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version 1.1, 1999/12/08 05:47:44 version 1.3, 1999/12/21 02:47:30
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   @comment $OpenXM$
   \BJP
 @node $BIUO?(B,,, Top  @node $BIUO?(B,,, Top
 @appendix $BIUO?(B  @appendix $BIUO?(B
   \E
   \BEG
   @node Appendix,,, Top
   @appendix Appendix
   \E
   
 @menu  @menu
   \BJP
 * $BJ8K!$N>\:Y(B::  * $BJ8K!$N>\:Y(B::
 * $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::  * $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::
 * $BF~NO%$%s%?%U%'!<%9(B::  * $BF~NO%$%s%?%U%'!<%9(B::
 * $BJQ99E@(B::  * $BJQ99E@(B::
 * $BJ88%(B::  * $BJ88%(B::
   \E
   \BEG
   * Details of syntax::
   * Files of user defined functions::
   * Input interfaces::
   * Changes::
   * References::
   \E
 @end menu  @end menu
   
   \BJP
 @node $BJ8K!$N>\:Y(B,,, $BIUO?(B  @node $BJ8K!$N>\:Y(B,,, $BIUO?(B
 @section $BJ8K!$N>\:Y(B  @section $BJ8K!$N>\:Y(B
   \E
   \BEG
   @node Details of syntax,,, Appendix
   @section Details of syntax
   \E
   
 @example  @example
 <$B<0(B>: (@xref{$B$5$^$6$^$J<0(B})  \BJP
   <$B<0(B>:
     @samp{(}<$B<0(B>@samp{)}      @samp{(}<$B<0(B>@samp{)}
     <$B<0(B> <$BFs9`1i;;;R(B> <$B<0(B>      <$B<0(B> <$BFs9`1i;;;R(B> <$B<0(B>
     @samp{+} <$B<0(B>      @samp{+} <$B<0(B>
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     @samp{!} <$B<0(B>      @samp{!} <$B<0(B>
     <$B<0(B> @samp{?} <$B<0(B> @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{)}
       <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{|} <$B%*%W%7%g%sJB$S(B> @samp{)}
     <$BJ8;zNs(B>      <$BJ8;zNs(B>
     <$B;X?t%Y%/%H%k(B>      <$B;X?t%Y%/%H%k(B>
     <$B%"%H%`(B>      <$B%"%H%`(B>
     <$B%j%9%H(B>      <$B%j%9%H(B>
   \E
   \BEG
   <expression>:
       @samp{(}<expression>@samp{)}
       <expression> <binary operator> <expression>
       @samp{+} <expression>
       @samp{-} <expression>
       <left value>
       <left value> <assignment operator> <expression>
       <left value> @samp{++}
       <left value> @samp{--}
       @samp{++} <left value>
       @samp{--} <left value>
       @samp{!} <expression>
       <expression> @samp{?} <expression> @samp{:} <expression>
       <function> @samp{(} <expr list> @samp{)}
       <function> @samp{(} <expr list> @samp{|} <option list> @samp{)}
       <string>
       <exponent vector>
       <atom>
       <list>
   \E
 @end example  @end example
   \JP (@xref{$B$5$^$6$^$J<0(B})
   \EG (@xref{various expressions})
   
 @example  @example
   \BJP
 <$B:8JUCM(B>:  <$B:8JUCM(B>:
     <$BJQ?t(B> [@samp{[}<$B<0(B>@samp{]}]*      <$BJQ?t(B> [@samp{[}<$B<0(B>@samp{]}]*
   \E
   \BEG
   <left value>:
       <program variable> [@samp{[}<expression>@samp{]}]*
   \E
 @end example  @end example
   
 @example  @example
   \BJP
 <$BFs9`1i;;;R(B>:  <$BFs9`1i;;;R(B>:
     @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B)      @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B)
   \E
   \BEG
   <binary operator>:
       @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}(exponentiation)
     @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}      @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
   \E
       @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
 @end example  @end example
   
 @example  @example
 <$BBeF~1i;;;R(B>:  \JP <$BBeF~1i;;;R(B>:
   \EG <assignment operator>:
     @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{%=} @samp{^=}      @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{%=} @samp{^=}
 @end example  @end example
   
 @example  @example
   \BJP
 <$B<0JB$S(B>:  <$B<0JB$S(B>:
     <$B6u(B>      <$B6u(B>
     <$B<0(B> [@samp{,} <$B<0(B>]*      <$B<0(B> [@samp{,} <$B<0(B>]*
   \E
   \BEG
   <expr list>:
       <empty>
       <expression> [@samp{,} <expression>]*
   \E
 @end example  @end example
   
 @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{=} <expression>
   \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
 <$B%j%9%H(B>:  <$B%j%9%H(B>:
     @samp{[} <$B<0JB$S(B> @samp{]}      @samp{[} <$B<0JB$S(B> @samp{]}
   \E
   \BEG
   <list>:
       @samp{[} <expr list> @samp{]}
   \E
 @end example  @end example
   
 @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)      $BBgJ8;z$G;O$^$kJ8;zNs(B (X,Y,Japan $B$J$I(B)
   \E
   \BEG
   <program variable>:
      Sequence of alphabetical letters or numeric digits or @code{_}
      that begins with a capital alphabetical letter
      (X,Y,Japan etc.)
   \E
 @end example  @end example
   \JP (@xref{$BJQ?t$*$h$SITDj85(B})
   \EG (@xref{variables and indeterminates})
   
 @example  @example
   \BJP
 <$BH!?t(B>:  <$BH!?t(B>:
    $B>.J8;z$G;O$^$kJ8;zNs(B (fctr,gcd $B$J$I(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  @end example
   
 @example  @example
   \BJP
 <$B%"%H%`(B>:  <$B%"%H%`(B>:
    <$BITDj85(B>     <$BITDj85(B>
    <$B?t(B>     <$B?t(B>
   \E
   \BEG
   <atom>:
      <indeterminate>
      <number>
   \E
 @end example  @end example
   
 @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)     $B>.J8;z$G;O$^$kJ8;zNs(B (a,bCD,c1_2 $B$J$I(B)
   \E
   \BEG
   <indeterminate>:
      Sequence of alphabetical letters or numeric digits or @code{_}
      that begin with a small alphabetical letter
      (a,bCD,c1_2 etc.)
   \E
 @end example  @end example
   \JP (@xref{$BJQ?t$*$h$SITDj85(B})
   \EG (@xref{variables and indeterminates})
   
 @example  @example
 <$B?t(B>: (@xref{$B?t$N7?(B})  \BJP
   <$B?t(B>:
    <$BM-M}?t(B>     <$BM-M}?t(B>
    <$BIbF0>.?t(B>     <$BIbF0>.?t(B>
    <$BBe?tE*?t(B>     <$BBe?tE*?t(B>
    <$BJ#AG?t(B>     <$BJ#AG?t(B>
   \E
   \BEG
   <number>:
      <rational number>
      <floating point number>
      <algebraic number>
      <complex number>
   \E
 @end example  @end example
   \JP (@xref{$B?t$N7?(B})
   \EG (@xref{Types of numbers})
   
 @example  @example
 <$BM-M}?t(B>:  \JP <$BM-M}?t(B>:
   \EG <rational number>:
    0, 1, -2, 3/4     0, 1, -2, 3/4
 @end example  @end example
   
 @example  @example
 <$BIbF0>.?t(B>:  \JP <$BIbF0>.?t(B>:
   \EG <floating point number>:
    0.0, 1.2e10     0.0, 1.2e10
 @end example  @end example
   
 @example  @example
 <$BBe?tE*?t(B>: (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})  \JP <$BBe?tE*?t(B>:
   \EG <algebraic number>:
    newalg(x^2+1), alg(0)^2+1     newalg(x^2+1), alg(0)^2+1
 @end example  @end example
   \JP (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
   \EG (@xref{Algebraic numbers})
   
 @example  @example
 <$BJ#AG?t(B>:  \JP <$BJ#AG?t(B>:
   \EG <complex number>:
    1+@code{@@i}, 2.3*@code{@@i}     1+@code{@@i}, 2.3*@code{@@i}
 @end example  @end example
   
 @example  @example
   \BJP
 <$BJ8;zNs(B>:  <$BJ8;zNs(B>:
    @samp{"} $B$G0O$^$l$?J8;zNs(B     @samp{"} $B$G0O$^$l$?J8;zNs(B
   \E
   \BEG
   <string>:
      character sequence enclosed by two @samp{"}'s.
   \E
 @end example  @end example
   
 @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{>>}     @samp{<<} <$B<0JB$S(B> @samp{>>}
   \E
   \BEG
   <exponent vector>:
      @samp{<<} <expr list> @samp{>>}
   \E
 @end example  @end example
   \JP (@xref{$B%0%l%V%J4pDl$N7W;;(B})
   \EG (@xref{Groebner basis computation})
   
 @example  @example
 <$BJ8(B>: (@xref{$BJ8(B})  \BJP
   <$BJ8(B>:
     <$B<0(B> <$B=*C<(B>      <$B<0(B> <$B=*C<(B>
     <$BJ#J8(B>      <$BJ#J8(B>
     @samp{break} <$B=*C<(B>      @samp{break} <$B=*C<(B>
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     @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>      @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$S(B> @samp{@}}      @samp{def} <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)} @samp{@{} <$BJQ?t@k8@(B> <$BJ8JB$S(B> @samp{@}}
     @samp{end(quit)} <$B=*C<(B>      @samp{end(quit)} <$B=*C<(B>
   \E
   \BEG
   <statement>:
       <expression> <terminator>
       <compound statement>
       @samp{break} <terminator>
       @samp{continue} <terminator>
       @samp{return} <terminator>
       @samp{return} <expression> <terminator>
       @samp{if} @samp{(} <expr list> @samp{)} <statement>
       @samp{if} @samp{(} <expr list> @samp{)} <statement> @samp{else} <statement>
       @samp{for} @samp{(} <expr list> @samp{;} <expr list> @samp{;} <expr list> @samp{)} <statement>
       @samp{do} <statement> @samp{while} @samp{(} <expr list> @samp{)} <terminator>
       @samp{while} @samp{(} <expr list> @samp{)} <statement>
       @samp{def} <function> @samp{(} <expr list> @samp{)} @samp{@{} <variable declaration> <stat list> @samp{@}}
       @samp{end(quit)} <terminator>
   \E
 @end example  @end example
   \JP (@xref{$BJ8(B})
   \EG (@xref{statements})
   
 @example  @example
 <$B=*C<(B>:  \JP <$B=*C<(B>:
   \EG <terminator>:
     @samp{;} @samp{$}      @samp{;} @samp{$}
 @end example  @end example
   
 @example  @example
   \BJP
 <$BJQ?t@k8@(B>:  <$BJQ?t@k8@(B>:
     [@samp{extern} <$BJQ?t(B> [@samp{,} <$BJQ?t(B>]* <$B=*C<(B>]*      [@samp{extern} <$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  @end example
   
 @example  @example
   \BJP
 <$BJ#J8(B>:  <$BJ#J8(B>:
     @samp{@{} <$BJ8JB$S(B> @samp{@}}      @samp{@{} <$BJ8JB$S(B> @samp{@}}
   \E
   \BEG
   <compound statement>:
       @samp{@{} <stat list> @samp{@}}
   \E
 @end example  @end example
   
 @example  @example
   \BJP
 <$BJ8JB$S(B>:  <$BJ8JB$S(B>:
     [<$BJ8(B>]*      [<$BJ8(B>]*
   \E
   \BEG
   <stat list>:
       [<statement>]*
   \E
 @end example  @end example
   
   \BJP
 @node $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B,,, $BIUO?(B  @node $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B,,, $BIUO?(B
 @section $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(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  @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  $BI8=`%i%$%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$$$F(B  $B$$$/$D$+$N%f!<%6Dj5AH!?t%U%!%$%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.  $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  @table @samp
 @item fff  @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  @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  @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  @item alpi
 @itemx bgk  @itemx bgk
 @itemx cyclic  @itemx cyclic
 @itemx katsura  @itemx katsura
 @itemx kimura  @itemx kimura
 $B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B.  \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})  (@xref{katsura hkatsura cyclic hcyclic})
 @item defs.h  @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  @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  $B@0?t>e$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$-$$$$$/$D$+$NNc$r4^$`(B. $B$3$l$O(B, @code{load()} $B$9$k$H(B  $B=EJ#EY$NBg$-$$$$$/$D$+$NNc$r4^$`(B. $B$3$l$O(B, @code{load()} $B$9$k$H(B
 $BD>$A$K7W;;$,;O$^$k(B. $BF~<j$7$?(B @b{Asir} $B$,@5$7$/F0:n$7$F$$$k$+$N(B  $BD>$A$K7W;;$,;O$^$k(B. $BF~<j$7$?(B @b{Asir} $B$,@5$7$/F0:n$7$F$$$k$+$N(B
 $B%F%9%H$K$b;H$&$3$H$,$G$-$k(B.  $B%F%9%H$K$b;H$&$3$H$,$G$-$k(B.
   \E
   \BEG
   Test program of factorization of integral polynomials.
   It includes  @samp{factor.tst} of REDUCE and several examples
   for large multiplicity factors.  If this file is @code{load()}'ed,
   computation will begin immediately.
   You may use it as a first test whether @b{Asir} at you hand runs
   correctly.
   \E
 @item fctrdata  @item fctrdata
   \BJP
 @samp{fctrtest} $B$G;H$o$l$F$$$kNc$r4^$`(B, $B0x?tJ,2r%F%9%HMQ$NNc(B.  @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$$$kNc$O(B, @code{af()} (@xref{asq af}) $BMQ$NNc$G$"$k(B.
   \E
   \BEG
   This contains example polynomials for factorization.  It includes
   polynomials used in @samp{fctrtest}.
   Polynomials contained in vector @code{Alg[]} is for the algebraic
   factorization @code{af()} (@xref{asq af}).
   \E
 @example  @example
 [45] load("sp")$  [45] load("sp")$
 [84] load("fctrdata")$  [84] load("fctrdata")$
Line 204  x^9-15*x^6-87*x^3-125
Line 445  x^9-15*x^6-87*x^3-125
 3.600sec + gc : 1.040sec  3.600sec + gc : 1.040sec
 @end example  @end example
 @item ifplot  @item ifplot
   \BJP
 $BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B  $BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
 $B6J@~$NNc(B, $BJQ?t(B @code{H, D, C, S} $B$K$O%H%i%s%W$N%O!<%H(B, $B%@%$%d(B, $B%/%i%V(B,  $B6J@~$NNc(B, $BJQ?t(B @code{H, D, C, S} $B$K$O%H%i%s%W$N%O!<%H(B, $B%@%$%d(B, $B%/%i%V(B,
 $B%9%Z!<%I(B ($B$i$7$-(B) $B6J@~$NNc$,F~$C$F$$$k(B.  $B%9%Z!<%I(B ($B$i$7$-(B) $B6J@~$NNc$,F~$C$F$$$k(B.
   \E
   \BEG
   Examples for plotting (@xref{ifplot conplot plot plotover}).
   Vector @code{IS[]} contains several famous algebraic curves.
   Variables @code{H, D, C, S} contains something like the suits
   (Heart, Diamond, Club, and Spade) of cards.
   \E
 @item num  @item num
 $B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B.  \JP $B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
   \EG Examples of simple operations on numbers.
 @item mat  @item mat
 $B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B.  \JP $B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
   \EG Examples of simple operations on matrices.
 @item ratint  @item ratint
   \BJP
 $BM-M}H!?t$NITDj@QJ,(B. @samp{sp}, @samp{gr} $B$,I,MW(B. @code{ratint()} $B$H$$$&(B  $BM-M}H!?t$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.  $BH!?t$,Dj5A$5$l$F$$$k$,(B, $B$=$NJV$97k2L$O$d$dJ#;($G$"$k(B. $BNc$G@bL@$9$k(B.
   \E
   \BEG
   Indefinite integration of rational functions.  For this,
   files @samp{sp} and @samp{gr} is necessary.  A function @code{ratint()}
   is defined.  Its returns a rather complex result.
   \E
 @example  @example
 [0] load("gr")$  [0] load("gr")$
 [45] load("sp")$  [45] load("sp")$
Line 223  x^9-15*x^6-87*x^3-125
Line 481  x^9-15*x^6-87*x^3-125
 [[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),161*t#2^3-23*t#2^2+15*t#2-1],  [[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),161*t#2^3-23*t#2^2+15*t#2-1],
 [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]  [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
 @end example  @end example
   \BJP
 $B$3$NNc$G$O(B, @code{x^6/(x^5+x+1)} $B$NITDj@QJ,$N7W;;$r9T$C$F$$$k(B.  $B$3$NNc$G$O(B, @code{x^6/(x^5+x+1)} $B$NITDj@QJ,$N7W;;$r9T$C$F$$$k(B.
 $B7k2L$O(B 2 $B$D$NMWAG$+$i$J$k%j%9%H$G(B, $BBh(B 1 $BMWAG$OITDj@QJ,$NM-M}ItJ,(B,  $B7k2L$O(B 2 $B$D$NMWAG$+$i$J$k%j%9%H$G(B, $BBh(B 1 $BMWAG$OITDj@QJ,$NM-M}ItJ,(B,
 $BBh(B 2 $BMWAG$OBP?tItJ,$rI=$9(B. $BBP?tItJ,$O99$K%j%9%H$H$J$C$F$$$F(B, $B3FMWAG$O(B,  $BBh(B 2 $BMWAG$OBP?tItJ,$rI=$9(B. $BBP?tItJ,$O99$K%j%9%H$H$J$C$F$$$F(B, $B3FMWAG$O(B,
Line 232  x^9-15*x^6-87*x^3-125
Line 491  x^9-15*x^6-87*x^3-125
 @code{root} $B$r4^$s$G$$$F(B, @code{root} $B$rF~$lBX$($k>l9g$K$O(B @code{poly}  @code{root} $B$r4^$s$G$$$F(B, @code{root} $B$rF~$lBX$($k>l9g$K$O(B @code{poly}
 $B$KBP$7$F$bF1$8A`:n$r9T$&$b$N$H$9$k(B. $B$3$NA`:n$r(B, $B7k2L$NBh(B 2 $BMWAG$N(B  $B$KBP$7$F$bF1$8A`:n$r9T$&$b$N$H$9$k(B. $B$3$NA`:n$r(B, $B7k2L$NBh(B 2 $BMWAG$N(B
 $B3F@.J,$KBP$7$F9T$C$F(B, $BA4$F$rB-$79g$o$;$?$b$N$,BP?tItJ,$H$J$k(B.  $B3F@.J,$KBP$7$F9T$C$F(B, $BA4$F$rB-$79g$o$;$?$b$N$,BP?tItJ,$H$J$k(B.
   \E
   \BEG
   In this example, indefinite integral of the rational function
    @code{x^6/(x^5+x+1)} is computed.
   The result is a list which comprises two elements:
   The first element is the rational part of the integral;
   The second part is the logarithmic part of the integral.
   The logarithmic part is again a list which comprises finite number of
   elements, each of which is of form @code{[root*log(poly),defpoly]}.
   This pair should be interpreted to sum up
   the expression @code{root*log(poly)}
   through all @b{root}'s @code{root}'s of the @code{defpoly}.
   Here, @code{poly} contains @code{root}, and substitution for @code{root}
   is equally applied to @code{poly}.
   The logarithmic part in total is obtained by applying such
   interpretation to all element pairs in the second element of the
   result and then summing them up all.
   \E
 @item primdec  @item primdec
   \BJP
 $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B  $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
 (@code{[Shimoyama,Yokoyama]} $B;2>H(B).  (@code{[Shimoyama,Yokoyama]} $B;2>H(B).
 $B=`AG%$%G%"%kJ,2r$O(B @code{primadec()}, $BAG%$%G%"%kJ,2r$O(B, @code{primedec()}  $B=`AG%$%G%"%kJ,2r$O(B @code{primadec()}, $BAG%$%G%"%kJ,2r$O(B, @code{primedec()}
Line 243  x^9-15*x^6-87*x^3-125
Line 521  x^9-15*x^6-87*x^3-125
 $B$=$N7k2L$O$$$:$l$b%0%l%V%J4pDl$K$J$C$F$$$k$,(B, $B$=$N(B  $B$=$N7k2L$O$$$:$l$b%0%l%V%J4pDl$K$J$C$F$$$k$,(B, $B$=$N(B
 $BJQ?t=g=x$O(B, $B$=$l$>$lBg0hJQ?t(B @code{PRIMAORD}, @code{PRIMEORD}  $BJQ?t=g=x$O(B, $B$=$l$>$lBg0hJQ?t(B @code{PRIMAORD}, @code{PRIMEORD}
  $B$NCM(B 0,1 $B$"$k$$$O(B 2 $B$K$h$C$F7h$^$k(B.   $B$NCM(B 0,1 $B$"$k$$$O(B 2 $B$K$h$C$F7h$^$k(B.
   \E
   \BEG
   Primary ideal decomposition of polynomial ideals and prime compotision
   of radicals
   (Refer to @code{[Shimoyama,Yokoyama]}).
   @code{primadec()}, @code{primedec()} are the function for primary
   ideal decomposition and prime decomposition of the radical respectively.
   The arguments are a list of polynomials and a list of variables.
   These functions accept ideals with rational function coefficients
   and non zero-dimenstional ideals.
   @code{primadec} returns the list of pair lists consisting a primary component
   and its associated prime.
   @code{primedec} returns the list of prime components.
   Each component is a Groebner basis and the corresponding term order
   is indicated by the global variables @code{PRIMAORD}, @code{PRIMEORD}
   respectively.
   \E
 @example  @example
 [84] load("primdec")$  [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,  [102] primedec([p*q*x-q^2*y^2+q^2*y,-p^2*x^2+p^2*x+p*q*y,
Line 254  x^9-15*x^6-87*x^3-125
Line 549  x^9-15*x^6-87*x^3-125
 @end example  @end example
 @end table  @end table
   
   \BJP
 @node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B  @node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B
 @section $BF~NO%$%s%?%U%'!<%9(B  @section $BF~NO%$%s%?%U%'!<%9(B
   \E
   \BEG
   @node Input interfaces,,, Appendix
   @section Input interfaces
   \E
   
   \BJP
 $B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B  $B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$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$$$k(B. UNIX $BHG$G$O(B  $B$7$F%3%^%s%I%i%$%sJT=8$*$h$S%R%9%H%jCV$-49$($,AH$_9~$^$l$F$$$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$3$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$$$k(B. $B$3$l$i$O(B @b{Asir} $B%P%$%J%j$H$H$b$K(B ftp $B2DG=$G$"$k(B.  $B$,MQ0U$5$l$F$$$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}.  ftp server $B$K4X$7$F$O(B @xref{$BF~<jJ}K!(B}.
   \E
   \BEG
   As already mentioned a command line editing facility and a history
   substitution facility are built-in for DOS, Windows Macintosh 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}.
   \E
   
 @menu  @menu
 * fep::  * fep::
 * asir.el::  * asir.el::
 @end menu  @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  @subsection fep
   
 @noindent  @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  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  $BMQ$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$$$O(B emacs $BIw$N%3%^%s%I%i%$%sJT=8$*$h$S(B csh $BIw$N%R%9%H%j(B  $B$3$H$K$h$j(B vi $B$"$k$$$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.  $BCV$-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  @example
 % fep asir  % fep asir
 ...  ...
 [0] fctr(x^5-1);  [0] fctr(x^5-1);
 [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]  [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
 [1] !!                              /* !!+Return                      */  [1] !!                              /* !!+Return                      */
   \BJP
 fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */  fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */
 ...                                 /* $BJT=8(B+Return                    */  ...                                 /* $BJT=8(B+Return                    */
   \E
   \BEG
   fctr(x^5-1);                        /* The last input appears.        */
   ...                                 /* Edit+Return                    */
   \E
 fctr(x^5+1);  fctr(x^5+1);
 [[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]  [[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]
 @end example  @end example
   
 @noindent  @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  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$$7$?$b$N(B  $B5!<o(B (OS) $B$,8B$i$l$F$$$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.  $B$,(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  @subsection asir.el
   
 @noindent  @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  @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$*$$$F$O(B,  $B5\Eh8w<#;a(B (@code{YVE25250@@pcvan.or.jp}).  @samp{asir.el} $B$K$*$$$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  $BDL>o$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$$$k(B.  $B$,<B8=$5$l$F$$$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  @noindent
   \BJP
 @samp{asir.el} $B$O(B PC-VAN $B$G(B  @samp{asir.el} $B$O(B PC-VAN $B$G(B
 $B4{$K8x3+$5$l$F$$$k$,(B, $B:#2s$N2~D{$KH<$&JQ99$r9T$C$?$b$N$,(B, $B$d$O$j(B ftp $B$G(B  $B4{$K8x3+$5$l$F$$$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.  $BF~<j2DG=$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  @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 $BJQ99E@(B,,, $BIUO?(B  @node $BJQ99E@(B,,, $BIUO?(B
 @section $BJQ99E@(B  @section $BJQ99E@(B
   \E
   \BEG
   @node Changes,,, Appendix
   @section Appendix
   \E
   
 @menu  @menu
 * Version 990831::  * Version 990831::
Line 320  fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $
Line 681  fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $
 * Version 940420::  * Version 940420::
 @end menu  @end menu
   
 @node Version 990831,,, $BJQ99E@(B  \JP @node Version 990831,,, $BJQ99E@(B
   \EG @node Version 990831,,, Changes
 @subsection Version 990831  @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,  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,  $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.  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  $B5lHG$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$$$&E@$G$"$k(B.  $B>l9g$O(B @code{bload27} $B$r;H$&I,MW$,$"$k(B, $B$H$$$&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  @subsection Version 950831
   
 @menu  @menu
   \BJP
 * $B%G%P%C%,(B($BJQ99(B)::  * $B%G%P%C%,(B($BJQ99(B)::
 * $BAH$_9~$_H!?t(B($BJQ99(B)::  * $BAH$_9~$_H!?t(B($BJQ99(B)::
 * $B%0%l%V%J4pDl(B($BJQ99(B)::  * $B%0%l%V%J4pDl(B($BJQ99(B)::
 * $B$=$NB>(B($BJQ99(B)::  * $B$=$NB>(B($BJQ99(B)::
   \E
   \BEG
   * Debugger(Changes)::
   * Built-in functions(Changes)::
   * Groebner basis computation(Changes)::
   * Others(Changes)::
   \E
 @end menu  @end menu
   
   \BJP
 @node $B%G%P%C%,(B($BJQ99(B),,, Version 950831  @node $B%G%P%C%,(B($BJQ99(B),,, Version 950831
 @subsubsection $B%G%P%C%,(B  @subsubsection $B%G%P%C%,(B
   \E
   \BEG
   @node Debugger(Changes),,, Version 950831
   @subsubsection Debugger
   \E
   
 @itemize @bullet  @itemize @bullet
 @item  @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  @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  @item
   \BJP
 @code{up}, @code{down}, @code{frame} $B%3%^%s%I$K$h$k(B, $BG$0U$N%9%?%C%/%U%l!<%`(B  @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  @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  @end itemize
   
   \BJP
 @node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831  @node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831
 @subsubsection $BAH$_9~$_H!?t(B  @subsubsection $BAH$_9~$_H!?t(B
   \E
   \BEG
   @node Built-in functions(Changes),,, Version 950831
   @subsubsection Built-in functions
   \E
   
 @itemize @bullet  @itemize @bullet
   \BJP
 @item  @item
 @code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B.  @code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B.
 @item  @item
Line 369  plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
Line 771  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.  @code{vtol()} ($B%Y%/%H%k$+$i%j%9%H$X$NJQ49(B) $B$NDI2C(B.
 @item  @item
 @code{map()} $B$NDI2C(B.  @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  @end itemize
   
   \BJP
 @node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831  @node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831
 @subsubsection $B%0%l%V%J4pDl(B  @subsubsection $B%0%l%V%J4pDl(B
   \E
   \BEG
   @node Groebner basis computation(Changes),,, Version 950831
   @subsubsection Groebner basis computation
   \E
   
 @itemize @bullet  @itemize @bullet
   \BJP
 @item  @item
 $B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B.  $B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B.
 @item  @item
Line 389  plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
Line 812  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.  $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl7W;;$N%5%]!<%H(B.
 @item  @item
 $B$$$/$D$+$N?7$7$$AH$_9~$_H!?t$NDs6!(B.  $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  @end itemize
   
   \BJP
 @node $B$=$NB>(B($BJQ99(B),,, Version 950831  @node $B$=$NB>(B($BJQ99(B),,, Version 950831
 @subsubsection $B$=$NB>(B  @subsubsection $B$=$NB>(B
   \E
   \BEG
   @node Others(Changes),,, Version 950831
   @subsubsection Others
   \E
   
 @itemize @bullet  @itemize @bullet
   \BJP
 @item  @item
 $BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.  $BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.
 @item  @item
Line 403  plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
Line 852  plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B. 
 $B%$%G%"%k$N=`AGJ,2r$N%5%]!<%H(B.  $B%$%G%"%k$N=`AGJ,2r$N%5%]!<%H(B.
 @item  @item
 Windows $B$X$N0\?"(B.  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  @end itemize
   
 @node Version 940420,,, $BJQ99E@(B  \JP @node Version 940420,,, $BJQ99E@(B
   \EG @node Version 940420,,, Changes
 @subsection Version 940420  @subsection Version 940420
   
 @noindent  @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  @node $BJ88%(B,,, $BIUO?(B
 @section $BJ88%(B  @section $BJ88%(B
   \E
   \BEG
   @node References,,, Appendix
   @section References
   \E
 @table @code  @table @code
 @item [Batut et al.]  @item [Batut et al.]
 Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",  Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",
Line 434  Proc. ISSAC'91, 49-54.
Line 903  Proc. ISSAC'91, 49-54.
 Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",  Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",
 Proc. ISSAC'92, 387-396.  Proc. ISSAC'92, 387-396.
 @item [Noro,Yokoyama]  @item [Noro,Yokoyama]
 Noro, M., Yokoyama, K., "New methods for the change-of-ordering in Groebner  Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate
 basis computation", ISIS Research Report ISIS-RR-95-8E, 1995.  Representation of Zero-Dimensional Ideals",
   J. Symb. Comp. 28/1 (1999), 243-263.
 @item [Shimoyama,Yokoyama]  @item [Shimoyama,Yokoyama]
 Shimoyama, T., Yokoyama, K.,  Shimoyama, T., Yokoyama, K.,
 "Localization and primary decomposition of polynomial ideals",  "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]  @item [Traverso]
 Traverso, C., "Groebner trace algorithms", Proc. ISSAC '88(LNCS 358), 125-138.  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.
 @end table  @end table
   

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