===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/parts/groebner.texi,v
retrieving revision 1.18
retrieving revision 1.21
diff -u -p -r1.18 -r1.21
--- OpenXM/src/asir-doc/parts/groebner.texi	2016/03/24 20:58:50	1.18
+++ OpenXM/src/asir-doc/parts/groebner.texi	2018/09/06 05:42:43	1.21
@@ -1,4 +1,4 @@
-@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.17 2006/09/06 23:53:31 noro Exp $
+@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.20 2017/08/31 04:54:36 takayama Exp $
 \BJP
 @node $B%0%l%V%J4pDl$N7W;;(B,,, Top
 @chapter $B%0%l%V%J4pDl$N7W;;(B
@@ -201,16 +201,16 @@ In an @b{Asir} session, it is displayed in the form li
 \EG and also can be input in such a form.
 
 \BJP
-@itemx $BF,C19`<0(B (head monomial)
 @item $BF,9`(B (head term)
+@itemx $BF,C19`<0(B (head monomial)
 @itemx $BF,78?t(B (head coefficient)
 $BJ,;6I=8=B?9`<0$K$*$1$k3FC19`<0$O(B, $B9`=g=x$K$h$j@0Ns$5$l$k(B. $B$3$N;~=g(B
 $B=x:GBg$NC19`<0$rF,C19`<0(B, $B$=$l$K8=$l$k9`(B, $B78?t$r$=$l$>$lF,9`(B, $BF,78?t(B
 $B$H8F$V(B. 
 \E
 \BEG
-@itemx head monomial
 @item head term
+@itemx head monomial
 @itemx head coefficient
       
 Monomials in a distributed polynomial is sorted by a total order.
@@ -220,7 +220,45 @@ the head term and the head coefficient respectively.
 \E
 @end table
 
+@noindent
+ChangeLog
+@itemize @bullet
 \BJP
+@item $BJ,;6I=8=B?9`<0$OG$0U$N%*%V%8%'%/%H$r78?t$K$b$F$k$h$&$K$J$C$?(B.
+$B$^$?2C72$N(Bk$B@.J,$NMWAG$r<!$N7A<0(B <<d0,d1,...:k>> $B$GI=8=$9$k$h$&$K$J$C$?(B (2017-08-31).
+\E
+\BEG
+@item Distributed polynomials accept objects as coefficients.
+The k-th element of a free module is expressed as <<d0,d1,...:k>> (2017-08-31).
+\E
+@item 
+1.15 algnum.c,
+1.53 ctrl.c,
+1.66 dp-supp.c,
+1.105 dp.c,
+1.73 gr.c,
+1.4 reduct.c,
+1.16 _distm.c,
+1.17 dalg.c,
+1.52 dist.c,
+1.20 distm.c,
+1.8  gmpq.c,
+1.238 engine/nd.c,
+1.102  ca.h,
+1.411  version.h,
+1.28 cpexpr.c,
+1.42 pexpr.c,
+1.20 pexpr_body.c,
+1.40 spexpr.c,
+1.27 arith.c,
+1.77 eval.c,
+1.56 parse.h,
+1.37 parse.y,
+1.8 stdio.c,
+1.31 plotf.c
+@end itemize
+
+\BJP
 @node $B%U%!%$%k$NFI$_9~$_(B,,, $B%0%l%V%J4pDl$N7W;;(B
 @section $B%U%!%$%k$NFI$_9~$_(B
 \E
@@ -1531,6 +1569,8 @@ Computation of the global b function is implemented as
 @item
 $BI8=`%i%$%V%i%j$N(B @samp{gr} $B$GDj5A$5$l$F$$$k(B. 
 @item
+gr $B$rL>A0$K4^$`4X?t$O8=:_%a%s%F$5$l$F$$$J$$(B. @code{nd_gr}$B7O$N4X?t$rBe$o$j$KMxMQ$9$Y$-$G$"$k(B(@fref{nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace}).
+@item
 $B$$$:$l$b(B, $BB?9`<0%j%9%H(B @var{plist} $B$N(B, $BJQ?t=g=x(B @var{vlist}, $B9`=g=x7?(B
 @var{order} $B$K4X$9$k%0%l%V%J4pDl$r5a$a$k(B. @code{gr()}, @code{hgr()}
 $B$O(B $BM-M}?t78?t(B, @code{gr_mod()} $B$O(B GF(@var{p}) $B78?t$H$7$F7W;;$9$k(B. 
@@ -1562,6 +1602,9 @@ CPU $B;~4V$G$"$j(B, $B$3$NH!?t$N>l9g$O$[$H$s$IDL?.$
 @item 
 These functions are defined in @samp{gr} in the standard library
 directory.
+@item
+Functions of which names contains gr are obsolted. 
+Functions of @code{nd_gr} families should be used (@fref{nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace}).
 @item 
 They compute a Groebner basis of a polynomial list @var{plist} with
 respect to the variable order @var{vlist} and the order type @var{order}.
@@ -2320,7 +2363,7 @@ except for lack of the argument for controlling homoge
 @itemx nd_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order})
 @itemx nd_f4(@var{plist},@var{vlist},@var{modular},@var{order})
 @itemx nd_f4_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order})
-@item nd_weyl_gr(@var{plist},@var{vlist},@var{p},@var{order})
+@itemx nd_weyl_gr(@var{plist},@var{vlist},@var{p},@var{order})
 @itemx nd_weyl_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order})
 \JP :: $B%0%l%V%J4pDl$N7W;;(B ($BAH$_9~$_H!?t(B)
 \EG :: Groebner basis computation (built-in functions)
@@ -2973,7 +3016,7 @@ These are used internally in @code{hgr()} etc.
 into an integral distributed polynomial such that GCD of all its coefficients
 is 1.
 \E
-@itemx dp_prim(@var{dpoly})
+@item dp_prim(@var{dpoly})
 \JP :: $BM-M}<0G\$7$F78?t$r@0?t78?tB?9`<078?t$+$D78?t$NB?9`<0(B GCD $B$r(B 1 $B$K$9$k(B. 
 \BEG
 :: Converts a distributed polynomial @var{poly} with rational function
@@ -3900,7 +3943,7 @@ refer to @code{dp_true_nf()} and @code{dp_true_nf_mod(
 @fref{dp_ptod},
 @fref{dp_dtop},
 @fref{dp_ord},
-@fref{dp_nf dp_nf_mod dp_true_nf dp_true_nf_mod}.
+@fref{dp_nf dp_nf_mod dp_true_nf dp_true_nf_mod dp_weyl_nf dp_weyl_nf_mod}.
 @end table
 
 \JP @node p_terms,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B