===================================================================
RCS file: /home/cvs/OpenXM/doc/Papers/rims2005-noro.tex,v
retrieving revision 1.1
retrieving revision 1.3
diff -u -p -r1.1 -r1.3
--- OpenXM/doc/Papers/rims2005-noro.tex	2005/12/18 11:06:23	1.1
+++ OpenXM/doc/Papers/rims2005-noro.tex	2006/03/27 22:16:05	1.3
@@ -151,7 +151,8 @@ $formula$ \>: Risa object
 $B4D$r$h$j0lHLE*$K$7$F$"$kE@$G0[$J$C$F$$$k(B 
 \footnote{Mathematica $B$K$*$$$F@Q$N(B {\tt Orderless} $BB0@-$r30$9$3$H$G(B,
 $B@Q$rHs2D49$K$G$-$k$,(B, $B4JC12=$K$*$$$F0[>o$J5sF0$r<($9$h$&$K$J$k(B (Ver. 4).
-Ver. 5 $B$G$O(B, $B78?t$^$GHs2D49$K$J$k(B.}.
+Ver. 5 $B$N=i4|$NHG$G$O(B, $B78?t$^$GHs2D49$K$J$C$?$,(B, $B:G6a$N$b$N$G$OD>$C$F$$$k(B
+$B$h$&$G$"$k(B.}.
 $B$5$i$K(B, $BI8=`7A$X$NJQ49;~$K(B, $B@Q$K4X$9$kJ,G[B'$rMxMQ$7$FE83+$5$l$?I8=`7A(B
 $B$rF@$k$3$H$b$G$-$k(B. 
 
@@ -274,7 +275,7 @@ $Condition$ $B$*$h$S(B $Action$ $B$K$O%f!<%6Dj5A4X?
 $B$K$"$k$,(B, $B$3$3$G$O?<F~$j$O$7$J$$(B. $B$3$3$G$O(B, $BL58B%k!<%W$K4Y$i$J$$$h$&$J(B
 $B<BMQE*$J;X?K$H$7$F(B, \FN $B$KBP$9$k=g=x$E$1$*$h$S(B weight $B$N;HMQ$rDs0F$9$k(B.  
 $B$3$NJ}K!$O8e=R$9$k$h$&$KB?9`<04D$dHyJ,:nMQAG4D$GMQ$$$i$l$k(B weight
-$B%Y%/%H%k$N9M$(7?$N<+A3$J0lHL2=$G$"$j(B, $BM}O@E*$K$b6=L#?<$$(B.
+$B%Y%/%H%k$N9M$(J}$N<+A3$J0lHL2=$G$"$j(B, $BM}O@E*$K$b6=L#?<$$(B.
 
 $BNc$H$7$F(B, $B2D49@-$rDj5A$9$k>l9g$r9M$($k(B. $B?t3XE*$K$O(B, $BG$0U$N(B $X$, $Y$ $B$K(B
 $BBP$7(B $XY=YX$ $B$G$h$$$,(B, $B$?$H$($P$3$N$^$^(B $[`X*Y,`Y*X]$ $B$H$$$&=q$-49$((B
@@ -375,17 +376,16 @@ $ \{ L_i \rightarrow R_i \} $
 \end{definition}
 %% z_2 z_1 --> z_1 z_2 + z_2 z_1  $BNc(B. z_1 > z_2 (lex) $B$H$9$k(B. $B$3$l$O$@$a(B.
 $B=q$-49$(5,B'$,$"$k@5?t%Y%/%H%k(B $H$ $B$K$D$$$FF1<!E*$G$"$k$3$H$+$i(B, 
-$B$3$l$i$N>r7o$K$h$j=q$-49$($,Dd;_@-$r$b$D$3$H$,J,$+$k(B. $B$5$i$K(B
-$B<!$NL?Bj$,@.$jN)$D(B.
+$B$3$l$i$N>r7o$K$h$j=q$-49$($,Dd;_@-$r$b$D$3$H$,J,$+$k(B. $B$5$i$K(B, 
 %%<hyperlink|G-algebra|http://www.singular.uni-kl.de/Manual/latest/sing_407.htm>
-\begin{proposition}\rm
-G-algebra \cite{LEV} $B$N>r7o$N$&$A(B, 
+%% z_j z_i \rightarrow c_{ij} z_i z_j + d_{ij}, i<j, c_{ij} \in K^*
+%% {\rm deg}_w(d_{ij}) \leq w_i + w_j
+$G$-algebra \cite{LEV} $B$N>r7o$N$&$A(B, 
 well order $B$NB8:_>r7o$r2>Dj$7$J$/$F$b(B,
 $BE,Ev$JF1<!2=(Bweight$B%Y%/%H%k(B, $BM-8z(B weight $B%Y%/%H%k$,B8:_$9$k$J$i$P(B,
 $h$ $B$r2C$($k@F<!2=(B,
 $h$ $B$r(B $1$ $B$H$*$/$3$H$K$h$kHs@F2=$K$h$j(B,
-$B%0%l%V%J!<4pDl$r7W;;$G$-$k$h$&$K$J$k(B.
-\end{proposition}
+$B%0%l%V%J!<4pDl$r7W;;$G$-$k$h$&$K$J$k$HM=A[$5$l$k(B.
 
 $B$3$N1~MQ$K:]$7$F$O(B, $BM?$($i$l$?=q$-49$(5,B'$KBP$7(B, $BM-8z(B weight $B%Y%/%H%k(B
 $w$ $B$r8+$D$1$kI,MW$,$"$k(B. 
@@ -510,18 +510,23 @@ Risa/Asir $B$K$*$1$k?t<0$NCf4VE*I=8=$G$"$k(B \FN $B
 $BI,MW$G$"$k(B.
 
 $B$3$N=q$-49$($H(Bweight $B%Y%/%H%k$K$h$kC19`<0Hf3S$rAH$_9g$o$;$k$3$H$K$h$j(B, 
-$B<+M37k9gBe?t$K$*$1$k0lHLE*$J%0%l%V%J4pDl$N7W;;$rO@$8$?(B.
+$B<+M37k9gBe?t$K$*$1$k0lHLE*$J=q$-49$(7W;;$rO@$8$?(B.
 $B$3$3$GDs0F$7$?0lHL2=$O(B Weyl $BBe?t$NF1<!2=$NM}O@$r4^$`(B.  Risa/Asir $B$G?7(B
 $B$7$/F3F~$7$?(B, \QT $B$KBP$9$k0lHLE*$J(B weight $B%Y%/%H%k$N%a%+%K%:%`(B
 \verb@ qt_set_weight @ $B$K$h$j$o$l$o$l$NM}O@$H%"%k%4%j%:%`$N%W%m%H%?%$(B
 $B%W$rMF0W$K;n$9$3$H$,2DG=$G$"$k(B.  V. Levandovskyy \cite{LEV} $B$O(B 
-$G$-algebra $B$N35G0$rF3F~$7$F(B, Singular $B$K<BAu$7$?$,(B, $B$o$l$o$l$N35G0$O(B
-$BF1<!2=$r$H$*$7$F(B, well order $B$G$J$$>l9g$K$bE,MQ$G$-$k(B.  
-$B$o$l$o$l$N%"%W%m!<%A$K$h$j(B, 
+$G$-algebra $B$N35G0$rF3F~$7$F(B, Singular $B$K<BAu$7$?(B.
+$B$o$l$o$l$N%"%W%m!<%A$rH/E8$5$;(B, 
+$BF1<!2=$r$H$*$7$F(B, well order $B$G$J$$>l9g$K$bE,MQ$G$-$k(B 
+$B%0%l%V%J!<4pDl$NM}O@$r9=@.$9$l$P(B,  
 $G$-algebra $B$h$j9-$$HO0O$N(B algebra $B$r07$&$3$H$,2DG=$H$J$k(B.  
 $B0lHLE*$JOHAH$_$N1~MQ$H$7$F(B, $B>-MhE*$K$O(B $D$-$B2C72$N%"%k%4%j%:%`$r3HD%$7(B,
 Calderon-Moreno $BEy$NF3F~$7$?(B algebra $B$r6I=jE*$K07$&$J$I$N1~MQ$,8+9~$^(B
 $B$l$k(B.
+
+$B$^$?(B, \FN $B$r%f!<%68@8l$h$jA`:n$9$k4X?t$rMQ$$$k$3$H$K$h$j(B,
+$BF~NO(B, $B=PNO$N%f!<%6%$%s%?%U%'!<%9$rBgI}$K2~A1$G$-$k$3$H$K$b(B
+$BCm0U$7$F$*$-$?$$(B.
 
 
 \begin{thebibliography}{99}