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version 1.9, 2002/09/03 01:50:57 version 1.14, 2003/04/28 03:09:23
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.8 2002/08/13 07:44:06 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.13 2003/04/24 08:13:24 noro Exp $
 \BJP  \BJP
 @node $BIUO?(B,,, Top  @node $BIUO?(B,,, Top
 @appendix $BIUO?(B  @appendix $BIUO?(B
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 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 (@ref{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 ann ann0}).
 @end table  @end table
   
 \BJP  \BJP
Line 594  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 1197  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 1208  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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