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version 1.6, 2000/03/17 08:27:28 version 1.13, 2003/04/24 08:13:24
Line 1 
Line 1 
 @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.5 2000/03/17 02:17:03 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.12 2003/04/21 03:07:31 noro Exp $
 \BJP  \BJP
 @node $BIUO?(B,,, Top  @node $BIUO?(B,,, Top
 @appendix $BIUO?(B  @appendix $BIUO?(B
Line 80 
Line 80 
     <list>      <list>
 \E  \E
 @end example  @end example
 \JP (@xref{$B$5$^$6$^$J<0(B})  \JP (@xref{$B$5$^$6$^$J<0(B}.)
 \EG (@xref{various expressions})  \EG (@xref{various expressions}.)
   
 @example  @example
 \BJP  \BJP
Line 133 
Line 133 
 \E  \E
 \BEG  \BEG
 <option>:  <option>:
     Character sequence beginning with an alphabetical letter @samp{=} <expression>      Character sequence beginning with an alphabetical letter @samp{=} <expr>
 \E  \E
 @end example  @end example
   
Line 174 
Line 174 
    (X,Y,Japan etc.)     (X,Y,Japan etc.)
 \E  \E
 @end example  @end example
 \JP (@xref{$BJQ?t$*$h$SITDj85(B})  \JP (@xref{$BJQ?t$*$h$SITDj85(B}.)
 \EG (@xref{variables and indeterminates})  \EG (@xref{variables and indeterminates}.)
   
 @example  @example
 \BJP  \BJP
Line 215 
Line 215 
    (a,bCD,c1_2 etc.)     (a,bCD,c1_2 etc.)
 \E  \E
 @end example  @end example
 \JP (@xref{$BJQ?t$*$h$SITDj85(B})  \JP (@xref{$BJQ?t$*$h$SITDj85(B}.)
 \EG (@xref{variables and indeterminates})  \EG (@xref{variables and indeterminates}.)
   
 @example  @example
 \BJP  \BJP
Line 234 
Line 234 
    <complex number>     <complex number>
 \E  \E
 @end example  @end example
 \JP (@xref{$B?t$N7?(B})  \JP (@xref{$B?t$N7?(B}.)
 \EG (@xref{Types of numbers})  \EG (@xref{Types of numbers}.)
   
 @example  @example
 \JP <$BM-M}?t(B>:  \JP <$BM-M}?t(B>:
Line 254 
Line 254 
 \EG <algebraic number>:  \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})  \JP (@xref{$BBe?tE*?t$K4X$9$k1i;;(B}.)
 \EG (@xref{Algebraic numbers})  \EG (@xref{Algebraic numbers}.)
   
 @example  @example
 \JP <$BJ#AG?t(B>:  \JP <$BJ#AG?t(B>:
Line 284 
Line 284 
    @samp{<<} <expr list> @samp{>>}     @samp{<<} <expr list> @samp{>>}
 \E  \E
 @end example  @end example
 \JP (@xref{$B%0%l%V%J4pDl$N7W;;(B})  \JP (@xref{$B%0%l%V%J4pDl$N7W;;(B}.)
 \EG (@xref{Groebner basis computation})  \EG (@xref{Groebner basis computation}.)
   
 @example  @example
 \BJP  \BJP
Line 321 
Line 321 
     @samp{end(quit)} <terminator>      @samp{end(quit)} <terminator>
 \E  \E
 @end example  @end example
 \JP (@xref{$BJ8(B})  \JP (@xref{$BJ8(B}.)
 \EG (@xref{statements})  \EG (@xref{statements}.)
   
 @example  @example
 \JP <$B=*C<(B>:  \JP <$B=*C<(B>:
Line 386  Here, we explain some of them.
Line 386  Here, we explain some of them.
   
 @table @samp  @table @samp
 @item fff  @item fff
 \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})  \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})  \EG Univariate factorizer over large finite fields (@xref{Finite fields}.)
 @item gr  @item gr
 \JP $B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B.  (@xref{$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})  \EG Groebner basis package.  (@xref{Groebner basis computation}.)
 @item sp  @item sp
 \JP $BBe?tE*?t$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})  \EG Operations over algebraic numbers and factorization, Splitting fields. (@xref{Algebraic numbers}.)
 @item alpi  @item alpi
 @itemx bgk  @itemx bgk
 @itemx cyclic  @itemx cyclic
Line 401  Here, we explain some of them.
Line 401  Here, we explain some of them.
 @itemx kimura  @itemx kimura
 \JP $B%0%l%V%J4pDl7W;;$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.  \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
 \JP $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})  \EG Macro definitions. (@xref{preprocessor}.)
 @item fctrtest  @item fctrtest
 \BJP  \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
Line 423  correctly.
Line 423  correctly.
 @item fctrdata  @item fctrdata
 \BJP  \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$$$kNc$O(B, @code{af()} (@xref{asq af af_noalg}) $BMQ$NNc$G$"$k(B.  @code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@ref{asq af af_noalg}) $BMQ$NNc$G$"$k(B.
 \E  \E
 \BEG  \BEG
 This contains example polynomials for factorization.  It includes  This contains example polynomials for factorization.  It includes
 polynomials used in @samp{fctrtest}.  polynomials used in @samp{fctrtest}.
 Polynomials contained in vector @code{Alg[]} is for the algebraic  Polynomials contained in vector @code{Alg[]} is for the algebraic
 factorization @code{af()} (@xref{asq af af_noalg}).  factorization @code{af()}. (@xref{asq af af_noalg}.)
 \E  \E
 @example  @example
 [45] load("sp")$  [45] load("sp")$
Line 440  factorization @code{af()} (@xref{asq af af_noalg}).
Line 440  factorization @code{af()} (@xref{asq af af_noalg}).
 x^9-15*x^6-87*x^3-125  x^9-15*x^6-87*x^3-125
 0msec  0msec
 [177] af(Alg[5],[newalg(Alg[5])]);  [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],  [[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x
 [75*x^2+(-10*#0^7+175*#0^4+395*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],  +(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],  [75*x^2+(-10*#0^7+175*#0^4+395*#0)*x
 [x+(-#0),1]]  +(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  3.600sec + gc : 1.040sec
 @end example  @end example
 @item ifplot  @item ifplot
 \BJP  \BJP
 $BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B  $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,  $B6J@~$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  \E
 \BEG  \BEG
 Examples for plotting (@xref{ifplot conplot plot plotover}).  Examples for plotting. (@xref{ifplot conplot plot polarplot plotover}.)
 Vector @code{IS[]} contains several famous algebraic curves.  Vector @code{IS[]} contains several famous algebraic curves.
 Variables @code{H, D, C, S} contains something like the suits  Variables @code{H, D, C, S} contains something like the suits
 (Heart, Diamond, Club, and Spade) of cards.  (Heart, Diamond, Club, and Spade) of cards.
Line 480  is defined.  Its returns a rather complex result.
Line 482  is defined.  Its returns a rather complex result.
 [84] load("ratint")$  [84] load("ratint")$
 [102] ratint(x^6/(x^5+x+1),x);  [102] ratint(x^6/(x^5+x+1),x);
 [1/2*x^2,  [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]]]  [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
 @end example  @end example
 \BJP  \BJP
Line 513  result and then summing them up all.
Line 516  result and then summing them up all.
 \E  \E
 @item primdec  @item primdec
 \BJP  \BJP
 $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B  $BM-M}?tBN>e$NB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
 (@pxref{primadec primedec}).  (@pxref{primadec primedec}).
 \E  \E
 \BEG  \BEG
 Primary ideal decomposition of polynomial ideals and prime compotision  Primary ideal decomposition of polynomial ideals and prime compotision
 of radicals (@pxref{primadec primedec}).  of radicals over the rationals (@pxref{primadec primedec}).
 \E  \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
   @item bfct
   \BJP
   b $B4X?t$N7W;;(B.
   \E
   \BEG
   Computation of b-function.
   \E
   (@pxref{bfunction bfct generic_bfct}).
 @end table  @end table
   
 \BJP  \BJP
Line 532  of radicals (@pxref{primadec primedec}).
Line 552  of radicals (@pxref{primadec primedec}).
 \E  \E
   
 \BJP  \BJP
 $B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B  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$$$k(B. UNIX $BHG$G$O(B  $B$7$F%3%^%s%I%i%$%sJT=8$*$h$S%R%9%H%jCV$-49$($,AH$_9~$^$l$F$$$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}.
   
   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  \E
 \BEG  \BEG
 As already mentioned a command line editing facility and a history  A command line editing facility and a history
 substitution facility are built-in for DOS, Windows Macintosh version  substitution facility are built-in for DOS, Windows version
 of @b{Asir}. UNIX versions of @b{Asir} do not have such built-in facilites.  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  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}.  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  \E
   
 @menu  @menu
Line 577  available for UNIX commands, including @samp{asir}.
Line 614  available for UNIX commands, including @samp{asir}.
 [[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  \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$FJT=8$G$-$k(B */
 ...                                 /* $BJT=8(B+Return                    */  ...                                 /* $BJT=8(B+Return                  */
 \E  \E
 \BEG  \BEG
 fctr(x^5-1);                        /* The last input appears.        */  fctr(x^5-1);                        /* The last input appears.        */
Line 662  distribution (@code{http://www.math.kobe-u.ac.jp/OpenX
Line 699  distribution (@code{http://www.math.kobe-u.ac.jp/OpenX
 It is possible to link an @b{Asir} library to use the functionalities of  It is possible to link an @b{Asir} library to use the functionalities of
 @b{Asir} from other programs.  @b{Asir} from other programs.
 The necessary libraries are included in the @b{OpenXM} distribution  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}).  (@code{http://www.math.kobe-u.ac.jp/OpenXM}).
 At present only the @b{OpenXM} interfaces are available. Here we assume  At present only the @b{OpenXM} interfaces are available. Here we assume
 that @b{OpenXM} is already installed. In the following  that @b{OpenXM} is already installed. In the following
Line 1177  Proc. ISSAC'92, 387-396.
Line 1217  Proc. ISSAC'92, 387-396.
 Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate  Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate
 Representation of Zero-Dimensional Ideals",  Representation of Zero-Dimensional Ideals",
 J. Symb. Comp. 28/1 (1999), 243-263.  J. Symb. Comp. 28/1 (1999), 243-263.
   @item [Saito,Sturmfels,Takayama]
   Saito, M., Sturmfels, B., Takayama, N.,
   "Groebner deformations of hypergeometric differential equations",
   Algorithms and Computation in Mathematics 6, Springer-Verlag (2000).
 @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",
Line 1188  J. Symb. Comp. 20 (1995), 364-397.
Line 1232  J. Symb. Comp. 20 (1995), 364-397.
 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]  @item [Weber]
 Weber, K., "The accelerated Integer GCD Algorithm", ACM TOMS, 21, 1(1995), 111-122.  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  @end table
   
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