version 1.4, 2002/07/14 13:14:37 |
version 1.6, 2002/08/23 08:16:13 |
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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 1.5 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} |
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*/ |
*/ |
/*&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 |
Line 1018 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 1066 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 1123 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 1133 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 1243 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 1389 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 1491 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 1535 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 1597 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 1637 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 1734 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 1765 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 1891 def sm1_res_div(A) { |
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Line 1846 def sm1_res_div(A) { |
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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 1938 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 2037 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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*/ |
*/ |
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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 2233 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 2267 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 2390 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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*/ |
*/ |
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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 2503 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 2533 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 2618 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 2648 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 2715 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 2747 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:: |
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@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 2808 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 2837 Grobner bases. This is the default. |
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Line 2747 Grobner bases. This is the default. |
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*/ |
*/ |
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/*&jp-texi |
/*&jp-texi |
@menu |
@node sm1_auto_reduce,,, SM1 Functions |
* sm1_auto_reduce:: |
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@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 2878 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 2910 of the system of differential equations @var{ii} |
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Line 2814 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 |
@menu |
@node sm1_slope,,, SM1 Functions |
* sm1_slope:: |
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@end menu |
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@node sm1_slope,,, SM1 $BH!?t(B |
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@subsection @code{sm1_slope} |
@subsection @code{sm1_slope} |
@findex sm1_slope |
@findex sm1_slope |
@table @t |
@table @t |
Line 2954 not bihomogeneous. |
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Line 2858 not bihomogeneous. |
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$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 |