version 1.2, 2001/07/11 06:23:16 |
version 1.6, 2002/08/23 08:16:13 |
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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 1.5 2002/08/11 08:39:47 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 |
*/ |
*/ |
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/*&C-texi |
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@node SM1 Functions,,, Top |
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*/ |
/*&jp-texi |
/*&jp-texi |
@node SM1 $BH!?t(B,,, Top |
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@chapter SM1 $BH!?t(B |
@chapter SM1 $BH!?t(B |
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$B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir} |
$B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir} |
Line 31 $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE |
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Line 33 $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE |
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@end tex |
@end tex |
*/ |
*/ |
/*&eg-texi |
/*&eg-texi |
@node SM1 Functions,,, Top |
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@chapter SM1 Functions |
@chapter SM1 Functions |
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This chapter describes interface functions for |
This chapter describes interface functions for |
Line 69 cohomology groups. |
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Line 70 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] |
Line 89 Grobner Deformations of Hypergeometric Differential Eq |
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Line 85 Grobner Deformations of Hypergeometric Differential Eq |
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1999, Springer. |
1999, Springer. |
See the appendix. |
See the appendix. |
*/ |
*/ |
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/* |
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@menu |
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* ox_sm1_forAsir:: |
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* sm1_start:: |
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* sm1:: |
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* sm1_push_int0:: |
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* sm1_gb:: |
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* sm1_deRham:: |
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* sm1_hilbert:: |
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* hilbert_polynomial:: |
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* sm1_genericAnn:: |
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* sm1_wTensor0:: |
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* sm1_reduction:: |
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* sm1_xml_tree_to_prefix_string:: |
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* sm1_syz:: |
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* sm1_mul:: |
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* sm1_distraction:: |
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* sm1_gkz:: |
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* sm1_appell1:: |
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* sm1_appell4:: |
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* sm1_rank:: |
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* sm1_auto_reduce:: |
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* sm1_slope:: |
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@end menu |
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*/ |
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/*&jp-texi |
/*&jp-texi |
@section @code{ox_sm1_forAsir} $B%5!<%P(B |
@section @code{ox_sm1_forAsir} $B%5!<%P(B |
*/ |
*/ |
Line 97 See the appendix. |
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Line 120 See the appendix. |
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*/ |
*/ |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* ox_sm1_forAsir:: |
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@end menu |
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@node ox_sm1_forAsir,,, Top |
@node ox_sm1_forAsir,,, Top |
@subsection @code{ox_sm1_forAsir} |
@subsection @code{ox_sm1_forAsir} |
@findex ox_sm1_forAsir |
@findex ox_sm1_forAsir |
Line 131 to build your own server by reading @code{sm1} macros. |
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Line 151 to build your own server by reading @code{sm1} macros. |
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@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@menu |
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* ox_sm1_forAsir:: |
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@end menu |
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@node ox_sm1_forAsir,,, Top |
@node ox_sm1_forAsir,,, Top |
@subsection @code{ox_sm1_forAsir} |
@subsection @code{ox_sm1_forAsir} |
@findex ox_sm1_forAsir |
@findex ox_sm1_forAsir |
Line 190 def sm1_check_server(P) { |
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Line 207 def sm1_check_server(P) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_start |
@c sort-sm1_start |
@menu |
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* sm1_start:: |
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@end menu |
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@node sm1_start,,, SM1 Functions |
@node sm1_start,,, SM1 Functions |
@subsection @code{sm1_start} |
@subsection @code{sm1_start} |
@findex sm1_start |
@findex sm1_start |
Line 233 differential operators in default. (cf. @code{Sm1_ord_ |
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Line 247 differential operators in default. (cf. @code{Sm1_ord_ |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_start |
@c sort-sm1_start |
@menu |
@node sm1_start,,, SM1 Functions |
* sm1_start:: |
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@end menu |
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@node sm1_start,,, SM1 $BH!?t(B |
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@subsection @code{sm1_start} |
@subsection @code{sm1_start} |
@findex sm1_start |
@findex sm1_start |
@table @t |
@table @t |
Line 337 def sm1push(P,F) { |
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Line 348 def sm1push(P,F) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1 |
@c sort-sm1 |
@menu |
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* sm1:: |
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@end menu |
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@node sm1,,, SM1 Functions |
@node sm1,,, SM1 Functions |
@subsection @code{sm1} |
@subsection @code{sm1} |
@findex sm1 |
@findex sm1 |
Line 363 to execute the command string @var{s}. |
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Line 371 to execute the command string @var{s}. |
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@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1,,, SM1 Functions |
* sm1:: |
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@end menu |
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@node sm1,,, SM1 $BH!?t(B |
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@subsection @code{sm1} |
@subsection @code{sm1} |
@findex sm1 |
@findex sm1 |
@table @t |
@table @t |
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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 523 def sm1_push_int0_R(A,P) { |
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Line 528 def sm1_push_int0_R(A,P) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_push_int0 |
@c sort-sm1_push_int0 |
@menu |
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* sm1_push_int0:: |
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@end menu |
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@node sm1_push_int0,,, SM1 Functions |
@node sm1_push_int0,,, SM1 Functions |
@subsection @code{sm1_push_int0} |
@subsection @code{sm1_push_int0} |
@findex sm1_push_int0 |
@findex sm1_push_int0 |
Line 564 Note that @code{ox_push_cmo(@var{p},1234)} send the bi |
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Line 566 Note that @code{ox_push_cmo(@var{p},1234)} send the bi |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_push_int0 |
@c sort-sm1_push_int0 |
@menu |
@node sm1_push_int0,,, SM1 Functions |
* sm1_push_int0:: |
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@end menu |
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@node sm1_push_int0,,, SM1 $BH!?t(B |
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@subsection @code{sm1_push_int0} |
@subsection @code{sm1_push_int0} |
@findex sm1_push_int0 |
@findex sm1_push_int0 |
@table @t |
@table @t |
Line 759 def sm1_isListOfVar(A) { |
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Line 758 def sm1_isListOfVar(A) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_gb |
@c sort-sm1_gb |
@menu |
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* sm1_gb:: |
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@end menu |
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@node sm1_gb,,, SM1 Functions |
@node sm1_gb,,, SM1 Functions |
@node sm1_gb_d,,, SM1 Functions |
@node sm1_gb_d,,, SM1 Functions |
@subsection @code{sm1_gb} |
@subsection @code{sm1_gb} |
@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 776 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 |
@c sort-sm1_gb |
@c sort-sm1_gb |
@menu |
@node sm1_gb,,, SM1 Functions |
* sm1_gb:: |
@node sm1_gb_d,,, SM1 Functions |
@end menu |
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@node sm1_gb,,, SM1 $BH!?t(B |
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@node sm1_gb_d,,, SM1 $BH!?t(B |
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@subsection @code{sm1_gb} |
@subsection @code{sm1_gb} |
@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 1014 def sm1_pgb(A) { |
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Line 1011 def sm1_pgb(A) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_deRham |
@c sort-sm1_deRham |
@menu |
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* sm1_deRham:: |
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@end menu |
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@node sm1_deRham,,, SM1 Functions |
@node sm1_deRham,,, SM1 Functions |
@subsection @code{sm1_deRham} |
@subsection @code{sm1_deRham} |
@findex sm1_deRham |
@findex sm1_deRham |
Line 1062 mode. So, it is strongly recommended to execute the co |
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Line 1056 mode. So, it is strongly recommended to execute the co |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_deRham |
@c sort-sm1_deRham |
@menu |
@node sm1_deRham,,, SM1 Functions |
* sm1_deRham:: |
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@end menu |
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@node sm1_deRham,,, SM1 $BH!?t(B |
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@subsection @code{sm1_deRham} |
@subsection @code{sm1_deRham} |
@findex sm1_deRham |
@findex sm1_deRham |
@table @t |
@table @t |
Line 1119 mode. So, it is strongly recommended to execute the co |
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Line 1110 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 1120 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 1239 def sm1_reduction_noH_d(F,G) { |
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Line 1230 def sm1_reduction_noH_d(F,G) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_hilbert |
@c sort-sm1_hilbert |
@menu |
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* sm1_hilbert:: |
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* hilbert_polynomial:: |
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@end menu |
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@node sm1_hilbert,,, SM1 Functions |
@node sm1_hilbert,,, SM1 Functions |
@subsection @code{sm1_hilbert} |
@subsection @code{sm1_hilbert} |
@findex sm1_hilbert |
@findex sm1_hilbert |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_hilbert |
@c sort-sm1_hilbert |
@menu |
@node sm1_hilbert,,, SM1 Functions |
* sm1_hilbert:: |
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* hilbert_polynomial:: |
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@end menu |
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@node sm1_hilbert,,, SM1 $BH!?t(B |
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@subsection @code{sm1_hilbert} |
@subsection @code{sm1_hilbert} |
@findex sm1_hilbert |
@findex sm1_hilbert |
@findex hilbert_polynomial |
@findex hilbert_polynomial |
Line 1385 def sm1_hilbert(A) { |
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Line 1368 def sm1_hilbert(A) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_genericAnn |
@c sort-sm1_genericAnn |
@menu |
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* sm1_genericAnn:: |
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@end menu |
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@node sm1_genericAnn,,, SM1 Functions |
@node sm1_genericAnn,,, SM1 Functions |
@subsection @code{sm1_genericAnn} |
@subsection @code{sm1_genericAnn} |
@findex sm1_genericAnn |
@findex sm1_genericAnn |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_genericAnn |
@c sort-sm1_genericAnn |
@menu |
@node sm1_genericAnn,,, SM1 Functions |
* sm1_genericAnn:: |
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@end menu |
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@node sm1_genericAnn,,, SM1 $BH!?t(B |
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@subsection @code{sm1_genericAnn} |
@subsection @code{sm1_genericAnn} |
@findex sm1_genericAnn |
@findex sm1_genericAnn |
@table @t |
@table @t |
Line 1487 def sm1_tensor0(F) { |
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Line 1464 def sm1_tensor0(F) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_wTensor0 |
@c sort-sm1_wTensor0 |
@menu |
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* sm1_wTensor0:: |
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@end menu |
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@node sm1_wTensor0,,, SM1 Functions |
@node sm1_wTensor0,,, SM1 Functions |
@subsection @code{sm1_wTensor0} |
@subsection @code{sm1_wTensor0} |
@findex sm1_wTensor0 |
@findex sm1_wTensor0 |
Line 1531 the inputs @var{f} and @var{g} are left ideals of D. |
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Line 1505 the inputs @var{f} and @var{g} are left ideals of D. |
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/*&jp-texi |
/*&jp-texi |
@c sort-sm1_wTensor0 |
@c sort-sm1_wTensor0 |
@menu |
@node sm1_wTensor0,,, SM1 Functions |
* sm1_wTensor0:: |
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@end menu |
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@node sm1_wTensor0,,, SM1 $BH!?t(B |
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@subsection @code{sm1_wTensor0} |
@subsection @code{sm1_wTensor0} |
@findex sm1_wTensor0 |
@findex sm1_wTensor0 |
@table @t |
@table @t |
Line 1593 def sm1_wTensor0(F) { |
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Line 1564 def sm1_wTensor0(F) { |
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_reduction |
@c sort-sm1_reduction |
@menu |
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* sm1_reduction:: |
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@end menu |
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@node sm1_reduction,,, SM1 Functions |
@node sm1_reduction,,, SM1 Functions |
@subsection @code{sm1_reduction} |
@subsection @code{sm1_reduction} |
@findex sm1_reduction |
@findex sm1_reduction |
Line 1633 are for distributed polynomials. |
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Line 1601 are for distributed polynomials. |
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@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_reduction,,, SM1 Functions |
* sm1_reduction:: |
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@end menu |
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@node sm1_reduction,,, SM1 $BH!?t(B |
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@subsection @code{sm1_reduction} |
@subsection @code{sm1_reduction} |
@findex sm1_reduction |
@findex sm1_reduction |
@table @t |
@table @t |
Line 1730 def sm1_reduction_noH(A) { |
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Line 1695 def sm1_reduction_noH(A) { |
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} |
} |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_xml_tree_to_prefix_string:: |
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@end menu |
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@node sm1_xml_tree_to_prefix_string,,, SM1 Functions |
@node sm1_xml_tree_to_prefix_string,,, SM1 Functions |
@subsection @code{sm1_xml_tree_to_prefix_string} |
@subsection @code{sm1_xml_tree_to_prefix_string} |
@findex sm1_xml_tree_to_prefix_string |
@findex sm1_xml_tree_to_prefix_string |
Line 1761 command search path.) |
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Line 1723 command search path.) |
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@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_xml_tree_to_prefix_string,,, SM1 Functions |
* sm1_xml_tree_to_prefix_string:: |
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@end menu |
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@node sm1_xml_tree_to_prefix_string,,, SM1 $BH!?t(B |
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@subsection @code{sm1_xml_tree_to_prefix_string} |
@subsection @code{sm1_xml_tree_to_prefix_string} |
@findex sm1_xml_tree_to_prefix_string |
@findex sm1_xml_tree_to_prefix_string |
@table @t |
@table @t |
Line 1887 def sm1_res_div(A) { |
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Line 1846 def sm1_res_div(A) { |
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|
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/*&eg-texi |
/*&eg-texi |
@c sort-sm1_syz |
@c sort-sm1_syz |
@menu |
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* sm1_syz:: |
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@end menu |
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@node sm1_syz,,, SM1 Functions |
@node sm1_syz,,, SM1 Functions |
@node sm1_syz_d,,, SM1 Functions |
@node sm1_syz_d,,, SM1 Functions |
@subsection @code{sm1_syz} |
@subsection @code{sm1_syz} |
Line 1934 In summary, @var{g} = @var{m} @var{f} and |
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Line 1890 In summary, @var{g} = @var{m} @var{f} and |
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*/ |
*/ |
/*&jp-texi |
/*&jp-texi |
@c sort-sm1_syz |
@c sort-sm1_syz |
@menu |
@node sm1_syz,,, SM1 Functions |
* sm1_syz:: |
@node sm1_syz_d,,, SM1 Functions |
@end menu |
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@node sm1_syz,,, SM1 $BH!?t(B |
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@node sm1_syz_d,,, SM1 $BH!?t(B |
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@subsection @code{sm1_syz} |
@subsection @code{sm1_syz} |
@findex sm1_syz |
@findex sm1_syz |
@findex sm1_syz_d |
@findex sm1_syz_d |
Line 2033 def sm1_mul(A,B,V) { |
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Line 1986 def sm1_mul(A,B,V) { |
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} |
} |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_mul:: |
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@end menu |
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@node sm1_mul,,, SM1 Functions |
@node sm1_mul,,, SM1 Functions |
@subsection @code{sm1_mul} |
@subsection @code{sm1_mul} |
@findex sm1_mul |
@findex sm1_mul |
|
|
*/ |
*/ |
|
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_mul,,, SM1 Functions |
* sm1_mul:: |
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@end menu |
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@node sm1_mul,,, SM1 $BH!?t(B |
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@subsection @code{sm1_mul} |
@subsection @code{sm1_mul} |
@findex sm1_mul |
@findex sm1_mul |
@table @t |
@table @t |
Line 2229 def sm1_distraction(A) { |
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Line 2176 def sm1_distraction(A) { |
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} |
} |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_distraction:: |
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@end menu |
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@node sm1_distraction,,, SM1 Functions |
@node sm1_distraction,,, SM1 Functions |
@subsection @code{sm1_distraction} |
@subsection @code{sm1_distraction} |
@findex sm1_distraction |
@findex sm1_distraction |
Line 2263 See Saito, Sturmfels, Takayama : Grobner Deformations |
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Line 2207 See Saito, Sturmfels, Takayama : Grobner Deformations |
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*/ |
*/ |
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_distraction,,, SM1 Functions |
* sm1_distraction:: |
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@end menu |
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@node sm1_distraction,,, SM1 $BH!?t(B |
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@subsection @code{sm1_distraction} |
@subsection @code{sm1_distraction} |
@findex sm1_distraction |
@findex sm1_distraction |
Line 2386 def sm1_gkz(S) { |
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Line 2327 def sm1_gkz(S) { |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_gkz:: |
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@end menu |
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@node sm1_gkz,,, SM1 Functions |
@node sm1_gkz,,, SM1 Functions |
@subsection @code{sm1_gkz} |
@subsection @code{sm1_gkz} |
@findex sm1_gkz |
@findex sm1_gkz |
|
|
*/ |
*/ |
|
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_gkz,,, SM1 Functions |
* sm1_gkz:: |
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@end menu |
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@node sm1_gkz,,, SM1 $BH!?t(B |
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@subsection @code{sm1_gkz} |
@subsection @code{sm1_gkz} |
@findex sm1_gkz |
@findex sm1_gkz |
@table @t |
@table @t |
Line 2499 def sm1aux_x(I) { |
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Line 2434 def sm1aux_x(I) { |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_appell1:: |
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@end menu |
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@node sm1_appell1,,, SM1 Functions |
@node sm1_appell1,,, SM1 Functions |
@subsection @code{sm1_appell1} |
@subsection @code{sm1_appell1} |
@findex sm1_appell1 |
@findex sm1_appell1 |
Line 2529 The parameters a, c, b1, ..., bn may be rational numbe |
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Line 2461 The parameters a, c, b1, ..., bn may be rational numbe |
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*/ |
*/ |
|
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_appell1,,, SM1 Functions |
* sm1_appell1:: |
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@end menu |
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@node sm1_appell1,,, SM1 $BH!?t(B |
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@subsection @code{sm1_appell1} |
@subsection @code{sm1_appell1} |
@findex sm1_appell1 |
@findex sm1_appell1 |
@table @t |
@table @t |
Line 2614 def sm1_appell4(S) { |
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Line 2543 def sm1_appell4(S) { |
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} |
} |
|
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_appell4:: |
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@end menu |
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@node sm1_appell4,,, SM1 Functions |
@node sm1_appell4,,, SM1 Functions |
@subsection @code{sm1_appell4} |
@subsection @code{sm1_appell4} |
@findex sm1_appell4 |
@findex sm1_appell4 |
Line 2644 The parameters a, b, c1, ..., cn may be rational numbe |
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Line 2570 The parameters a, b, c1, ..., cn may be rational numbe |
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*/ |
*/ |
|
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_appell4,,, SM1 Functions |
* sm1_appell4:: |
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@end menu |
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@node sm1_appell4,,, SM1 $BH!?t(B |
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@subsection @code{sm1_appell4} |
@subsection @code{sm1_appell4} |
@findex sm1_appell4 |
@findex sm1_appell4 |
@table @t |
@table @t |
Line 2711 def sm1_rrank(A) { |
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Line 2634 def sm1_rrank(A) { |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_rank:: |
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@end menu |
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@node sm1_rank,,, SM1 Functions |
@node sm1_rank,,, SM1 Functions |
@subsection @code{sm1_rank} |
@subsection @code{sm1_rank} |
@findex sm1_rank |
@findex sm1_rank |
Line 2743 holonomic. It is generally faster than @code{sm1_rank} |
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Line 2663 holonomic. It is generally faster than @code{sm1_rank} |
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*/ |
*/ |
|
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_rank,,, SM1 Functions |
* sm1_rank:: |
|
@end menu |
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@node sm1_rank,,, SM1 $BH!?t(B |
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@subsection @code{sm1_rank} |
@subsection @code{sm1_rank} |
@findex sm1_rank |
@findex sm1_rank |
@table @t |
@table @t |
Line 2804 def sm1_auto_reduce(T) { |
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Line 2721 def sm1_auto_reduce(T) { |
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} |
} |
|
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_auto_reduce:: |
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@end menu |
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@node sm1_auto_reduce,,, SM1 Functions |
@node sm1_auto_reduce,,, SM1 Functions |
@subsection @code{sm1_auto_reduce} |
@subsection @code{sm1_auto_reduce} |
@findex sm1_auto_reduce |
@findex sm1_auto_reduce |
Line 2833 Grobner bases. This is the default. |
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Line 2747 Grobner bases. This is the default. |
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*/ |
*/ |
|
|
/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_auto_reduce,,, SM1 Functions |
* sm1_auto_reduce:: |
|
@end menu |
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@node sm1_auto_reduce,,, SM1 $BH!?t(B |
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@subsection @code{sm1_auto_reduce} |
@subsection @code{sm1_auto_reduce} |
@findex sm1_auto_reduce |
@findex sm1_auto_reduce |
@table @t |
@table @t |
Line 2874 def sm1_slope(II,V,FF,VF) { |
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Line 2785 def sm1_slope(II,V,FF,VF) { |
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/*&eg-texi |
/*&eg-texi |
@menu |
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* sm1_slope:: |
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@end menu |
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@node sm1_slope,,, SM1 Functions |
@node sm1_slope,,, SM1 Functions |
@subsection @code{sm1_slope} |
@subsection @code{sm1_slope} |
@findex sm1_slope |
@findex sm1_slope |
Line 2906 of the system of differential equations @var{ii} |
|
Line 2814 of the system of differential equations @var{ii} |
|
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, |
|
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. |
@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 |
|
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 |
/*&jp-texi |
@menu |
@node sm1_slope,,, SM1 Functions |
* sm1_slope:: |
|
@end menu |
|
@node sm1_slope,,, SM1 $BH!?t(B |
|
@subsection @code{sm1_slope} |
@subsection @code{sm1_slope} |
@findex sm1_slope |
@findex sm1_slope |
@table @t |
@table @t |
Line 2950 not bihomogeneous. |
|
Line 2858 not bihomogeneous. |
|
$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$$$F$O(B, |
@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B. |
|
$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B |
|
microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B. |
|
@end itemize |
|
|
|
@noindent |
|
Algorithm: |
"A.Assi, F.J.Castro-Jimenez and J.M.Granger, |
"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. |
|
$B@.J,%j%9%H$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 |
/*&C-texi |
Line 2992 microcharacteristic variety $B$,(B bihomogeneous $B |
|
Line 2902 microcharacteristic variety $B$,(B bihomogeneous $B |
|
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm_gb} |
@code{sm_gb} |
@end table |
@end table |
|
*/ |
|
|
|
|
|
/*&eg-texi |
|
@include sm1-auto-en.texi |
|
*/ |
|
|
|
/*&jp-texi |
|
@include sm1-auto-ja.texi |
*/ |
*/ |
|
|
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