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version 1.7, 2001/03/16 05:18:04

version 1.13, 2003/04/24 08:13:24

Line 1

@comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.6 2000/03/17 08:27:28 noro Exp $

@comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.12 2003/04/21 03:07:31 noro Exp $

\BJP

@node $BIUO?(B,,, Top

@appendix $BIUO?(B

Line 80

<list>

@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

\BJP

Line 133

\BEG

<option>:

Character sequence beginning with an alphabetical letter @samp{=} <expression>

Character sequence beginning with an alphabetical letter @samp{=} <expr>

@end example

Line 174

(X,Y,Japan etc.)

@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

\BJP

Line 215

(a,bCD,c1_2 etc.)

@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

\BJP

Line 234

@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

\JP <$BM-M}?t(B>:

Line 254

\EG <algebraic number>:

newalg(x^2+1), alg(0)^2+1

@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

\JP <$BJ#AG?t(B>:

Line 284

@samp{<<} <expr list> @samp{>>}

@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

\BJP

Line 321

@samp{end(quit)} <terminator>

@end example

\JP (@xref{$BJ8(B})

\JP (@xref{$BJ8(B}.)

\EG (@xref{statements})

\EG (@xref{statements}.)

@example

\JP <$B=*C<(B>:

Line 386 Here, we explain some of them.

@table @samp

@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

\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

\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

@itemx bgk

@itemx cyclic

Line 401 Here, we explain some of them.

@itemx kimura

\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

\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

\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

Line 423 correctly.

@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 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.

\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}).

factorization @code{af()}. (@xref{asq af af_noalg}.)

@example

[45] load("sp")$

Line 440 factorization @code{af()} (@xref{asq af af_noalg}).

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],

[[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

@end example

@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 (@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.

\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.

Variables @code{H, D, C, S} contains something like the suits

(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")$

[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

Line 513 result and then summing them up all.

Line 516 result and then summing them up all.

@item primdec

\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}).

\BEG

Primary ideal decomposition of polynomial ideals and prime compotision

of radicals (@pxref{primadec primedec}).

of radicals over the rationals (@pxref{primadec primedec}).

@item primdec_mod

\BJP

$BM-8BBN>e$NB?9`<0%$%G%"%k$N:,4p$NAG%$%G%"%kJ,2r(B

(@pxref{primedec_mod}).

\BEG

Prime decomposition of radicals of polynomial ideals

over finite fields (@pxref{primedec_mod}).

@item bfct

\BJP

b $B4X?t$N7W;;(B.

\BEG

Computation of b-function.

(@pxref{bfunction bfct generic_bfct}).

@end table

\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] !! /* !!+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$FJT=8$G$-$k(B */

... /* $BJT=8(B+Return */

\BEG

fctr(x^5-1); /* The last input appears. */

Line 679 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

@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

Line 1194 Proc. ISSAC'92, 387-396.

Line 1217 Proc. ISSAC'92, 387-396.

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 [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]

Shimoyama, T., Yokoyama, K.,

"Localization and primary decomposition of polynomial ideals",

Line 1205 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.

@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

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