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Diff for /OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw between version 1.4 and 1.9

version 1.4, 2012/06/11 05:23:52 version 1.9, 2020/02/25 02:21:53
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Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.3 2010/02/06 00:50:32 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.8 2019/09/13 05:21:33 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},ring_var=@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 559  List
Line 559  List
    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,     When the optional variable @var{r} is set to one,
    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,
   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,initial, gb,1,all,[groebner basis, backward transformation]]
   @item The default value of ring_var is ring_var_for_asir. The server ox_sm1 saves the ring structure used to the global this ring_var. See also reduction.
 @end itemize  @end itemize
 */  */
 /*&ja  /*&ja
Line 568  List
Line 572  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},dehomogenize=@var{r})  @item sm1.gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r},needBack=@var{n},ring_var=@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 609  List
Line 613  List
     $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$$$k$H$-$O(B,      $B%*%W%7%g%J%kJQ?t(B @var{r} $B$,%;%C%H$5$l$F$$$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).      $BLa$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;;$7$?$$$H$-$O(B, $B$3$N4X?t$N<B9T$NA0$K(B
   sm1.auto_reduce(1) $B$r<B9T$7$F$*$/$3$H(B.
   @item needBack $B%*%W%7%g%s$,(B 1 $B$N;~$O(B, $BB>$N>l9g$H$O0[$J$k7A<0(B
   [groebner basis, initial, gb,1,all, [groebner basis, backward transformation]]
   $B$GEz$($rLa$9(B. (sm1 $B$N(B getAttribute $B$r;2>H(B)
   @item ring_var $B%*%W%7%g%s$N4{DjCM$O(B ring_var_for_asir $B$G$"$k(B. sm1 $B$O$3$NBg0hJQ?tL>$G7W;;$KMQ$$$?(B ring $B9=B$BN$rJ]B8$9$k(B.  reduction $B$r;2>H(B.
 @end itemize  @end itemize
 */  */
 /*&C  /*&C
Line 706  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
Line 716  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 ,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  @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
   */
   
 /*&en  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.reduction}, @code{sm1.rat_to_p}      @code{sm1.auto_reduce}, @code{sm1.reduction}, @code{sm1.rat_to_p}
 @end table  @end table
 */  */
 /*&ja  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.reduction}, @code{sm1.rat_to_p}      @code{sm1.auto_reduce}, @code{sm1.reduction}, @code{sm1.rat_to_p}
 @end table  @end table
 */  */
   
Line 1147  the inputs @var{f} and @var{g} are left ideals of D.
Line 1163  the inputs @var{f} and @var{g} are left ideals of D.
 @findex sm1.reduction  @findex sm1.reduction
 @table @t  @table @t
 @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})  @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
   @item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})
   @item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})
 ::  ::
 @end table  @end table
   
Line 1176  in lower order terms.
Line 1194  in lower order terms.
 @item  The functions  @item  The functions
 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)  sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
 are for distributed polynomials.  are for distributed polynomials.
   @item When the arguments are two, the function mod_reduction is called. It uses the ring
   structure saved in the global variable ring_var in the ox_sm1 server.
 @end itemize  @end itemize
 */  */
 /*&ja  /*&ja
Line 1184  are for distributed polynomials.
Line 1204  are for distributed polynomials.
 @findex sm1.reduction  @findex sm1.reduction
 @table @t  @table @t
 @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})  @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
   @item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})
   @item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})
 ::  ::
 @end table  @end table
   
Line 1215  r/c0 $B$,(B normal form $B$G$"$k(B.
Line 1237  r/c0 $B$,(B normal form $B$G$"$k(B.
 @item  $BH!?t(B  @item  $BH!?t(B
 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_d(P,F,G)  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_d(P,F,G)
 $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.  $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.
   @item $B0z?t$,#2$D$N;~$O(B mod_reduction $B4X?t$,8F$P$l$k(B. $B$3$l$O(B ox_sm1 $B$NBg0hJQ?t(B
   ring_var $BJQ?t$KJ]B8$5$l$?(B ring $B$K$*$$$F4JLs$r9T$&(B. auto_reduce(1) $B$,<+F0$G%;%C%H$5$l$k(B.
   gb $B$r;2>H(B.
 @end itemize  @end itemize
 */  */
 /*&C  /*&C
Line 1223  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
Line 1248  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]  [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
 [260] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);  [260] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);
 [0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]  [0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]
   
   [1837] XM_debug=0$ S=sm1.syz([ [x^2-1,x^3-1,x^4-1],[x]])$
   [1838] sm1.auto_reduce(1);
   1
   [1839] S0=sm1.gb([S[0],[x]]);
   [[[-x^2-x-1,x+1,0],[x^2+1,0,-1]],[[0,x,0],[0,0,-1]]]
   [1840] sm1.reduction([ [-x^4-x^3-x^2-x,x^3+x^2+x+1,-1], S0[0]]);
   [[0,0,0],-1,[[x^2+1,0,0],[1,0,0]],[[-x^2-x-1,x+1,0],[x^2+1,0,-1]]]
 @end example  @end example
 */  */
 /*&en  /*&en
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