| version 1.1, 2001/07/11 01:00:23 |
version 1.2, 2001/07/11 06:23:16 |
|
|
| /*$OpenXM$ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.1 2001/07/11 01:00:23 takayama Exp $ */ |
| |
|
| /*&C-texi |
/*&C-texi |
| @c DO NOT EDIT THIS FILE oxphc.texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
| Line 768 def sm1_isListOfVar(A) { |
|
| Line 768 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}) |
@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q}) |
| :: 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 780 The result will be returned as a list of distributed p |
|
| @table @var |
@table @var |
| @item return |
@item return |
| List |
List |
| @item p |
@item p, q |
| Number |
Number |
| @item f, v, w |
@item f, v, w |
| List |
List |
|
|
| When a non-term order is given, the Grobner basis is computed in |
When a non-term order is given, the Grobner basis is computed in |
| the homogenized Weyl algebra (See Section 1.2 of the book of SST). |
the homogenized Weyl algebra (See Section 1.2 of the book of SST). |
| The homogenization variable h is automatically added. |
The homogenization variable h is automatically added. |
| |
@item |
| |
When the optional variable @var{q} is set, @code{sm1_gb} returns, |
| |
as the third return value, a list of |
| |
the Grobner basis and the initial ideal |
| |
with sums of monomials sorted by the given order. |
| |
Each polynomial is expressed as a string temporally for now. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&jp-texi |
/*&jp-texi |
|
|
| @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}) |
@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q}) |
| :: @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. |
|
|
| @table @var |
@table @var |
| @item return |
@item return |
| $B%j%9%H(B |
$B%j%9%H(B |
| @item p |
@item p, q |
| $B?t(B |
$B?t(B |
| @item f, v, w |
@item f, v, w |
| $B%j%9%H(B |
$B%j%9%H(B |
|
|
| @item |
@item |
| Term order $B$G$J$$=g=x$,M?$($i$l$?>l9g$O(B, $BF1<!2=%o%$%kBe?t$G%0%l%V%J4pDl$,7W;;$5$l$k(B (SST $B$NK\$N(B Section 1.2 $B$r8+$h(B). |
Term order $B$G$J$$=g=x$,M?$($i$l$?>l9g$O(B, $BF1<!2=%o%$%kBe?t$G%0%l%V%J4pDl$,7W;;$5$l$k(B (SST $B$NK\$N(B Section 1.2 $B$r8+$h(B). |
| $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B. |
$BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B. |
| |
@item $B%*%W%7%g%J%kJQ?t(B @var{q} $B$,%;%C%H$5$l$F$$$k$H$-$O(B, |
| |
3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(B |
| |
$BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B. |
| |
$B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C-texi |
| Line 919 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| Line 929 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| ($B$D$^$j(B $50c+2d+a = 50c'+2d'+a'$ $B$N$H$-(B reverse lexicographic order $B$GHf3S(B |
($B$D$^$j(B $50c+2d+a = 50c'+2d'+a'$ $B$N$H$-(B reverse lexicographic order $B$GHf3S(B |
| $B$5$l$k(B). |
$B$5$l$k(B). |
| @end tex |
@end tex |
| |
*/ |
| |
/*&C-texi |
| |
@example |
| |
[294] F=sm1_gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1); |
| |
map(print,F[2][0])$ |
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map(print,F[2][1])$ |
| |
@end example |
| */ |
*/ |
| /*&C-texi |
/*&C-texi |
| @example |
@example |
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