| version 1.4, 2012/06/11 05:23:52 |
version 1.6, 2019/08/31 06:36:28 |
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| /*$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 1.5 2012/11/28 05:07:31 takayama Exp $ */ |
| |
|
| /*&C |
/*&C |
| @c DO NOT EDIT THIS FILE |
@c DO NOT EDIT THIS FILE |
|
|
| @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}) |
|
|
| 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,[gb,1,all,[groebner basis, backward transformation]]] |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&ja |
/*&ja |
|
|
| @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. |
|
|
| $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. |
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@item needBack $B%*%W%7%g%s$,(B 1 $B$N;~$O(B, $BB>$N>l9g$H$O0[$J$k7A<0(B |
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[groebner basis, [gb,1,all, [groebner basis, backward transformation]]] |
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$B$GEz$($rLa$9(B. (sm1 $B$N(B getAttribute $B$r;2>H(B) |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C |
/*&C |
| Line 706 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| Line 714 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| ,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 |
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[1834] sm1.gb([[dx^2-x,dx],[x]] | needBack=1); |
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[[[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]]]]] |
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@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 |
| */ |
*/ |
| |
|
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