version 1.2, 2001/07/11 06:23:16 |
version 1.5, 2002/08/11 08:39:47 |
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/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.1 2001/07/11 01:00:23 takayama Exp $ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.4 2002/07/14 13:14:37 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 69 cohomology groups. |
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Line 69 cohomology groups. |
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/*&C-texi |
/*&C-texi |
@example |
@example |
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This is Risa/Asir, Version 20000126. |
@include opening.texi |
Copyright (C) FUJITSU LABORATORIES LIMITED. |
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1994-1999. All rights reserved. |
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xm version 20000202. Copyright (C) OpenXM Developing Team. 2000. |
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ox_help(0); ox_help("keyword"); ox_grep("keyword"); for help message |
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Loading ~/.asirrc |
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[283] sm1_deRham([x*(x-1),[x]]); |
[283] sm1_deRham([x*(x-1),[x]]); |
[1,2] |
[1,2] |
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/*&jp-texi |
/*&jp-texi |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}. |
@code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}. |
@end table |
@end table |
*/ |
*/ |
/*&eg-texi |
/*&eg-texi |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}. |
@code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}. |
@end table |
@end table |
*/ |
*/ |
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Line 768 def sm1_isListOfVar(A) { |
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Line 763 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},sorted=@var{q}) |
@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 775 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, q |
@item p, q, r |
Number |
Number |
@item f, v, w |
@item f, v, w |
List |
List |
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the Grobner basis and the initial ideal |
the Grobner basis and the initial ideal |
with sums of monomials sorted by the given order. |
with sums of monomials sorted by the given order. |
Each polynomial is expressed as a string temporally for now. |
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},sorted=@var{q}) |
@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, q |
@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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3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(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. |
$BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B. |
$B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B. |
$B$$$^$N$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 1119 mode. So, it is strongly recommended to execute the co |
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Line 1118 mode. So, it is strongly recommended to execute the co |
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@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1_start}, @code{deRham} (sm1 command) |
@code{sm1_start}, @code{deRham} (sm1 command) |
@item Reference paper |
@item Algorithm: |
Oaku, Takayama, An algorithm for de Rham cohomology groups of the |
Oaku, Takayama, An algorithm for de Rham cohomology groups of the |
complement of an affine variety via D-module computation, |
complement of an affine variety via D-module computation, |
Journal of pure and applied algebra 139 (1999), 201--233. |
Journal of pure and applied algebra 139 (1999), 201--233. |
Line 1129 mode. So, it is strongly recommended to execute the co |
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Line 1128 mode. So, it is strongly recommended to execute the co |
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@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1_start}, @code{deRham} (sm1 command) |
@code{sm1_start}, @code{deRham} (sm1 command) |
@item $B;29MO@J8(B |
@item Algorithm: |
Oaku, Takayama, An algorithm for de Rham cohomology groups of the |
Oaku, Takayama, An algorithm for de Rham cohomology groups of the |
complement of an affine variety via D-module computation, |
complement of an affine variety via D-module computation, |
Journal of pure and applied algebra 139 (1999), 201--233. |
Journal of pure and applied algebra 139 (1999), 201--233. |
Line 2906 of the system of differential equations @var{ii} |
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Line 2905 of the system of differential equations @var{ii} |
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along the hyperplane specified by |
along the hyperplane specified by |
the V filtration @var{v_filtration}. |
the V filtration @var{v_filtration}. |
@item @var{v} is a list of variables. |
@item @var{v} is a list of variables. |
@item As to the algorithm, |
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see "A.Assi, F.J.Castro-Jimenez and J.M.Granger, |
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How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996" |
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Note that the signs of the slopes are negative, but the absolute values |
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of the slopes are returned. |
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@item The return value is a list of lists. |
@item The return value is a list of lists. |
The first entry of each list is the slope and the second entry |
The first entry of each list is the slope and the second entry |
is the weight vector for which the microcharacteristic variety is |
is the weight vector for which the microcharacteristic variety is |
not bihomogeneous. |
not bihomogeneous. |
@end itemize |
@end itemize |
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@noindent |
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Algorithm: |
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see "A.Assi, F.J.Castro-Jimenez and J.M.Granger, |
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How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996" |
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Note that the signs of the slopes are negative, but the absolute values |
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of the slopes are returned. |
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*/ |
*/ |
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/*&jp-texi |
/*&jp-texi |
Line 2950 not bihomogeneous. |
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Line 2952 not bihomogeneous. |
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$BHyJ,J}Dx<07O(B @var{ii} $B$N(B V filtration @var{v_filtration} |
$BHyJ,J}Dx<07O(B @var{ii} $B$N(B V filtration @var{v_filtration} |
$B$G;XDj$9$kD6J?LL$K1h$C$F$N(B (geomeric) slope $B$r7W;;$9$k(B. |
$B$G;XDj$9$kD6J?LL$K1h$C$F$N(B (geomeric) slope $B$r7W;;$9$k(B. |
@item @var{v} $B$OJQ?t$N%j%9%H(B. |
@item @var{v} $B$OJQ?t$N%j%9%H(B. |
@item $B;HMQ$7$F$$$k%"%k%4%j%:%`$K$D$$$F$O(B, |
@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B. |
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$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B |
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microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B. |
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@end itemize |
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@noindent |
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Algorithm: |
"A.Assi, F.J.Castro-Jimenez and J.M.Granger, |
"A.Assi, F.J.Castro-Jimenez and J.M.Granger, |
How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996" |
How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996" |
$B$r$_$h(B. |
$B$r$_$h(B. |
Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B, |
Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B, |
Slope $B$N@dBPCM$rLa$9(B. |
Slope $B$N@dBPCM$rLa$9(B. |
@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B. |
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$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B |
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microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B. |
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@end itemize |
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*/ |
*/ |
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/*&C-texi |
/*&C-texi |
Line 2992 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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