=================================================================== RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave,v retrieving revision 1.2 retrieving revision 1.5 diff -u -p -r1.2 -r1.5 --- OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave 2001/07/11 06:23:16 1.2 +++ OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave 2002/08/11 08:39:47 1.5 @@ -1,4 +1,4 @@ -/*$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 $ */ /*&C-texi @c DO NOT EDIT THIS FILE oxphc.texi @@ -69,12 +69,7 @@ cohomology groups. /*&C-texi @example -This is Risa/Asir, Version 20000126. -Copyright (C) FUJITSU LABORATORIES LIMITED. -1994-1999. All rights reserved. -xm version 20000202. Copyright (C) OpenXM Developing Team. 2000. -ox_help(0); ox_help("keyword"); ox_grep("keyword"); for help message -Loading ~/.asirrc +@include opening.texi [283] sm1_deRham([x*(x-1),[x]]); [1,2] @@ -407,13 +402,13 @@ def sm1(P,F) { /*&jp-texi @table @t @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 */ /*&eg-texi @table @t @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 */ @@ -768,7 +763,7 @@ def sm1_isListOfVar(A) { @findex sm1_gb @findex sm1_gb_d @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 operators with the variable @var{v}. @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p}) @@ -780,7 +775,7 @@ The result will be returned as a list of distributed p @table @var @item return List -@item p, q +@item p, q, r Number @item f, v, w List @@ -814,6 +809,8 @@ List 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. + When the optional variable @var{r} is set to one, + the polynomials are dehomogenized (,i.e., h is set to 1). @end itemize */ /*&jp-texi @@ -827,7 +824,7 @@ List @findex sm1_gb @findex sm1_gb_d @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$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B. @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p}) :: @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$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. @@ -836,7 +833,7 @@ List @table @var @item return $B%j%9%H(B -@item p, q +@item p, q, r $B?t(B @item f, v, w $B%j%9%H(B @@ -866,6 +863,8 @@ List 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$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B. + $B%*%W%7%g%J%kJQ?t(B @var{r} $B$,%;%C%H$5$l$F$$$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). @end itemize */ /*&C-texi @@ -1119,7 +1118,7 @@ mode. So, it is strongly recommended to execute the co @table @t @item Reference @code{sm1_start}, @code{deRham} (sm1 command) -@item Reference paper +@item Algorithm: Oaku, Takayama, An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation, Journal of pure and applied algebra 139 (1999), 201--233. @@ -1129,7 +1128,7 @@ mode. So, it is strongly recommended to execute the co @table @t @item $B;2>H(B @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 complement of an affine variety via D-module computation, Journal of pure and applied algebra 139 (1999), 201--233. @@ -2906,16 +2905,19 @@ of the system of differential equations @var{ii} along the hyperplane specified by the V filtration @var{v_filtration}. @item @var{v} is a list of variables. -@item As to the algorithm, -see "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" -Note that the signs of the slopes are negative, but the absolute values -of the slopes are returned. @item The return value is a list of lists. The first entry of each list is the slope and the second entry is the weight vector for which the microcharacteristic variety is not bihomogeneous. @end itemize + +@noindent +Algorithm: +see "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" +Note that the signs of the slopes are negative, but the absolute values +of the slopes are returned. + */ /*&jp-texi @@ -2950,16 +2952,18 @@ not bihomogeneous. $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. @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$G$"$k(B. +$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 +microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B. +@end itemize + +@noindent +Algorithm: "A.Assi, F.J.Castro-Jimenez and J.M.Granger, How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996" $B$r$_$h(B. Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B, Slope $B$N@dBPCM$rLa$9(B. -@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B. -$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B -microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B. -@end itemize */ /*&C-texi @@ -2992,6 +2996,15 @@ microcharacteristic variety $B$,(B bihomogeneous $B @item $B;2>H(B @code{sm_gb} @end table +*/ + + +/*&eg-texi +@include sm1-auto-en.texi +*/ + +/*&jp-texi +@include sm1-auto-ja.texi */