===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/parts/appendix.texi,v
retrieving revision 1.1.1.1
retrieving revision 1.11
diff -u -p -r1.1.1.1 -r1.11
--- OpenXM/src/asir-doc/parts/appendix.texi	1999/12/08 05:47:44	1.1.1.1
+++ OpenXM/src/asir-doc/parts/appendix.texi	2003/04/20 08:01:24	1.11
@@ -1,19 +1,44 @@
+@comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.10 2002/09/10 01:40:01 noro Exp $
+\BJP
 @node $BIUO?(B,,, Top
 @appendix $BIUO?(B
+\E
+\BEG
+@node Appendix,,, Top
+@appendix Appendix
+\E
 
 @menu
+\BJP
 * $BJ8K!$N>\:Y(B::
 * $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::
 * $BF~NO%$%s%?%U%'!<%9(B::
+* $B%i%$%V%i%j%$%s%?%U%'!<%9(B::
 * $BJQ99E@(B::
 * $BJ88%(B::
+\E
+\BEG
+* Details of syntax:: 
+* Files of user defined functions::
+* Input interfaces::
+* Library interfaces::
+* Changes:: 
+* References::
+\E
 @end menu
 
+\BJP
 @node $BJ8K!$N>\:Y(B,,, $BIUO?(B
 @section $BJ8K!$N>\:Y(B
+\E
+\BEG
+@node Details of syntax,,, Appendix
+@section Details of syntax
+\E
 
 @example
-<$B<0(B>: (@xref{$B$5$^$6$^$J<0(B})
+\BJP
+<$B<0(B>: 
     @samp{(}<$B<0(B>@samp{)}
     <$B<0(B> <$BFs9`1i;;;R(B> <$B<0(B>
     @samp{+} <$B<0(B>
@@ -27,100 +52,244 @@
     @samp{!} <$B<0(B>
     <$B<0(B> @samp{?} <$B<0(B> @samp{:} <$B<0(B>
     <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)}
+    <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{|} <$B%*%W%7%g%sJB$S(B> @samp{)}
     <$BJ8;zNs(B>
     <$B;X?t%Y%/%H%k(B>
     <$B%"%H%`(B>
     <$B%j%9%H(B>
+\E
+\BEG
+<expression>:
+    @samp{(}<expression>@samp{)}
+    <expression> <binary operator> <expression>
+    @samp{+} <expression>
+    @samp{-} <expression>
+    <left value>
+    <left value> <assignment operator> <expression>
+    <left value> @samp{++}
+    <left value> @samp{--}
+    @samp{++} <left value>
+    @samp{--} <left value>
+    @samp{!} <expression>
+    <expression> @samp{?} <expression> @samp{:} <expression>
+    <function> @samp{(} <expr list> @samp{)}
+    <function> @samp{(} <expr list> @samp{|} <option list> @samp{)}
+    <string>
+    <exponent vector>
+    <atom>
+    <list>
+\E
 @end example
+\JP (@xref{$B$5$^$6$^$J<0(B}.)
+\EG (@xref{various expressions}.)
 
 @example
+\BJP
 <$B:8JUCM(B>:
     <$BJQ?t(B> [@samp{[}<$B<0(B>@samp{]}]*
+\E
+\BEG
+<left value>:
+    <program variable> [@samp{[}<expression>@samp{]}]*
+\E
 @end example
 
 @example
+\BJP
 <$BFs9`1i;;;R(B>:
     @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B) 
+\E
+\BEG
+<binary operator>:
+    @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}(exponentiation)
     @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
+\E
+    @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
 @end example
 
 @example
-<$BBeF~1i;;;R(B>:
+\JP <$BBeF~1i;;;R(B>:
+\EG <assignment operator>:
     @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{%=} @samp{^=} 
 @end example
 
 @example
+\BJP
 <$B<0JB$S(B>:
     <$B6u(B>
     <$B<0(B> [@samp{,} <$B<0(B>]*
+\E
+\BEG
+<expr list>:
+    <empty>
+    <expression> [@samp{,} <expression>]*
+\E
 @end example
 
 @example
+\BJP
+<$B%*%W%7%g%s(B>:
+    alphabet $B$G;O$^$kJ8;zNs(B @samp{=} <$B<0(B>
+\E
+\BEG
+<option>:
+    Character sequence beginning with an alphabetical letter @samp{=} <expr>
+\E
+@end example
+
+@example
+\BJP
+<$B%*%W%7%g%sJB$S(B>:
+    <$B%*%W%7%g%s(B>
+    <$B%*%W%7%g%s(B> [@samp{,} <$B%*%W%7%g%s(B>]*
+\E
+\BEG
+<option list>:
+    <option>
+    <option> [@samp{,} <option>]*
+\E
+@end example
+
+
+@example
+\BJP
 <$B%j%9%H(B>:
     @samp{[} <$B<0JB$S(B> @samp{]}
+\E
+\BEG
+<list>:
+    @samp{[} <expr list> @samp{]}
+\E
 @end example
 
 @example
-<$BJQ?t(B>: (@xref{$BJQ?t$*$h$SITDj85(B})
+\BJP
+<$BJQ?t(B>: 
     $BBgJ8;z$G;O$^$kJ8;zNs(B (X,Y,Japan $B$J$I(B)
+\E
+\BEG
+<program variable>:
+   Sequence of alphabetical letters or numeric digits or @code{_}
+   that begins with a capital alphabetical letter
+   (X,Y,Japan etc.)
+\E
 @end example
+\JP (@xref{$BJQ?t$*$h$SITDj85(B}.)
+\EG (@xref{variables and indeterminates}.)
 
 @example
+\BJP
 <$BH!?t(B>:
    $B>.J8;z$G;O$^$kJ8;zNs(B (fctr,gcd $B$J$I(B)
+\E
+\BEG
+<function>:
+   Sequence of alphabetical letters or numeric digits or @code{_}
+   that begins with a small alphabetical letter
+   (fctr,gcd etc.)
+\E
 @end example
 
 @example
+\BJP
 <$B%"%H%`(B>:
    <$BITDj85(B>
    <$B?t(B>
+\E
+\BEG
+<atom>:
+   <indeterminate>
+   <number>
+\E
 @end example
 
 @example
-<$BITDj85(B>: (@xref{$BJQ?t$*$h$SITDj85(B})
+\BJP
+<$BITDj85(B>: 
    $B>.J8;z$G;O$^$kJ8;zNs(B (a,bCD,c1_2 $B$J$I(B)
+\E
+\BEG
+<indeterminate>:
+   Sequence of alphabetical letters or numeric digits or @code{_}
+   that begin with a small alphabetical letter
+   (a,bCD,c1_2 etc.)
+\E
 @end example
+\JP (@xref{$BJQ?t$*$h$SITDj85(B}.)
+\EG (@xref{variables and indeterminates}.)
 
 @example
-<$B?t(B>: (@xref{$B?t$N7?(B})
+\BJP
+<$B?t(B>: 
    <$BM-M}?t(B>
    <$BIbF0>.?t(B>
    <$BBe?tE*?t(B>
    <$BJ#AG?t(B>
+\E
+\BEG
+<number>:
+   <rational number>
+   <floating point number>
+   <algebraic number>
+   <complex number>
+\E
 @end example
+\JP (@xref{$B?t$N7?(B}.)
+\EG (@xref{Types of numbers}.)
 
 @example
-<$BM-M}?t(B>:
+\JP <$BM-M}?t(B>:
+\EG <rational number>:
    0, 1, -2, 3/4
 @end example
 
 @example
-<$BIbF0>.?t(B>:
+\JP <$BIbF0>.?t(B>:
+\EG <floating point number>:
    0.0, 1.2e10
 @end example
 
 @example
-<$BBe?tE*?t(B>: (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
+\JP <$BBe?tE*?t(B>: 
+\EG <algebraic number>: 
    newalg(x^2+1), alg(0)^2+1
 @end example
+\JP (@xref{$BBe?tE*?t$K4X$9$k1i;;(B}.)
+\EG (@xref{Algebraic numbers}.)
 
 @example
-<$BJ#AG?t(B>:
+\JP <$BJ#AG?t(B>:
+\EG <complex number>:
    1+@code{@@i}, 2.3*@code{@@i}
 @end example
 
 @example
+\BJP
 <$BJ8;zNs(B>:
    @samp{"} $B$G0O$^$l$?J8;zNs(B 
+\E
+\BEG
+<string>:
+   character sequence enclosed by two @samp{"}'s.
+\E
 @end example
 
 @example
-<$B;X?t%Y%/%H%k(B>: (@xref{$B%0%l%V%J4pDl$N7W;;(B})
+\BJP
+<$B;X?t%Y%/%H%k(B>:
    @samp{<<} <$B<0JB$S(B> @samp{>>}
+\E
+\BEG
+<exponent vector>:
+   @samp{<<} <expr list> @samp{>>}
+\E
 @end example
+\JP (@xref{$B%0%l%V%J4pDl$N7W;;(B}.)
+\EG (@xref{Groebner basis computation}.)
 
 @example
-<$BJ8(B>: (@xref{$BJ8(B})
+\BJP
+<$BJ8(B>:
     <$B<0(B> <$B=*C<(B>
     <$BJ#J8(B>
     @samp{break} <$B=*C<(B>
@@ -134,60 +303,134 @@
     @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>
     @samp{def} <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)} @samp{@{} <$BJQ?t@k8@(B> <$BJ8JB$S(B> @samp{@}}
     @samp{end(quit)} <$B=*C<(B> 
+\E
+\BEG
+<statement>:
+    <expression> <terminator>
+    <compound statement>
+    @samp{break} <terminator>
+    @samp{continue} <terminator>
+    @samp{return} <terminator>
+    @samp{return} <expression> <terminator>
+    @samp{if} @samp{(} <expr list> @samp{)} <statement>
+    @samp{if} @samp{(} <expr list> @samp{)} <statement> @samp{else} <statement>
+    @samp{for} @samp{(} <expr list> @samp{;} <expr list> @samp{;} <expr list> @samp{)} <statement>
+    @samp{do} <statement> @samp{while} @samp{(} <expr list> @samp{)} <terminator>
+    @samp{while} @samp{(} <expr list> @samp{)} <statement>
+    @samp{def} <function> @samp{(} <expr list> @samp{)} @samp{@{} <variable declaration> <stat list> @samp{@}}
+    @samp{end(quit)} <terminator>
+\E
 @end example
+\JP (@xref{$BJ8(B}.)
+\EG (@xref{statements}.)
 
 @example
-<$B=*C<(B>:
+\JP <$B=*C<(B>:
+\EG <terminator>:
     @samp{;} @samp{$}
 @end example
 
 @example
+\BJP
 <$BJQ?t@k8@(B>:
     [@samp{extern} <$BJQ?t(B> [@samp{,} <$BJQ?t(B>]* <$B=*C<(B>]*
+\E
+\BEG
+<variable declaration>:
+    [@samp{extern} <program variable> [@samp{,} <program variable>]* <terminator>]*
+\E
 @end example
 
 @example
+\BJP
 <$BJ#J8(B>:
     @samp{@{} <$BJ8JB$S(B> @samp{@}}
+\E
+\BEG
+<compound statement>:
+    @samp{@{} <stat list> @samp{@}}
+\E
 @end example
 
 @example
+\BJP
 <$BJ8JB$S(B>:
     [<$BJ8(B>]*
+\E
+\BEG
+<stat list>:
+    [<statement>]*
+\E
 @end example
 
+\BJP
 @node $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B,,, $BIUO?(B
 @section $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B
+\E
+\BEG
+@node Files of user defined functions,,, Appendix
+@section Files of user defined functions
+\E
 
 @noindent
+\BJP
 $BI8=`%i%$%V%i%j%G%#%l%/%H%j(B ($B%G%U%)%k%H$G$O(B @samp{/usr/local/lib/asir}) $B$K$O(B
 $B$$$/$D$+$N%f!<%6Dj5AH!?t%U%!%$%k$,$*$+$l$F$$$k(B. $B$3$l$i$N$&$A$N<g$J$b$N$K$D$$$F(B
 $B@bL@$9$k(B. 
+\E
+\BEG
+There are several files of user defined functions under the standard
+library directory. (@samp{/usr/local/lib/asir} by default.)
+Here, we explain some of them.
+\E
 
 @table @samp
 @item fff
-$BBgI8?tAGBN$*$h$SI8?t(B 2 $B$NM-8BBN>e$N0lJQ?tB?9`<00x?tJ,2r(B (@xref{$BM-8BBN$K4X$9$k1i;;(B})
+\JP $BBgI8?tAGBN$*$h$SI8?t(B 2 $B$NM-8BBN>e$N0lJQ?tB?9`<00x?tJ,2r(B (@xref{$BM-8BBN$K4X$9$k1i;;(B}.)
+\EG Univariate factorizer over large finite fields (@xref{Finite fields}.)
 @item gr
-$B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B.  (@xref{$B%0%l%V%J4pDl$N7W;;(B})
+\JP $B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B.  (@xref{$B%0%l%V%J4pDl$N7W;;(B}.)
+\EG Groebner basis package.  (@xref{Groebner basis computation}.)
 @item sp
-$BBe?tE*?t$N1i;;$*$h$S0x?tJ,2r(B, $B:G>.J,2rBN(B. (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
+\JP $BBe?tE*?t$N1i;;$*$h$S0x?tJ,2r(B, $B:G>.J,2rBN(B. (@xref{$BBe?tE*?t$K4X$9$k1i;;(B}.)
+\EG Operations over algebraic numbers and factorization, Splitting fields. (@xref{Algebraic numbers}.)
 @item alpi
 @itemx bgk
 @itemx cyclic
 @itemx katsura
 @itemx kimura
-$B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B. 
-(@xref{katsura hkatsura cyclic hcyclic})
+\JP $B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B. 
+\EG Example polynomial sets for benchmarks of Groebner basis computation.
+(@xref{katsura hkatsura cyclic hcyclic}.)
 @item defs.h
-$B$$$/$D$+$N%^%/%mDj5A(B. (@xref{$B%W%j%W%m%;%C%5(B})
+\JP $B$$$/$D$+$N%^%/%mDj5A(B. (@xref{$B%W%j%W%m%;%C%5(B}.)
+\EG Macro definitions. (@xref{preprocessor}.)
 @item fctrtest
+\BJP
 $B@0?t>e$NB?9`<0$N0x?tJ,2r$N%F%9%H(B. REDUCE $B$N(B @samp{factor.tst} $B$*$h$S(B
 $B=EJ#EY$NBg$-$$$$$/$D$+$NNc$r4^$`(B. $B$3$l$O(B, @code{load()} $B$9$k$H(B
 $BD>$A$K7W;;$,;O$^$k(B. $BF~<j$7$?(B @b{Asir} $B$,@5$7$/F0:n$7$F$$$k$+$N(B
 $B%F%9%H$K$b;H$&$3$H$,$G$-$k(B. 
+\E
+\BEG
+Test program of factorization of integral polynomials.
+It includes  @samp{factor.tst} of REDUCE and several examples
+for large multiplicity factors.  If this file is @code{load()}'ed,
+computation will begin immediately.
+You may use it as a first test whether @b{Asir} at you hand runs
+correctly.
+\E
 @item fctrdata
+\BJP
 @samp{fctrtest} $B$G;H$o$l$F$$$kNc$r4^$`(B, $B0x?tJ,2r%F%9%HMQ$NNc(B. 
-@code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@xref{asq af}) $BMQ$NNc$G$"$k(B. 
+@code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@ref{asq af af_noalg}) $BMQ$NNc$G$"$k(B. 
+\E
+\BEG
+This contains example polynomials for factorization.  It includes
+polynomials used in @samp{fctrtest}.
+Polynomials contained in vector @code{Alg[]} is for the algebraic
+factorization @code{af()}. (@xref{asq af af_noalg}.)
+\E
 @example
 [45] load("sp")$
 [84] load("fctrdata")$
@@ -197,32 +440,53 @@
 x^9-15*x^6-87*x^3-125
 0msec
 [177] af(Alg[5],[newalg(Alg[5])]);
-[[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
-[75*x^2+(-10*#0^7+175*#0^4+395*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
-[25*x^2+(25*#0)*x+(#0^8-15*#0^5-87*#0^2),1],[x^2+(#0)*x+(#0^2),1],
-[x+(-#0),1]]
+[[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x
++(3*#0^8-45*#0^5-261*#0^2),1],
+[75*x^2+(-10*#0^7+175*#0^4+395*#0)*x
++(3*#0^8-45*#0^5-261*#0^2),1],
+[25*x^2+(25*#0)*x+(#0^8-15*#0^5-87*#0^2),1],
+[x^2+(#0)*x+(#0^2),1],[x+(-#0),1]]
 3.600sec + gc : 1.040sec
 @end example
 @item ifplot
-$BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
+\BJP
+$BIA2h(B (@ref{ifplot conplot plot polarplot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
 $B6J@~$NNc(B, $BJQ?t(B @code{H, D, C, S} $B$K$O%H%i%s%W$N%O!<%H(B, $B%@%$%d(B, $B%/%i%V(B, 
 $B%9%Z!<%I(B ($B$i$7$-(B) $B6J@~$NNc$,F~$C$F$$$k(B. 
+\E
+\BEG
+Examples for plotting. (@xref{ifplot conplot plot polarplot plotover}.)
+Vector @code{IS[]} contains several famous algebraic curves.
+Variables @code{H, D, C, S} contains something like the suits
+(Heart, Diamond, Club, and Spade) of cards.
+\E
 @item num
-$B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
+\JP $B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
+\EG Examples of simple operations on numbers.
 @item mat
-$B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
+\JP $B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B. 
+\EG Examples of simple operations on matrices.
 @item ratint
+\BJP
 $BM-M}H!?t$NITDj@QJ,(B. @samp{sp}, @samp{gr} $B$,I,MW(B. @code{ratint()} $B$H$$$&(B
 $BH!?t$,Dj5A$5$l$F$$$k$,(B, $B$=$NJV$97k2L$O$d$dJ#;($G$"$k(B. $BNc$G@bL@$9$k(B. 
+\E
+\BEG
+Indefinite integration of rational functions.  For this,
+files @samp{sp} and @samp{gr} is necessary.  A function @code{ratint()}
+is defined.  Its returns a rather complex result.
+\E
 @example
 [0] load("gr")$
 [45] load("sp")$
 [84] load("ratint")$
 [102] ratint(x^6/(x^5+x+1),x);
 [1/2*x^2,
-[[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),161*t#2^3-23*t#2^2+15*t#2-1],
+[[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),
+161*t#2^3-23*t#2^2+15*t#2-1],
 [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
 @end example
+\BJP
 $B$3$NNc$G$O(B, @code{x^6/(x^5+x+1)} $B$NITDj@QJ,$N7W;;$r9T$C$F$$$k(B. 
 $B7k2L$O(B 2 $B$D$NMWAG$+$i$J$k%j%9%H$G(B, $BBh(B 1 $BMWAG$OITDj@QJ,$NM-M}ItJ,(B, 
 $BBh(B 2 $BMWAG$OBP?tItJ,$rI=$9(B. $BBP?tItJ,$O99$K%j%9%H$H$J$C$F$$$F(B, $B3FMWAG$O(B, 
@@ -232,87 +496,487 @@ x^9-15*x^6-87*x^3-125
 @code{root} $B$r4^$s$G$$$F(B, @code{root} $B$rF~$lBX$($k>l9g$K$O(B @code{poly}
 $B$KBP$7$F$bF1$8A`:n$r9T$&$b$N$H$9$k(B. $B$3$NA`:n$r(B, $B7k2L$NBh(B 2 $BMWAG$N(B
 $B3F@.J,$KBP$7$F9T$C$F(B, $BA4$F$rB-$79g$o$;$?$b$N$,BP?tItJ,$H$J$k(B. 
+\E
+\BEG
+In this example, indefinite integral of the rational function
+ @code{x^6/(x^5+x+1)} is computed.
+The result is a list which comprises two elements:
+The first element is the rational part of the integral;
+The second part is the logarithmic part of the integral.
+The logarithmic part is again a list which comprises finite number of
+elements, each of which is of form @code{[root*log(poly),defpoly]}.
+This pair should be interpreted to sum up
+the expression @code{root*log(poly)}
+through all @b{root}'s @code{root}'s of the @code{defpoly}.
+Here, @code{poly} contains @code{root}, and substitution for @code{root}
+is equally applied to @code{poly}.
+The logarithmic part in total is obtained by applying such
+interpretation to all element pairs in the second element of the
+result and then summing them up all.
+\E
 @item primdec
-$BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
-(@code{[Shimoyama,Yokoyama]} $B;2>H(B).
-$B=`AG%$%G%"%kJ,2r$O(B @code{primadec()}, $BAG%$%G%"%kJ,2r$O(B, @code{primedec()}
-$B$H$$$&4X?t$G(B, $BMQ0U$5$l$F$$$k(B. $B0z?t$O(B, $BB?9`<0%j%9%H$HJQ?t$G$"$k(B. 
-$BM-M}<078?t$NB?9`<0%$%G%"%k$d(B, 0$B<!85$G$J$$%$%G%"%k$b07$($k(B. 
-@code{primadec} $B$O(B, $B=`AG@.J,$H$=$NAG@.J,$N%Z%"%j%9%H$N%j%9%H$rJV$9(B. 
-@code{primedec} $B$O(B, $BAG@.J,$N%j%9%H$rJV$9(B. 
-$B$=$N7k2L$O$$$:$l$b%0%l%V%J4pDl$K$J$C$F$$$k$,(B, $B$=$N(B
-$BJQ?t=g=x$O(B, $B$=$l$>$lBg0hJQ?t(B @code{PRIMAORD}, @code{PRIMEORD}
- $B$NCM(B 0,1 $B$"$k$$$O(B 2 $B$K$h$C$F7h$^$k(B. 
-@example
-[84] load("primdec")$
-[102] primedec([p*q*x-q^2*y^2+q^2*y,-p^2*x^2+p^2*x+p*q*y,
-(q^3*y^4-2*q^3*y^3+q^3*y^2)*x-q^3*y^4+q^3*y^3,
--q^3*y^4+2*q^3*y^3+(-q^3+p*q^2)*y^2],[p,q,x,y]);
-[[y,x],[y,p],[x,q],[q,p],[x-1,q],[y-1,p],[(y-1)*x-y,q*y^2-2*q*y-p+q]]
-[103] primadec([x,z*y,w*y^2,w^2*y-z^3,y^3],[x,y,z,w]);
-[[[x,z*y,y^2,w^2*y-z^3],[z,y,x]],[[w,x,z*y,z^3,y^3],[w,z,y,x]]]
-@end example
+\BJP
+$BM-M}?tBN>e$NB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
+(@pxref{primadec primedec}).
+\E
+\BEG
+Primary ideal decomposition of polynomial ideals and prime compotision
+of radicals over the rationals (@pxref{primadec primedec}).
+\E
+@item primdec_mod
+\BJP
+$BM-8BBN>e$NB?9`<0%$%G%"%k$N:,4p$NAG%$%G%"%kJ,2r(B
+(@pxref{primedec_mod}).
+\E
+\BEG
+Prime decomposition of radicals of polynomial ideals
+over finite fields (@pxref{primedec_mod}).
+\E
 @end table
 
+\BJP
 @node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B
 @section $BF~NO%$%s%?%U%'!<%9(B
+\E
+\BEG
+@node Input interfaces,,, Appendix
+@section Input interfaces
+\E
 
-$B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B
+\BJP
+DOS $BHG(B, Windows $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B
 $B$7$F%3%^%s%I%i%$%sJT=8$*$h$S%R%9%H%jCV$-49$($,AH$_9~$^$l$F$$$k(B. UNIX $BHG$G$O(B
 $B$3$N$h$&$J5!G=$OAH$_9~$^$l$F$$$J$$$,(B, $B0J2<$G=R$Y$k$h$&$JF~NO%$%s%?%U%'!<%9(B
 $B$,MQ0U$5$l$F$$$k(B. $B$3$l$i$O(B @b{Asir} $B%P%$%J%j$H$H$b$K(B ftp $B2DG=$G$"$k(B. 
 ftp server $B$K4X$7$F$O(B @xref{$BF~<jJ}K!(B}.
 
+Windows $BHG(B @samp{asirgui.exe} $B$O(B, $BDL>o$N(B Windows $B$K$*$1$k47=,$H$O0[$J$k(B
+$B7A$N%3%T!<%Z!<%9%H5!G=$rDs6!$7$F$$$k(B. Window $B>e$KI=<($5$l$F$$$kJ8;zNs(B
+$B$KBP$7%^%&%9:8%\%?%s$r2!$7$J$,$i%I%i%C%0$9$k$HJ8;zNs$,A*Br$5$l$k(B. 
+$B%\%?%s$rN%$9$HH?E>I=<($,85$KLa$k$,(B, $B$=$NJ8;zNs$O%3%T!<%P%C%U%!$K(B
+$B<h$j9~$^$l$F$$$k(B. $B%^%&%91&%\%?%s$r2!$9$H(B, $B%3%T!<%P%C%U%!Fb$NJ8;zNs$,(B
+$B8=:_$N%+!<%=%k0LCV$KA^F~$5$l$k(B. $B4{$KI=<($5$l$?ItJ,$O(B readonly
+$B$G$"$j(B, $B$=$NItJ,$r2~JQ$G$-$J$$$3$H$KCm0U$7$FM_$7$$(B. 
+\E
+\BEG
+A command line editing facility and a history
+substitution facility are built-in for DOS, Windows version
+of @b{Asir}. UNIX versions of @b{Asir} do not have such built-in facilites.
+Instead, the following input interfaces are prepared. This are also available
+from our ftp server. As for our ftp server @xref{How to get Risa/Asir}.
+
+On Windows, @samp{asirgui.exe} has a copy and paste functionality
+different from Windows convention. Press the left button of the mouse
+and drag the mouse cursor on a text, then the text is selected and is
+highlighted.  When the button is released, highlighted text returns to
+the normal state and it is saved in the copy buffer.  If the right
+button is pressed, the text in the copy buffer is inserted at the
+current text cursor position. Note that the existing text is read-only and 
+one cannot modify it.
+\E
+
 @menu
 * fep::
 * asir.el::
 @end menu
 
-@node fep,,, $BF~NO%$%s%?%U%'!<%9(B
+\JP @node fep,,, $BF~NO%$%s%?%U%'!<%9(B
+\EG @node fep,,, Input interfaces
 @subsection fep
 
 @noindent
+\BJP
 fep $B$H$O(B, SRA $B$N2NBe;a$K$h$j3+H/$5$l$?%3%^%s%I%i%$%sJT=8(B, $B%R%9%H%jCV$-49$((B
 $BMQ$NF~NO%U%m%s%H%(%s%I$G$"$k(B. $B$3$N%W%m%0%i%`$N85$G(B @samp{asir} $B$r5/F0$9$k(B
 $B$3$H$K$h$j(B vi $B$"$k$$$O(B emacs $BIw$N%3%^%s%I%i%$%sJT=8$*$h$S(B csh $BIw$N%R%9%H%j(B
 $BCV$-49$($,2DG=$K$J$k(B. 
+\E
+\BEG
+Fep is a general purpose front end processor. The author is
+K. Utashiro (SRA Inc.).
 
+Under fep,
+emacs- or vi-like command line editing and csh-like history substitution are
+available for UNIX commands, including @samp{asir}.
+\E
 @example
 % fep asir
 ...
 [0] fctr(x^5-1);
 [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
 [1] !!                              /* !!+Return                      */
-fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */
-...                                 /* $BJT=8(B+Return                    */
+\BJP
+fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$FJT=8$G$-$k(B */
+...                                 /* $BJT=8(B+Return                  */
+\E
+\BEG
+fctr(x^5-1);                        /* The last input appears.        */
+...                                 /* Edit+Return                    */
+\E
 fctr(x^5+1);
 [[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]
 @end example
 
 @noindent
+\BJP
 fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $B%*%j%8%J%k$N$b$N$O(B make $B$G$-$k(B
 $B5!<o(B (OS) $B$,8B$i$l$F$$$k(B. $B$$$/$D$+$N5!<o>e$GF0:n$9$k$h$&$K2f!9$,2~B$$7$?$b$N(B
 $B$,(B, ftp $B$GF~<j2DG=$G$"$k(B.
+\E
+\BEG
+Fep is a free software and the source is available. However
+machines or operating systems on which the original one can run are limited.
+The modified version by us running on several unsupported environments
+is available from our ftp server.
+\E
 
-@node asir.el,,, $BF~NO%$%s%?%U%'!<%9(B
+\JP @node asir.el,,, $BF~NO%$%s%?%U%'!<%9(B
+\EG @node asir.el,,, Input interfaces
 @subsection asir.el
 
 @noindent
+\BJP
 @samp{asir.el} $B$O(B, @b{Asir} $B$N(B GNU Emacs $B%$%s%?%U%'!<%9$G$"$k(B ($BCx<T$O(B
 $B5\Eh8w<#;a(B (@code{YVE25250@@pcvan.or.jp}).  @samp{asir.el} $B$K$*$$$F$O(B, 
 $BDL>o$N(B emacs $B$G2DG=$JJT=85!G=$NB>$K(B, $B%U%!%$%kL>(B, $B%3%^%s%IL>$N(B completion
 $B$,<B8=$5$l$F$$$k(B. 
+\E
+\BEG
+@samp{asir.el} is a GNU Emacs interface for @b{Asir}.
+The author is Koji Miyajima (@code{YVE25250@@pcvan.or.jp}).
+In @samp{asir.el}, completion of file names and command names is
+realized other than the ordinary editing functions
+which are available on Emacs.
+\E
 
 @noindent
+\BJP
 @samp{asir.el} $B$O(B PC-VAN $B$G(B
 $B4{$K8x3+$5$l$F$$$k$,(B, $B:#2s$N2~D{$KH<$&JQ99$r9T$C$?$b$N$,(B, $B$d$O$j(B ftp $B$G(B
 $BF~<j2DG=$G$"$k(B. 
+\E
+\BEG
+@samp{asir.el} is distributed on PC-VAN. The version where several
+changes have been made according to the current version of @b{Asir}
+is available via ftp.
+\E
 
 @noindent
-$B%;%C%H%"%C%W(B, $B;HMQJ}K!$O(B, @samp{asir.el} $B$N@hF,$K5-=R$5$l$F$$$k(B. 
+\JP $B%;%C%H%"%C%W(B, $B;HMQJ}K!$O(B, @samp{asir.el} $B$N@hF,$K5-=R$5$l$F$$$k(B. 
+\BEG
+The way of setting up and the usage can be found at the top of
+@samp{asir.el}.
+\E
 
+\BJP
+@node $B%i%$%V%i%j%$%s%?%U%'!<%9(B,,, $BIUO?(B
+@section $B%i%$%V%i%j%$%s%?%U%'!<%9(B
+\E
+\BEG
+@node Library interfaces,,, Appendix
+@section Library interfaces
+\E
+
+\BJP
+@b{Asir} $B$NDs6!$9$k5!G=$rB>$N%W%m%0%i%`$+$i;HMQ$9$kJ}K!$H$7$F(B, @b{OpenXM} $B$K$h$k(B
+$BB>$K(B, $B%i%$%V%i%j$ND>@\%j%s%/$K$h$kJ}K!$,2DG=$G$"$k(B. $B%i%$%V%i%j$O(B,
+GC $B%i%$%V%i%j$G$"$k(B @samp{libasir-gc.a} $B$H$H$b$K(B @b{OpenXM}
+distribution (@code{http://www.math.kobe-u.ac.jp/OpenXM}) $B$K4^$^$l$k(B. 
+$B8=>u$G$O(B@b{OpenXM} $B%$%s%?%U%'!<%9$N$_$,8x3+$5$l$F$$$k$?$a(B, $B0J2<$G$O(B
+@b{OpenXM} $B$,%$%s%9%H!<%k$5$l$F$$$k$H2>Dj$9$k(B. @b{OpenXM} root $B%G%#%l%/%H%j$r(B
+@code{$OpenXM_HOME}$B$H=q$/(B. $B%i%$%V%i%j%U%!%$%k$OA4$F(B @samp{$OpenXM_HOME/lib}
+$B$K$*$+$l$F$$$k(B. $B%i%$%V%i%j$K$O0J2<$N(B 3 $B<oN`$,$"$k(B. 
+\E
+\BEG
+It is possible to link an @b{Asir} library to use the functionalities of
+@b{Asir} from other programs.
+The necessary libraries are included in the @b{OpenXM} distribution
+@ifhtml
+(<A HREF="http://www.math.kobe-u.ac.jp/OpenXM">OpenXM </A>)
+@end ifhtml
+(@code{http://www.math.kobe-u.ac.jp/OpenXM}).
+At present only the @b{OpenXM} interfaces are available. Here we assume
+that @b{OpenXM} is already installed. In the following 
+@code{$OpenXM_HOME} denotes the @b{OpenXM} root directory.
+All the library files are placed in @samp{$OpenXM_HOME/lib}.
+There are three kinds of libraries as follows.
+\E
+@itemize @bullet
+@item @samp{libasir.a}
+@*
+\BJP
+@b{PARI}, @b{X11} $B4XO"$N5!G=$r4^$^$J$$(B. 
+$B%j%s%/$K$O(B @samp{libasir-gc.a} $B$N$_$,I,MW(B. 
+\E
+\BEG
+It does not contain the functionalities related to @b{PARI} and @b{X11}.
+Only @samp{libasir-gc.a} is necessary for linking.
+\E
+
+@item @samp{libasir_pari.a}
+@*
+\BJP
+@b{X11} $B4XO"$N5!G=$r4^$^$J$$(B. $B%j%s%/$K$O(B @samp{libasir-gc.a},
+@samp{libpari.a} $B$,I,MW(B.
+\E
+\BEG
+It does not contain the functionalities related to @b{X11}.
+@samp{libasir-gc.a}, @samp{libpari.a} are necessary for linking.
+\E
+
+@item @samp{libasir_pari_X.a}
+@*
+\BJP
+$BA4$F$N5!G=$r4^$`(B. $B%j%s%/$K$O(B @samp{libasir-gc.a}, @samp{libpari.a}
+$B$*$h$S(B @b{X11} $B4XO"$N%i%$%V%i%j;XDj$,I,MW(B.
+\E
+\BEG
+All the functionalities are included. @samp{libasir-gc.a}, @samp{libpari.a}
+and libraries related to @b{X11} are necessary for linking.
+\E
+@end itemize
+\BJP
+$BDs6!$5$l$F$$$k4X?t$O0J2<$NDL$j$G$"$k(B. 
+\E
+@itemize @bullet
+@item @code{int asir_ox_init(int @var{byteorder})}
+@*
+\BJP
+$B%i%$%V%i%j$N=i4|2=(B. @var{byteorder} $B$O%a%b%j>e$X$N%P%$%J%j(B CMO $B%G!<%?(B
+$B$X$NE83+J}K!$r;XDj$9$k(B. @var{byteorder} $B$,(B 0 $B$N$H$-%^%7%s8GM-$N(B byteorder
+$B$rMQ$$$k(B. 1 $B$N$H$-(B network byteorder $B$rMQ$$$k(B. $B=i4|2=$K@.8y$7$?>l9g(B 0,
+$B<:GT$N;~(B -1 $B$rJV$9(B. 
+\E
+\BEG
+It initializes the library.
+@var{byteorder} specifies the format of binary CMO data on the memory.
+If @var{byteorder} is 0, the byteorder native to the machine is used.
+If @var{byteorder} is 1, the network byteorder is used. It returns
+0 if the initialization is successful, -1 otherwise.
+\E
+
+@item @code{void asir_ox_push_cmo(void *@var{cmo})}
+@*
+\BJP
+$B%a%b%j>e$KCV$+$l$?(B CMO $B%G!<%?$r(B @b{Asir} $B$NFbIt7A<0$KJQ49$7$F%9%?%C%/$K(B
+push $B$9$k(B. 
+\E
+\BJP
+It converts CMO data pointed by @var{cmo} into an @b{Asir} object and
+it pushes the object onto the stack.
+\E
+
+@item @code{int asir_ox_peek_cmo_size()}
+@*
+\BJP
+$B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B CMO $B$KJQ49$7$?$H$-$N%5%$%:$rJV$9(B. 
+$BJQ49ITG=$J>l9g$K$O(B -1 $B$rJV$9(B. 
+\E
+\BEG
+It returns the size of the object at the top of the stack as CMO object.
+It returns -1 if the object cannot be converted into CMO object.
+\E
+
+@item @code{int asir_ox_pop_cmo(void *@var{cmo}, int @var{limit})}
+@*
+\BJP
+$B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B pop $B$7(B, CMO $B$KJQ49$7$F(B @var{cmo}$B$G(B
+$B;X$5$l$kG[Ns$K=q$-(B, CMO $B$N%5%$%:$rJV$9(B. $B$3$N$H$-(B, CMO $B$N%5%$%:$,(B 
+@var{limit} $B$h$jBg$-$$>l9g$K$O(B -1 $B$rJV$9(B. @var{cmo} $B$OD9$5$,>/$J$/$H$b(B 
+@var{limit}$B%P%$%H$NG[Ns$r;X$9I,MW$,$"$k(B. $BJQ49$5$l$?(B CMO $B$r<}MF$G$-$k(B
+$BG[Ns$ND9$5$rCN$k$?$a$K(B, @code{asir_ox_peek_cmo_size} $B$rMQ$$$k(B. 
+\E
+\BEG
+It pops an @b{Asir} object at the top of the stack and it converts
+the object into CMO data. If the size of the CMO data is not greater
+than @var{limit}, then the data is written in @var{cmo} and the size
+is returned. Otherwise -1 is returned. The size of the array pointed
+by @var{cmo} must be at least @var{limit}. In order to know the size
+of converted CMO data in advance @code{asir_ox_peek_cmo_size} is called.
+\E
+
+@item @code{void asir_ox_push_cmd(int @var{cmd})}
+@*
+\BJP
+$B%9%?%C%/%^%7%s%3%^%s%I(B @var{cmd} $B$r<B9T$9$k(B. 
+\E
+\BEG
+It executes a stack machine command @var{cmd}.
+\E
+
+@item @code{void asir_ox_execute_string(char *@var{str})}
+@*
+\BJP
+@b{Asir} $B$,<B9T2DG=$JJ8;zNs(B @var{str} $B$r<B9T$7(B, $B$=$N7k2L$r%9%?%C%/$K(B push $B$9$k(B.
+\E
+\BEG
+It evaluates @var{str} as a string written in the @b{Asir} user language.
+The result is pushed onto the stack.
+\E
+@end itemize
+
+\BJP
+include $B$9$Y$-(B header file $B$O(B @samp{$OpenXM_HOME/include/asir/ox.h} $B$G$"$k(B. 
+$B$3$N(B header file $B$K$O(B, @b{OpenXM} $B$K4X$9$kA4$F$N(B tag, command $B$NDj5A$,4^$^$l$F(B
+$B$$$k(B. 
+$B<!$NNc(B (@samp{$OpenXM_HOME/doc/oxlib/test3.c}) $B$O>e5-4X?t$N;HMQ(B
+$BK!$r<($9(B. 
+\E
+\BEG
+A program calling the above functions should include 
+@samp{$OpenXM_HOME/include/asir/ox.h}.
+In this file all the definitions of @b{OpenXM} tags and commands.
+The following example
+(@samp{$OpenXM_HOME/doc/oxlib/test3.c}) illustrates the usage of
+the above functions.
+\E
+
+@example
+#include <asir/ox.h>
+#include <signal.h>
+
+main(int argc, char **argv)
+@{
+  char buf[BUFSIZ+1];
+  int c;
+  unsigned char sendbuf[BUFSIZ+10];
+  unsigned char *result;
+  unsigned char h[3];
+  int len,i,j;
+  static int result_len = 0;
+  char *kwd,*bdy;
+  unsigned int cmd;
+
+  signal(SIGINT,SIG_IGN);
+  asir_ox_init(1); /* 1: network byte order; 0: native byte order */
+  result_len = BUFSIZ;
+  result = (void *)malloc(BUFSIZ);
+  while ( 1 ) @{
+    printf("Input>"); fflush(stdout);
+    fgets(buf,BUFSIZ,stdin);
+    for ( i = 0; buf[i] && isspace(buf[i]); i++ );
+    if ( !buf[i] )
+      continue;
+    kwd = buf+i;
+    for ( ; buf[i] && !isspace(buf[i]); i++ );
+    buf[i] = 0;
+    bdy = buf+i+1;
+    if ( !strcmp(kwd,"asir") ) @{
+      sprintf(sendbuf,"%s;",bdy);
+      asir_ox_execute_string(sendbuf);
+    @} else if ( !strcmp(kwd,"push") ) @{
+      h[0] = 0;
+      h[2] = 0;
+      j = 0;
+      while ( 1 ) @{
+        for ( ; (c= *bdy) && isspace(c); bdy++ );
+        if ( !c )
+          break;
+        else if ( h[0] ) @{
+          h[1] = c;
+          sendbuf[j++] = strtoul(h,0,16);
+          h[0] = 0;
+        @} else
+          h[0] = c;
+        bdy++;
+      @}
+      if ( h[0] )
+        fprintf(stderr,"Number of characters is odd.\n");
+      else @{
+        sendbuf[j] = 0;
+        asir_ox_push_cmo(sendbuf);
+      @}
+    @} else if ( !strcmp(kwd,"cmd") ) @{
+      cmd = atoi(bdy);
+      asir_ox_push_cmd(cmd);
+    @} else if ( !strcmp(kwd,"pop") ) @{
+      len = asir_ox_peek_cmo_size();
+      if ( !len )
+        continue;
+      if ( len > result_len ) @{
+        result = (char *)realloc(result,len);
+        result_len = len;
+      @}
+      asir_ox_pop_cmo(result,len);
+      printf("Output>"); fflush(stdout);
+      printf("\n");
+      for ( i = 0; i < len; ) @{
+        printf("%02x ",result[i]);
+        i++;
+        if ( !(i%16) )
+          printf("\n");
+      @}
+      printf("\n");
+    @}
+  @}
+@}
+@end example
+\BJP
+$B$3$N%W%m%0%i%`$O(B, @var{keyword} @var{body} $B$J$k(B 1 $B9T$rF~NO$H$7$F<u$1<h$j(B
+@var{keyword} $B$K1~$8$F<!$N$h$&$JF0:n$r9T$&(B. 
+\E
+\BEG
+This program receives a line in the form of @var{keyword} @var{body}
+as an input and it executes the following operations according to
+@var{keyword}.
+\E
+@itemize @bullet
+@item @code{asir} @var{body}
+@*
+\BJP
+@var{body} $B$r(B @b{Asir} $B8@8l$G=q$+$l$?<0$H$_$J$7(B, $B<B9T7k2L$r%9%?%C%/$K(B push $B$9$k(B. 
+@code{asir_ox_execute_string()} $B$,MQ$$$i$l$k(B. 
+\E
+\BEG
+@var{body} is regarded as an expression written in the @b{Asir} user language.
+The expression is evaluated and the result is pushed onto the stack.
+@code{asir_ox_execute_string()} is called.
+\E
+
+@item @code{push} @var{body}
+@*
+\BJP
+@var{body} $B$r(B 16 $B?J?t$GI=<($5$l$?(B CMO $B%G!<%?$H$_$J$7(B, @b{Asir} $B%*%V%8%'%/%H$KJQ49(B
+$B$7$F%9%?%C%/$K(B push $B$9$k(B. @code{asir_ox_push_cmo()} $B$,MQ$$$i$l$k(B. 
+\E
+\BEG
+@var{body} is regarded as a CMO object in the hexadecimal form.
+The CMO object is converted into an @b{Asir} object and is pushed onto the stack.
+@code{asir_ox_push_cmo()} is called.
+\E
+
+@item @code{pop}
+@*
+\BJP
+$B%9%?%C%/:G>e0L$N%*%V%8%'%/%H$r(B CMO $B$KJQ49$7(B, 16 $B?J?t$GI=<($9$k(B. 
+@code{asir_ox_peek_cmo_size()} $B$*$h$S(B @code{asir_ox_pop_cmo()} $B$,MQ$$$i$l$k(B. 
+\E
+\BEG
+The object at the top of the stack is converted into a CMO object
+and it is displayed in the hexadecimal form.
+@code{asir_ox_peek_cmo_size()} and @code{asir_ox_pop_cmo()} are called.
+\E
+
+@item @code{cmd} @var{body}
+@*
+\BJP
+@var{body} $B$r(B SM $B%3%^%s%I$H$_$J$7(B, $B<B9T$9$k(B. 
+@code{asir_ox_push_cmd()} $B$,MQ$$$i$l$k(B. 
+\E
+\BEG
+@var{body} is regarded as an SM command and the command is executed.
+@code{asir_ox_push_cmd()} is called.
+\E
+@end itemize
+
+\BJP
 @node $BJQ99E@(B,,, $BIUO?(B
 @section $BJQ99E@(B
+\E
+\BEG
+@node Changes,,, Appendix
+@section Appendix
+\E
 
 @menu
 * Version 990831::
@@ -320,45 +984,86 @@ fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $
 * Version 940420::
 @end menu
 
-@node Version 990831,,, $BJQ99E@(B
+\JP @node Version 990831,,, $BJQ99E@(B
+\EG @node Version 990831,,, Changes
 @subsection Version 990831
 
+\BJP
 4 $BG/$V$j$NBg2~D{(B. $B@0?t$N(B 32bit $B2=B>(B, $BCf?H$O$:$$$V$sJQ$o$C$F$$$k$b$N$N(B, 
 $B8+3]$1$O$=$l$[$IJQ$o$C$F$$$k$h$&$K$O8+$($J$$(B. $B$`$7$m(B, Windows $BHG$J$I$O(B, 
 plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
 
 $B5lHG$N%f!<%6$,$b$C$H$bCm0U$9$Y$-E@$O(B, $B5lHG$G:n$C$?(B bsave file $B$rFI$_9~$`(B
 $B>l9g$O(B @code{bload27} $B$r;H$&I,MW$,$"$k(B, $B$H$$$&E@$G$"$k(B. 
+\E
 
-@node Version 950831,,, $BJQ99E@(B
+\BEG
+Four years have passed since the last distribution.
+Though the look and feel seem unchanged, internally there are
+several changes such as 32-bit representation of bignums.
+Plotting facilities are not available on Windows.
+
+If you have files created by @code{bsave} on the older version,
+you have to use @code{bload27} to read such files.
+\E
+
+\JP @node Version 950831,,, $BJQ99E@(B
+\EG @node Version 950831,,, Changes
 @subsection Version 950831
 
 @menu
+\BJP
 * $B%G%P%C%,(B($BJQ99(B)::
 * $BAH$_9~$_H!?t(B($BJQ99(B)::
 * $B%0%l%V%J4pDl(B($BJQ99(B)::
 * $B$=$NB>(B($BJQ99(B)::
+\E
+\BEG
+* Debugger(Changes)::
+* Built-in functions(Changes)::
+* Groebner basis computation(Changes)::
+* Others(Changes)::
+\E
 @end menu
 
+\BJP
 @node $B%G%P%C%,(B($BJQ99(B),,, Version 950831
 @subsubsection $B%G%P%C%,(B
+\E
+\BEG
+@node Debugger(Changes),,, Version 950831
+@subsubsection Debugger
+\E
 
 @itemize @bullet
 @item
-$BG$0U$N;~E@$K%G%P%C%0%b!<%I$KF~$l$k(B.
+\JP $BG$0U$N;~E@$K%G%P%C%0%b!<%I$KF~$l$k(B.
+\EG One can enter the debug mode anytime.
 @item
-@code{finish} $B%3%^%s%I$NDI2C(B. 
+\JP @code{finish} $B%3%^%s%I$NDI2C(B. 
+\EG A command @code{finish} has been appended.
 @item
+\BJP
 @code{up}, @code{down}, @code{frame} $B%3%^%s%I$K$h$k(B, $BG$0U$N%9%?%C%/%U%l!<%`(B
-$B$N;2>H(B. 
+$B$N;2>H(B.
+\E
+\EG One can examine any stack frame with @code{up}, @code{down} and @code{frame}.
 @item
-@code{trace} $B%3%^%s%I$NDI2C(B. 
+\JP @code{trace} $B%3%^%s%I$NDI2C(B. 
+\EG A command @code{trace} has been appended.
 @end itemize
 
+\BJP
 @node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831
 @subsubsection $BAH$_9~$_H!?t(B
+\E
+\BEG
+@node Built-in functions(Changes),,, Version 950831
+@subsubsection Built-in functions
+\E
 
 @itemize @bullet
+\BJP
 @item
 @code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B. 
 @item
@@ -369,12 +1074,33 @@ plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
 @code{vtol()} ($B%Y%/%H%k$+$i%j%9%H$X$NJQ49(B) $B$NDI2C(B. 
 @item
 @code{map()} $B$NDI2C(B. 
+\E
+\BEG
+@item
+One can specify a main variable for @code{sdiv()} etc.
+@item
+Functions for polynomial division over finite fields
+such as @code{sdivm()} have been appended.
+@item
+@code{det()}, @code{res()} can produce results over finite fields.
+@item
+@code{vtol()}, conversion from a vector to a list has been appended.
+@item
+@code{map()} has been appended.
+\E
 @end itemize
 
+\BJP
 @node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831
 @subsubsection $B%0%l%V%J4pDl(B
+\E
+\BEG
+@node Groebner basis computation(Changes),,, Version 950831
+@subsubsection Groebner basis computation
+\E
 
 @itemize @bullet
+\BJP
 @item
 $B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B. 
 @item
@@ -389,12 +1115,38 @@ plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
 $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl7W;;$N%5%]!<%H(B. 
 @item
 $B$$$/$D$+$N?7$7$$AH$_9~$_H!?t$NDs6!(B. 
+\E
+\BEG
+@item Functions for Groebner basis computation have been implemented
+as built-in functions.
+@item
+@code{grm()} and @code{hgrm()} have been changed to @code{gr()} and
+@code{hgr()} respectively.
+@item
+@code{gr()} and @code{hgr()} requires explicit specification of
+an ordering type.
+@item
+Extension of specification of a term ordering type.
+@item
+Groebner basis computations over finite fields.
+@item
+Lex order Groebner basis computation via a modular change of ordering algorithm.
+@item
+Several new built-in functions.
+\E
 @end itemize
 
+\BJP
 @node $B$=$NB>(B($BJQ99(B),,, Version 950831
 @subsubsection $B$=$NB>(B
+\E
+\BEG
+@node Others(Changes),,, Version 950831
+@subsubsection Others
+\E
 
 @itemize @bullet
+\BJP
 @item
 $BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.
 @item
@@ -403,16 +1155,36 @@ plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
 $B%$%G%"%k$N=`AGJ,2r$N%5%]!<%H(B. 
 @item
 Windows $B$X$N0\?"(B.
+\E
+\BEG
+@item
+Implementation of tools for distributed computation.
+@item
+Application of modular computation for GCD computation over algebraic number
+fields.
+@item
+Implementation of primary decompostion of ideals.
+@item
+Porting to Windows.
+\E
 @end itemize
 
-@node Version 940420,,, $BJQ99E@(B
+\JP @node Version 940420,,, $BJQ99E@(B
+\EG @node Version 940420,,, Changes
 @subsection Version 940420
 
 @noindent
-$B:G=i$N8x3+HG(B. 
+\JP $B:G=i$N8x3+HG(B. 
+\EG The first public verion.
 
+\BJP
 @node $BJ88%(B,,, $BIUO?(B
 @section $BJ88%(B
+\E
+\BEG
+@node References,,, Appendix
+@section References
+\E
 @table @code
 @item [Batut et al.]
 Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",
@@ -434,13 +1206,21 @@ Proc. ISSAC'91, 49-54.
 Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",
 Proc. ISSAC'92, 387-396.
 @item [Noro,Yokoyama] 
-Noro, M., Yokoyama, K., "New methods for the change-of-ordering in Groebner
-basis computation", ISIS Research Report ISIS-RR-95-8E, 1995.
+Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate
+Representation of Zero-Dimensional Ideals", 
+J. Symb. Comp. 28/1 (1999), 243-263.
 @item [Shimoyama,Yokoyama]
 Shimoyama, T., Yokoyama, K.,
 "Localization and primary decomposition of polynomial ideals",
-to appear in J. Symb. Comp.
+J. Symb. Comp. 22 (1996), 247-277.
+@item [Shoup]
+Shoup, V., "A new polynomial factorization algorithm and its implementation",
+J. Symb. Comp. 20 (1995), 364-397.
 @item [Traverso]
 Traverso, C., "Groebner trace algorithms", Proc. ISSAC '88(LNCS 358), 125-138.
+@item [Weber]
+Weber, K., "The accelerated Integer GCD Algorithm", ACM TOMS, 21, 1(1995), 111-122.
+@item [Yokoyama]
+Yokoyama, K., "Prime decomposition of polynomial ideals over finite fields", 
+Proc. ICMS, (2002), 217-227.
 @end table
-