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Diff for /OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave between version 1.3 and 1.7

version 1.3, 2001/07/12 00:46:29 version 1.7, 2003/05/04 08:37:40
Line 1 
Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.2 2001/07/11 06:23:16 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.6 2002/08/23 08:16:13 takayama Exp $ */
   
 /*&C-texi  /*&C-texi
 @c DO NOT EDIT THIS FILE   oxphc.texi  @c DO NOT EDIT THIS FILE   oxphc.texi
 */  */
   /*&C-texi
   @node SM1 Functions,,, Top
   */
 /*&jp-texi  /*&jp-texi
 @node SM1 $BH!?t(B,,, Top  
 @chapter SM1 $BH!?t(B  @chapter SM1 $BH!?t(B
   
 $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
Line 33  $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE
 @end tex  @end tex
 */  */
 /*&eg-texi  /*&eg-texi
 @node SM1 Functions,,, Top  
 @chapter SM1 Functions  @chapter SM1 Functions
   
 This chapter describes  interface functions for  This chapter describes  interface functions for
Line 69  cohomology groups.
Line 70  cohomology groups.
 /*&C-texi  /*&C-texi
 @example  @example
   
 This is Risa/Asir, Version 20000126.  @include opening.texi
 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  
   
 [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
Line 85  Grobner Deformations of Hypergeometric Differential Eq
 1999, Springer.  1999, Springer.
 See the appendix.  See the appendix.
 */  */
   
   /*
   @menu
   * ox_sm1_forAsir::
   * sm1_start::
   * sm1::
   * sm1_push_int0::
   * sm1_gb::
   * sm1_deRham::
   * sm1_hilbert::
   * hilbert_polynomial::
   * sm1_genericAnn::
   * sm1_wTensor0::
   * sm1_reduction::
   * sm1_xml_tree_to_prefix_string::
   * sm1_syz::
   * sm1_mul::
   * sm1_distraction::
   * sm1_gkz::
   * sm1_appell1::
   * sm1_appell4::
   * sm1_rank::
   * sm1_auto_reduce::
   * sm1_slope::
   @end menu
   */
   
 /*&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.
Line 120  See the appendix.
 */  */
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * ox_sm1_forAsir::  
 @end menu  
 @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.
Line 151  to build your own server by reading @code{sm1} macros.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&jp-texi
 @menu  
 * ox_sm1_forAsir::  
 @end menu  
 @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) {
Line 207  def sm1_check_server(P) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_start  @c sort-sm1_start
 @menu  
 * sm1_start::  
 @end menu  
 @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_
Line 247  differential operators in default. (cf. @code{Sm1_ord_
 */  */
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_start  @c sort-sm1_start
 @menu  @node sm1_start,,, SM1 Functions
 * sm1_start::  
 @end menu  
 @node sm1_start,,, SM1 $BH!?t(B  
 @subsection @code{sm1_start}  @subsection @code{sm1_start}
 @findex sm1_start  @findex sm1_start
 @table @t  @table @t
Line 337  def sm1push(P,F) {
Line 348  def sm1push(P,F) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1  @c sort-sm1
 @menu  
 * sm1::  
 @end menu  
 @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}.
Line 371  to execute the command string @var{s}.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1,,, SM1 Functions
 * sm1::  
 @end menu  
 @node sm1,,, SM1 $BH!?t(B  
 @subsection @code{sm1}  @subsection @code{sm1}
 @findex sm1  @findex sm1
 @table @t  @table @t
Line 407  def sm1(P,F) {
Line 412  def sm1(P,F) {
 /*&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
 */  */
   
Line 523  def sm1_push_int0_R(A,P) {
Line 528  def sm1_push_int0_R(A,P) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_push_int0  @c sort-sm1_push_int0
 @menu  
 * sm1_push_int0::  
 @end menu  
 @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
Line 566  Note that @code{ox_push_cmo(@var{p},1234)} send the bi
 */  */
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_push_int0  @c sort-sm1_push_int0
 @menu  @node sm1_push_int0,,, SM1 Functions
 * sm1_push_int0::  
 @end menu  
 @node sm1_push_int0,,, SM1 $BH!?t(B  
 @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) {
Line 758  def sm1_isListOfVar(A) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_gb  @c sort-sm1_gb
 @menu  
 * sm1_gb::  
 @end menu  
 @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}
Line 820  List
Line 816  List
 */  */
 /*&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  
 @node sm1_gb,,, SM1 $BH!?t(B  
 @node sm1_gb_d,,, SM1 $BH!?t(B  
 @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) {
Line 1011  def sm1_pgb(A) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_deRham  @c sort-sm1_deRham
 @menu  
 * sm1_deRham::  
 @end menu  
 @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
Line 1056  mode. So, it is strongly recommended to execute the co
 */  */
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_deRham  @c sort-sm1_deRham
 @menu  @node sm1_deRham,,, SM1 Functions
 * sm1_deRham::  
 @end menu  
 @node sm1_deRham,,, SM1 $BH!?t(B  
 @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
Line 1110  mode. So, it is strongly recommended to execute the co
 @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
Line 1120  mode. So, it is strongly recommended to execute the co
 @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) {
Line 1230  def sm1_reduction_noH_d(F,G) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_hilbert  @c sort-sm1_hilbert
 @menu  
 * sm1_hilbert::  
 * hilbert_polynomial::  
 @end menu  
 @node sm1_hilbert,,, SM1 Functions  @node sm1_hilbert,,, SM1 Functions
 @subsection @code{sm1_hilbert}  @subsection @code{sm1_hilbert}
 @findex sm1_hilbert  @findex sm1_hilbert
Line 1289  List
Line 1272  List
 */  */
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_hilbert  @c sort-sm1_hilbert
 @menu  @node sm1_hilbert,,, SM1 Functions
 * sm1_hilbert::  
 * hilbert_polynomial::  
 @end menu  
 @node sm1_hilbert,,, SM1 $BH!?t(B  
 @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) {
Line 1368  def sm1_hilbert(A) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_genericAnn  @c sort-sm1_genericAnn
 @menu  
 * sm1_genericAnn::  
 @end menu  
 @node sm1_genericAnn,,, SM1 Functions  @node sm1_genericAnn,,, SM1 Functions
 @subsection @code{sm1_genericAnn}  @subsection @code{sm1_genericAnn}
 @findex sm1_genericAnn  @findex sm1_genericAnn
Line 1421  List
Line 1397  List
 */  */
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_genericAnn  @c sort-sm1_genericAnn
 @menu  @node sm1_genericAnn,,, SM1 Functions
 * sm1_genericAnn::  
 @end menu  
 @node sm1_genericAnn,,, SM1 $BH!?t(B  
 @subsection @code{sm1_genericAnn}  @subsection @code{sm1_genericAnn}
 @findex sm1_genericAnn  @findex sm1_genericAnn
 @table @t  @table @t
Line 1491  def sm1_tensor0(F) {
Line 1464  def sm1_tensor0(F) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_wTensor0  @c sort-sm1_wTensor0
 @menu  
 * sm1_wTensor0::  
 @end menu  
 @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.
Line 1505  the inputs @var{f} and @var{g} are left ideals of D.
   
 /*&jp-texi  /*&jp-texi
 @c sort-sm1_wTensor0  @c sort-sm1_wTensor0
 @menu  @node sm1_wTensor0,,, SM1 Functions
 * sm1_wTensor0::  
 @end menu  
 @node sm1_wTensor0,,, SM1 $BH!?t(B  
 @subsection @code{sm1_wTensor0}  @subsection @code{sm1_wTensor0}
 @findex sm1_wTensor0  @findex sm1_wTensor0
 @table @t  @table @t
Line 1597  def sm1_wTensor0(F) {
Line 1564  def sm1_wTensor0(F) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_reduction  @c sort-sm1_reduction
 @menu  
 * sm1_reduction::  
 @end menu  
 @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 1627  division algorithm to @var{f}. The set of variables is
Line 1591  division algorithm to @var{f}. The set of variables is
 @code{sm1_reduction_noH} is for the Weyl algebra.  @code{sm1_reduction_noH} is for the Weyl algebra.
 @item The return value is of the form  @item The return value is of the form
 [r,c0,[c1,...,cm],[g1,...gm]] where @var{g}=[g1, ..., gm] and  [r,c0,[c1,...,cm],[g1,...gm]] where @var{g}=[g1, ..., gm] and
 r/c0 + c1 g1 + ... + cm gm = 0.  c0 f + c1 g1 + ... + cm gm = r.
 r/c0 is the normal form.  r/c0 is the normal form.
 @item The function reduction reduces reducible terms that appear  @item The function reduction reduces reducible terms that appear
 in lower order terms.  in lower order terms.
Line 1637  are for distributed polynomials.
Line 1601  are for distributed polynomials.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_reduction,,, SM1 Functions
 * sm1_reduction::  
 @end menu  
 @node sm1_reduction,,, SM1 $BH!?t(B  
 @subsection @code{sm1_reduction}  @subsection @code{sm1_reduction}
 @findex sm1_reduction  @findex sm1_reduction
 @table @t  @table @t
Line 1668  are for distributed polynomials.
Line 1629  are for distributed polynomials.
 $B>JN,$7$F$b$h$$(B.  $B>JN,$7$F$b$h$$(B.
 @code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B.  @code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B.
 @item $BLa$jCM$O<!$N7A$r$7$F$$$k(B:  @item $BLa$jCM$O<!$N7A$r$7$F$$$k(B:
 [r,c0,[c1,...,cm],[g1,...gm]] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,  [r,c0,[c1,...,cm],g] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,
 r/c0 + c1 g1 + ... + cm gm = 0  c0 f + c1 g1 + ... + cm gm = r
 $B$,$J$j$?$D(B.  $B$,$J$j$?$D(B.
 r/c0 $B$,(B normal form $B$G$"$k(B.  r/c0 $B$,(B normal form $B$G$"$k(B.
 @item $B$3$NH!?t$O(B, $BDc<!9`$K$"$i$o$l$k(B reducible $B$J9`$b4JC12=$9$k(B.  @item $B$3$NH!?t$O(B, $BDc<!9`$K$"$i$o$l$k(B reducible $B$J9`$b4JC12=$9$k(B.
Line 1681  sm1_reduction_d(P,F,G) $B$*$h$S(B sm1_reduction_noH_
Line 1642  sm1_reduction_d(P,F,G) $B$*$h$S(B sm1_reduction_noH_
 /*&C-texi  /*&C-texi
 @example  @example
 [259] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);  [259] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);
 [x^2+y^2-4,1,[0,0],[x+y^3-4*y,y^4-4*y^2+1]]  [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
 [260] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);  [260] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);
 [0,1,[-y^2+4,-x+y^3-4*y],[x+y^3-4*y,y^4-4*y^2+1]]  [0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]
 @end example  @end example
 */  */
 /*&eg-texi  /*&eg-texi
Line 1734  def sm1_reduction_noH(A) {
Line 1695  def sm1_reduction_noH(A) {
 }  }
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_xml_tree_to_prefix_string::  
 @end menu  
 @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.)
Line 1723  command search path.)
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_xml_tree_to_prefix_string,,, SM1 Functions
 * sm1_xml_tree_to_prefix_string::  
 @end menu  
 @node sm1_xml_tree_to_prefix_string,,, SM1 $BH!?t(B  
 @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) {
Line 1846  def sm1_res_div(A) {
   
 /*&eg-texi  /*&eg-texi
 @c sort-sm1_syz  @c sort-sm1_syz
 @menu  
 * sm1_syz::  
 @end menu  
 @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
Line 1890  In summary, @var{g} = @var{m} @var{f} and
 */  */
 /*&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  
 @node sm1_syz,,, SM1 $BH!?t(B  
 @node sm1_syz_d,,, SM1 $BH!?t(B  
 @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) {
Line 1986  def sm1_mul(A,B,V) {
 }  }
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_mul::  
 @end menu  
 @node sm1_mul,,, SM1 Functions  @node sm1_mul,,, SM1 Functions
 @subsection @code{sm1_mul}  @subsection @code{sm1_mul}
 @findex sm1_mul  @findex sm1_mul
Line 2066  List
Line 2012  List
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_mul,,, SM1 Functions
 * sm1_mul::  
 @end menu  
 @node sm1_mul,,, SM1 $BH!?t(B  
 @subsection @code{sm1_mul}  @subsection @code{sm1_mul}
 @findex sm1_mul  @findex sm1_mul
 @table @t  @table @t
Line 2233  def sm1_distraction(A) {
Line 2176  def sm1_distraction(A) {
 }  }
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_distraction::  
 @end menu  
 @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 
Line 2207  See Saito, Sturmfels, Takayama : Grobner Deformations 
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_distraction,,, SM1 Functions
 * sm1_distraction::  
 @end menu  
 @node sm1_distraction,,, SM1 $BH!?t(B  
   
 @subsection @code{sm1_distraction}  @subsection @code{sm1_distraction}
 @findex sm1_distraction  @findex sm1_distraction
Line 2390  def sm1_gkz(S) {
Line 2327  def sm1_gkz(S) {
   
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_gkz::  
 @end menu  
 @node sm1_gkz,,, SM1 Functions  @node sm1_gkz,,, SM1 Functions
 @subsection @code{sm1_gkz}  @subsection @code{sm1_gkz}
 @findex sm1_gkz  @findex sm1_gkz
Line 2418  List
Line 2352  List
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_gkz,,, SM1 Functions
 * sm1_gkz::  
 @end menu  
 @node sm1_gkz,,, SM1 $BH!?t(B  
 @subsection @code{sm1_gkz}  @subsection @code{sm1_gkz}
 @findex sm1_gkz  @findex sm1_gkz
 @table @t  @table @t
Line 2503  def sm1aux_x(I) {
Line 2434  def sm1aux_x(I) {
   
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_appell1::  
 @end menu  
 @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
Line 2461  The parameters a, c, b1, ..., bn may be rational numbe
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_appell1,,, SM1 Functions
 * sm1_appell1::  
 @end menu  
 @node sm1_appell1,,, SM1 $BH!?t(B  
 @subsection @code{sm1_appell1}  @subsection @code{sm1_appell1}
 @findex sm1_appell1  @findex sm1_appell1
 @table @t  @table @t
Line 2618  def sm1_appell4(S) {
Line 2543  def sm1_appell4(S) {
 }  }
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_appell4::  
 @end menu  
 @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
Line 2570  The parameters a, b, c1, ..., cn may be rational numbe
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_appell4,,, SM1 Functions
 * sm1_appell4::  
 @end menu  
 @node sm1_appell4,,, SM1 $BH!?t(B  
 @subsection @code{sm1_appell4}  @subsection @code{sm1_appell4}
 @findex sm1_appell4  @findex sm1_appell4
 @table @t  @table @t
Line 2715  def sm1_rrank(A) {
Line 2634  def sm1_rrank(A) {
   
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_rank::  
 @end menu  
 @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}
Line 2663  holonomic. It is generally faster than @code{sm1_rank}
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_rank,,, SM1 Functions
 * sm1_rank::  
 @end menu  
 @node sm1_rank,,, SM1 $BH!?t(B  
 @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) {
Line 2721  def sm1_auto_reduce(T) {
 }  }
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_auto_reduce::  
 @end menu  
 @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.
Line 2747  Grobner bases.  This is the default.
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node sm1_auto_reduce,,, SM1 Functions
 * sm1_auto_reduce::  
 @end menu  
 @node sm1_auto_reduce,,, SM1 $BH!?t(B  
 @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) {
Line 2785  def sm1_slope(II,V,FF,VF) {
   
   
 /*&eg-texi  /*&eg-texi
 @menu  
 * sm1_slope::  
 @end menu  
 @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}
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
   
   @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 2954  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 2996  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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