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Diff for /OpenXM/src/asir-doc/parts/groebner.texi between version 1.7 and 1.9

version 1.7, 2003/04/21 03:07:32 version 1.9, 2003/04/24 08:13:24
Line 1 
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.6 2003/04/20 09:55:18 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.8 2003/04/21 08:30:01 noro Exp $
 \BJP  \BJP
 @node $B%0%l%V%J4pDl$N7W;;(B,,, Top  @node $B%0%l%V%J4pDl$N7W;;(B,,, Top
 @chapter $B%0%l%V%J4pDl$N7W;;(B  @chapter $B%0%l%V%J4pDl$N7W;;(B
Line 1354  Computation of the global b function is implemented as
Line 1354  Computation of the global b function is implemented as
 * lex_hensel_gsl tolex_gsl tolex_gsl_d::  * lex_hensel_gsl tolex_gsl tolex_gsl_d::
 * primadec primedec::  * primadec primedec::
 * primedec_mod::  * primedec_mod::
 * bfunction generic_bfct::  * bfunction bfct generic_bfct::
 @end menu  @end menu
   
 \JP @node gr hgr gr_mod,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B  \JP @node gr hgr gr_mod,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
Line 1690  processes.
Line 1690  processes.
 @item lex_hensel_gsl(@var{plist},@var{vlist1},@var{order},@var{vlist2},@var{homo})  @item lex_hensel_gsl(@var{plist},@var{vlist1},@var{order},@var{vlist2},@var{homo})
 \JP :: GSL $B7A<0$N%$%G%"%k4pDl$N7W;;(B  \JP :: GSL $B7A<0$N%$%G%"%k4pDl$N7W;;(B
 \EG ::Computation of an GSL form ideal basis  \EG ::Computation of an GSL form ideal basis
 @item tolex_gsl(@var{plist},@var{vlist1},@var{order},@var{vlist2},@var{homo})  @item tolex_gsl(@var{plist},@var{vlist1},@var{order},@var{vlist2})
 @itemx tolex_gsl_d(@var{plist},@var{vlist1},@var{order},@var{vlist2},@var{homo},@var{procs})  @itemx tolex_gsl_d(@var{plist},@var{vlist1},@var{order},@var{vlist2},@var{procs})
 \JP :: $B%0%l%V%J4pDl$rF~NO$H$9$k(B, GSL $B7A<0$N%$%G%"%k4pDl$N7W;;(B  \JP :: $B%0%l%V%J4pDl$rF~NO$H$9$k(B, GSL $B7A<0$N%$%G%"%k4pDl$N7W;;(B
 \EG :: Computation of an GSL form ideal basis stating from a Groebner basis  \EG :: Computation of an GSL form ideal basis stating from a Groebner basis
 @end table  @end table
Line 3918  execute @code{dp_gr_print(2)} in advance.
Line 3918  execute @code{dp_gr_print(2)} in advance.
 @fref{dp_gr_flags dp_gr_print}.  @fref{dp_gr_flags dp_gr_print}.
 @end table  @end table
   
 \JP @node bfunction generic_bfct,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B  \JP @node bfunction bfct generic_bfct,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
 \EG @node bfunction generic_bfct,,, Functions for Groebner basis computation  \EG @node bfunction bfct generic_bfct,,, Functions for Groebner basis computation
 @subsection @code{bfunction}, @code{generic_bfct}  @subsection @code{bfunction}, @code{bfct}, @code{generic_bfct}
 @findex bfunction  @findex bfunction
   @findex bfct
 @findex generic_bfct  @findex generic_bfct
   
 @table @t  @table @t
 @item bfunction(@var{f})  @item bfunction(@var{f})
   @item bfct(@var{f})
 @item generic_bfct(@var{plist},@var{vlist},@var{dvlist},@var{weight})  @item generic_bfct(@var{plist},@var{vlist},@var{dvlist},@var{weight})
 \JP :: b $B4X?t$N7W;;(B  \JP :: b $B4X?t$N7W;;(B
 \EG :: Computes the global b function of a polynomial or an ideal  \EG :: Computes the global b function of a polynomial or an ideal
Line 3946  execute @code{dp_gr_print(2)} in advance.
Line 3948  execute @code{dp_gr_print(2)} in advance.
 @itemize @bullet  @itemize @bullet
 \BJP  \BJP
 @item @samp{bfct} $B$GDj5A$5$l$F$$$k(B.  @item @samp{bfct} $B$GDj5A$5$l$F$$$k(B.
 @item @code{bfunction(@var{f})} $B$OB?9`<0(B @var{f} $B$N(B global b $B4X?t(B @code{b(s)} $B$r(B  @item @code{bfunction(@var{f})}, @code{bfct(@var{f})} $B$OB?9`<0(B @var{f} $B$N(B global b $B4X?t(B @code{b(s)} $B$r(B
 $B7W;;$9$k(B. @code{b(s)} $B$O(B, Weyl $BBe?t(B @code{D} $B>e$N0lJQ?tB?9`<04D(B @code{D[s]}  $B7W;;$9$k(B. @code{b(s)} $B$O(B, Weyl $BBe?t(B @code{D} $B>e$N0lJQ?tB?9`<04D(B @code{D[s]}
 $B$N85(B @code{P(x,s)} $B$,B8:_$7$F(B, @code{P(x,s)f^(s+1)=b(s)f^s} $B$rK~$?$9$h$&$J(B  $B$N85(B @code{P(x,s)} $B$,B8:_$7$F(B, @code{P(x,s)f^(s+1)=b(s)f^s} $B$rK~$?$9$h$&$J(B
 $BB?9`<0(B @code{b(s)} $B$NCf$G(B, $B<!?t$,:G$bDc$$$b$N$G$"$k(B.  $BB?9`<0(B @code{b(s)} $B$NCf$G(B, $B<!?t$,:G$bDc$$$b$N$G$"$k(B.
Line 3955  execute @code{dp_gr_print(2)} in advance.
Line 3957  execute @code{dp_gr_print(2)} in advance.
 $B%&%'%$%H(B @var{weight} $B$K4X$9$k(B global b $B4X?t$r7W;;$9$k(B.  $B%&%'%$%H(B @var{weight} $B$K4X$9$k(B global b $B4X?t$r7W;;$9$k(B.
 @var{vlist} $B$O(B @code{x}-$BJQ?t(B, @var{vlist} $B$OBP1~$9$k(B @code{D}-$BJQ?t(B  @var{vlist} $B$O(B @code{x}-$BJQ?t(B, @var{vlist} $B$OBP1~$9$k(B @code{D}-$BJQ?t(B
 $B$r=g$KJB$Y$k(B.  $B$r=g$KJB$Y$k(B.
   @item @code{bfunction} $B$H(B @code{bfct} $B$G$OMQ$$$F$$$k%"%k%4%j%:%`$,(B
   $B0[$J$k(B. $B$I$A$i$,9bB.2=$OF~NO$K$h$k(B.
 @item $B>\:Y$K$D$$$F$O(B, [Saito,Sturmfels,Takayama] $B$r8+$h(B.  @item $B>\:Y$K$D$$$F$O(B, [Saito,Sturmfels,Takayama] $B$r8+$h(B.
 \E  \E
 \BEG  \BEG
 @item These functions are defined in @samp{bfct}.  @item These functions are defined in @samp{bfct}.
 @item @code{bfunction(@var{f})} computes the global b-function @code{b(s)} of  @item @code{bfunction(@var{f})} and @code{bfct(@var{f})} compute the global b-function @code{b(s)} of
 a polynomial @var{f}.  a polynomial @var{f}.
 @code{b(s)} is a polynomial of the minimal degree  @code{b(s)} is a polynomial of the minimal degree
 such that there exists @code{P(x,s)} in D[s], which is a polynomial  such that there exists @code{P(x,s)} in D[s], which is a polynomial
Line 3969  computes the global b-function of a left ideal @code{I
Line 3973  computes the global b-function of a left ideal @code{I
 generated by @var{plist}, with respect to @var{weight}.  generated by @var{plist}, with respect to @var{weight}.
 @var{vlist} is the list of @code{x}-variables,  @var{vlist} is the list of @code{x}-variables,
 @var{vlist} is the list of corresponding @code{D}-variables.  @var{vlist} is the list of corresponding @code{D}-variables.
   @item @code{bfunction(@var{f})} and @code{bfct(@var{f})} implement
   different algorithms and the efficiency depends on inputs.
 @item See [Saito,Sturmfels,Takayama] for the details.  @item See [Saito,Sturmfels,Takayama] for the details.
 \E  \E
 @end itemize  @end itemize
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