&C-texi  /*&C-texi
Line 2992  microcharacteristic variety $B$,(B bihomogeneous $B
Line 2996  microcharacteristic variety $B$,(B bihomogeneous $B
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm_gb}      @code{sm_gb}
 @end table  @end table
   */
   
   
   /*&eg-texi
   @include sm1-auto-en.texi
   */
   
   /*&jp-texi
   @include sm1-auto-ja.texi
 */  */
   
   
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