version 1.4, 2002/07/14 13:14:37 |
version 1.5, 2002/08/11 08:39:47 |
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/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.3 2001/07/12 00:46:29 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 1123 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 1133 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 2910 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 2954 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 |