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Diff for /OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw between version 1.7 and 1.8

version 1.7, 2019/09/09 23:39:52 version 1.8, 2019/09/13 05:21:33
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 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.6 2019/08/31 06:36:28 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.7 2019/09/09 23:39:52 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},needBack=@var{n})  @item sm1.gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r},needBack=@var{n},ring_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 562  List
Line 562  List
 @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,initial, gb,1,all,[groebner basis, backward transformation]]  @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 571  execute sm1.auto_reduce(1) before executing this funct
Line 572  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},needBack=@var{n})  @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 617  sm1.auto_reduce(1) $B$r<B9T$7$F$*$/$3$H(B.
Line 618  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  @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]]  [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)  $B$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 1161  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 1190  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 1198  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 1229  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 1237  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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