===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/parts/groebner.texi,v
retrieving revision 1.8
retrieving revision 1.9
diff -u -p -r1.8 -r1.9
--- OpenXM/src/asir-doc/parts/groebner.texi	2003/04/21 08:30:01	1.8
+++ OpenXM/src/asir-doc/parts/groebner.texi	2003/04/24 08:13:24	1.9
@@ -1,4 +1,4 @@
-@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.7 2003/04/21 03:07:32 noro Exp $
+@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.8 2003/04/21 08:30:01 noro Exp $
 \BJP
 @node グレブナ基底の計算,,, Top
 @chapter グレブナ基底の計算
@@ -1354,7 +1354,7 @@ Computation of the global b function is implemented as
 * lex_hensel_gsl tolex_gsl tolex_gsl_d::
 * primadec primedec::
 * primedec_mod::
-* bfunction generic_bfct::
+* bfunction bfct generic_bfct::
 @end menu
 
 \JP @node gr hgr gr_mod,,, グレブナ基底に関する函数
@@ -3918,14 +3918,16 @@ execute @code{dp_gr_print(2)} in advance.
 @fref{dp_gr_flags dp_gr_print}.
 @end table
 
-\JP @node bfunction generic_bfct,,, グレブナ基底に関する函数
-\EG @node bfunction generic_bfct,,, Functions for Groebner basis computation
-@subsection @code{bfunction}, @code{generic_bfct}
+\JP @node bfunction bfct generic_bfct,,, グレブナ基底に関する函数
+\EG @node bfunction bfct generic_bfct,,, Functions for Groebner basis computation
+@subsection @code{bfunction}, @code{bfct}, @code{generic_bfct}
 @findex bfunction
+@findex bfct
 @findex generic_bfct
 
 @table @t
 @item bfunction(@var{f})
+@item bfct(@var{f})
 @item generic_bfct(@var{plist},@var{vlist},@var{dvlist},@var{weight})
 \JP :: b 関数の計算
 \EG :: Computes the global b function of a polynomial or an ideal
@@ -3946,7 +3948,7 @@ execute @code{dp_gr_print(2)} in advance.
 @itemize @bullet
 \BJP
 @item @samp{bfct} で定義されている. 
-@item @code{bfunction(@var{f})} は多項式 @var{f} の global b 関数 @code{b(s)} を
+@item @code{bfunction(@var{f})}, @code{bfct(@var{f})} は多項式 @var{f} の global b 関数 @code{b(s)} を
 計算する. @code{b(s)} は, Weyl 代数 @code{D} 上の一変数多項式環 @code{D[s]}
 の元 @code{P(x,s)} が存在して, @code{P(x,s)f^(s+1)=b(s)f^s} を満たすような
 多項式 @code{b(s)} の中で, 次数が最も低いものである. 
@@ -3955,11 +3957,13 @@ execute @code{dp_gr_print(2)} in advance.
 ウェイト @var{weight} に関する global b 関数を計算する. 
 @var{vlist} は @code{x}-変数, @var{vlist} は対応する @code{D}-変数
 を順に並べる. 
+@item @code{bfunction} と @code{bfct} では用いているアルゴリズムが
+異なる. どちらが高速化は入力による.
 @item 詳細については, [Saito,Sturmfels,Takayama] を見よ. 
 \E
 \BEG
 @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}.
 @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
@@ -3969,6 +3973,8 @@ computes the global b-function of a left ideal @code{I
 generated by @var{plist}, with respect to @var{weight}.
 @var{vlist} is the list of @code{x}-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.
 \E
 @end itemize