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Diff for /OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw between version 1.5 and 1.6

version 1.5, 2012/11/28 05:07:31 version 1.6, 2019/08/31 06:36:28
Line 1 
Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.4 2012/06/11 05:23:52 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.5 2012/11/28 05:07:31 takayama Exp $ */
   
 /*&C  /*&C
 @c DO NOT EDIT THIS FILE  @c DO NOT EDIT THIS FILE
Line 511  x*dx+1
Line 511  x*dx+1
 @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},dehomogenize=@var{r})  @item sm1.gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r},needBack=@var{n})
 ::  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 561  List
Line 561  List
    the polynomials are dehomogenized (,i.e., h is set to 1).     the polynomials are dehomogenized (,i.e., h is set to 1).
 @item If you want to have a reduced basis or compute the initial form ideal exactly,  @item If you want to have a reduced basis or compute the initial form ideal exactly,
 execute sm1.auto_reduce(1) before executing this function.  execute sm1.auto_reduce(1) before executing this function.
   @item When the needBack option @var{n} is 1, it returns the answer is a different format as [groebner basis,[gb,1,all,[groebner basis, backward transformation]]]
 @end itemize  @end itemize
 */  */
 /*&ja  /*&ja
Line 570  execute sm1.auto_reduce(1) before executing this funct
Line 571  execute sm1.auto_reduce(1) before executing this funct
 @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},dehomogenize=@var{r})  @item sm1.gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r},needBack=@var{n})
 ::  @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 613  execute sm1.auto_reduce(1) before executing this funct
Line 614  execute sm1.auto_reduce(1) before executing this funct
     $BLa$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).      $BLa$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).
 @item Reduced $B%0%l%V%J!<4pDl$^$?$O(B in_w $B$r7W;;$7$?$$$H$-$O(B, $B$3$N4X?t$N<B9T$NA0$K(B  @item Reduced $B%0%l%V%J!<4pDl$^$?$O(B in_w $B$r7W;;$7$?$$$H$-$O(B, $B$3$N4X?t$N<B9T$NA0$K(B
 sm1.auto_reduce(1) $B$r<B9T$7$F$*$/$3$H(B.  sm1.auto_reduce(1) $B$r<B9T$7$F$*$/$3$H(B.
   @item needBack $B%*%W%7%g%s$,(B 1 $B$N;~$O(B, $BB>$N>l9g$H$O0[$J$k7A<0(B
   [groebner basis, [gb,1,all, [groebner basis, backward transformation]]]
   $B$GEz$($rLa$9(B. (sm1 $B$N(B getAttribute $B$r;2>H(B)
 @end itemize  @end itemize
 */  */
 /*&C  /*&C
Line 708  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
Line 712  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
  [(1)*<<0,0,1,0,0,1,1,0>>+(1)*<<0,1,0,0,0,2,0,0>>+(-1)*<<0,0,0,0,0,1,0,2>>,(1)*<   [(1)*<<0,0,1,0,0,1,1,0>>+(1)*<<0,1,0,0,0,2,0,0>>+(-1)*<<0,0,0,0,0,1,0,2>>,(1)*<
 <0,0,1,0,0,0,2,0>>+(1)*<<0,1,0,0,0,1,1,0>>+(-1)*<<0,0,0,0,0,0,1,2>>+(-1)*<<0,0,0  <0,0,1,0,0,0,2,0>>+(1)*<<0,1,0,0,0,1,1,0>>+(-1)*<<0,0,0,0,0,0,1,2>>+(-1)*<<0,0,0
 ,0,0,0,0,3>>,(1)*<<0,0,0,0,0,1,0,3>>]]]  ,0,0,0,0,3>>,(1)*<<0,0,0,0,0,1,0,3>>]]]
   @end example
   */
   /*&C
   @example
   [1834] sm1.gb([[dx^2-x,dx],[x]] | needBack=1);
   [[[dx,dx^2-x,1],[dx,dx^2,1]],[gb,1,all,[[dx,dx^2-x,1],[[0,1],[1,0],[-dx,dx^2-x]]]]]
 @end example  @end example
 */  */
   
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