version 1.1, 2001/07/11 01:00:23 |
version 1.4, 2002/07/14 13:14:37 |
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/*$OpenXM$ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.3 2001/07/12 00:46:29 takayama Exp $ */ |
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/*&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) { |
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Line 768 def sm1_isListOfVar(A) { |
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@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},dehomogenize=@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 780 The result will be returned as a list of distributed p |
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Line 780 The result will be returned as a list of distributed p |
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@table @var |
@table @var |
@item return |
@item return |
List |
List |
@item p |
@item p, q, r |
Number |
Number |
@item f, v, w |
@item f, v, w |
List |
List |
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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. |
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@item |
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When the optional variable @var{q} is set, @code{sm1_gb} returns, |
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as the third return value, a list of |
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the Grobner basis and the initial ideal |
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with sums of monomials sorted by the given order. |
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Each polynomial is expressed as a string temporally for now. |
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When the optional variable @var{r} is set to one, |
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the polynomials are dehomogenized (,i.e., h is set to 1). |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
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@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},dehomogenize=@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. |
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@table @var |
@table @var |
@item return |
@item return |
$B%j%9%H(B |
$B%j%9%H(B |
@item p |
@item p, q, r |
$B?t(B |
$B?t(B |
@item f, v, w |
@item f, v, w |
$B%j%9%H(B |
$B%j%9%H(B |
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@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. |
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@item $B%*%W%7%g%J%kJQ?t(B @var{q} $B$,%;%C%H$5$l$F$$$k$H$-$O(B, |
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3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(B |
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$BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B. |
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$B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B. |
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$B%*%W%7%g%J%kJQ?t(B @var{r} $B$,%;%C%H$5$l$F$$$k$H$-$O(B, |
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$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). |
@end itemize |
@end itemize |
*/ |
*/ |
/*&C-texi |
/*&C-texi |
Line 922 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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Line 936 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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*/ |
*/ |
/*&C-texi |
/*&C-texi |
@example |
@example |
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[294] F=sm1_gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1); |
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map(print,F[2][0])$ |
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map(print,F[2][1])$ |
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@end example |
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*/ |
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/*&C-texi |
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@example |
[595] |
[595] |
sm1_gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"], |
sm1_gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"], |
[x,y],[[dx,1,x,-1],[dy,1]]]); |
[x,y],[[dx,1,x,-1],[dy,1]]]); |
Line 2975 microcharacteristic variety $B$,(B bihomogeneous $B |
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Line 2996 microcharacteristic variety $B$,(B bihomogeneous $B |
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@item $B;2>H(B |
@item $B;2>H(B |
@code{sm_gb} |
@code{sm_gb} |
@end table |
@end table |
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*/ |
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/*&eg-texi |
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@include sm1-auto-en.texi |
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*/ |
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/*&jp-texi |
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@include sm1-auto-ja.texi |
*/ |
*/ |
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