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version 1.2, 1999/12/10 06:58:49

version 1.3, 1999/12/21 02:47:30

Line 1

@comment $OpenXM$

\BJP

@node $BIUO?(B,,, Top

@appendix $BIUO?(B

\BEG

@node Appendix,,, Top

@appendix Appendix

@menu

\BJP

* $BJ8K!$N>\:Y(B::

* $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::

* $BF~NO%$%s%?%U%'!<%9(B::

* $BJQ99E@(B::

* $BJ88%(B::

\BEG

* Details of syntax::

* Files of user defined functions::

* Input interfaces::

* Changes::

* References::

@end menu

\BJP

@node $BJ8K!$N>\:Y(B,,, $BIUO?(B

@section $BJ8K!$N>\:Y(B

\BEG

@node Details of syntax,,, Appendix

@section Details of syntax

@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>

Line 32

Line 55

<$B;X?t%Y%/%H%k(B>

<$B%"%H%`(B>

<$B%j%9%H(B>

\BEG

<expression>:

@samp{(}<expression>@samp{)}

@samp{+} <expression>

@samp{-} <expression>

<left value> @samp{++}

<left value> @samp{--}

@samp{++} <left value>

@samp{--} <left value>

@samp{!} <expression>

<function> @samp{(} <expr list> @samp{)}

<function> @samp{(} <expr list> @samp{|} <option list> @samp{)}

<atom>

<list>

@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{]}]*

\BEG

<left value>:

<program variable> [@samp{[}<expression>@samp{]}]*

@end example

@example

\BJP

<$BFs9`1i;;;R(B>:

@samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B)

\BEG

<binary operator>:

@samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}(exponentiation)

@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>]*

\BEG

<expr list>:

<empty>

<expression> [@samp{,} <expression>]*

@end example

@example

\BJP

<$B%*%W%7%g%s(B>:

alphabet $B$G;O$^$kJ8;zNs(B @samp{=} $B<0(B

alphabet $B$G;O$^$kJ8;zNs(B @samp{=} <$B<0(B>

\BEG

<option>:

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

@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>]*

\BEG

<option list>:

<option> [@samp{,} <option>]*

@end example

@example

\BJP

<$B%j%9%H(B>:

@samp{[} <$B<0JB$S(B> @samp{]}

\BEG

<list>:

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

@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)

\BEG

<program variable>:

Sequence of alphabetical letters or numeric digits or @code{_}

that begins with a capital alphabetical letter

(X,Y,Japan etc.)

@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)

\BEG

<function>:

Sequence of alphabetical letters or numeric digits or @code{_}

that begins with a small alphabetical letter

(fctr,gcd etc.)

@end example

@example

\BJP

<$B%"%H%`(B>:

<$BITDj85(B>

<$B?t(B>

\BEG

<atom>:

@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)

\BEG

<indeterminate>:

Sequence of alphabetical letters or numeric digits or @code{_}

that begin with a small alphabetical letter

(a,bCD,c1_2 etc.)

@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>

\BEG

<number>:

@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

\BEG

<string>:

character sequence enclosed by two @samp{"}'s.

@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{>>}

\BEG

<exponent vector>:

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

@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>

Line 147

Line 301

@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>

\BEG

<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>

@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>]*

\BEG

<variable declaration>:

[@samp{extern} <program variable> [@samp{,} <program variable>]* <terminator>]*

@end example

@example

\BJP

<$BJ#J8(B>:

@samp{@{} <$BJ8JB$S(B> @samp{@}}

\BEG

<compound statement>:

@samp{@{} <stat list> @samp{@}}

@end example

@example

\BJP

<$BJ8JB$S(B>:

[<$BJ8(B>]*

\BEG

<stat list>:

[<statement>]*

@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

\BEG

@node Files of user defined functions,,, Appendix

@section Files of user defined functions

@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.

\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.

@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.

\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.

\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.

@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.

\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}).

@example

[45] load("sp")$

[84] load("fctrdata")$

Line 217 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

@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

$B6J@~$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}).

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.

@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.

\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.

@example

[0] load("gr")$

[45] load("sp")$

Line 236 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],

[(#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,

Line 245 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}

$B$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.

\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.

@item primdec

\BJP

$BB?9`<0%$%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()}

Line 256 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

$BJQ?t=g=x$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.

\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.

@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,

Line 267 x^9-15*x^6-87*x^3-125

Line 549 x^9-15*x^6-87*x^3-125

@end example

@end table

\BJP

@node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B

@section $BF~NO%$%s%?%U%'!<%9(B

\BEG

@node Input interfaces,,, Appendix

@section Input interfaces

\BJP

$B4{$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$3$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}.

\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}.

@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.

\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}.

@example

% fep asir

...

[0] fctr(x^5-1);

[[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 */

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

\BEG

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

... /* Edit+Return */

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.

\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.

@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.

\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.

@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.

\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.

@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}.

\BJP

@node $BJQ99E@(B,,, $BIUO?(B

@section $BJQ99E@(B

\BEG

@node Changes,,, Appendix

@section Appendix

@menu

* Version 990831::

Line 333 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::

@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.

@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.

\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)::

\BEG

* Debugger(Changes)::

* Built-in functions(Changes)::

* Groebner basis computation(Changes)::

* Others(Changes)::

@end menu

\BJP

@node $B%G%P%C%,(B($BJQ99(B),,, Version 950831

@subsubsection $B%G%P%C%,(B

\BEG

@node Debugger(Changes),,, Version 950831

@subsubsection Debugger

@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.

\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

\BEG

@node Built-in functions(Changes),,, Version 950831

@subsubsection Built-in functions

@itemize @bullet

\BJP

@item

@code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B.

@item

Line 382 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.

@item

@code{map()} $B$NDI2C(B.

\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.

@end itemize

\BJP

@node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831

@subsubsection $B%0%l%V%J4pDl(B

\BEG

@node Groebner basis computation(Changes),,, Version 950831

@subsubsection Groebner basis computation

@itemize @bullet

\BJP

@item

$B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B.

@item

Line 402 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.

@item

$B$$$/$D$+$N?7$7$$AH$_9~$_H!?t$NDs6!(B.

\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.

@end itemize

\BJP

@node $B$=$NB>(B($BJQ99(B),,, Version 950831

@subsubsection $B$=$NB>(B

\BEG

@node Others(Changes),,, Version 950831

@subsubsection Others

@itemize @bullet

\BJP

@item

$BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.

@item

Line 416 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.

@item

Windows $B$X$N0\?"(B.

\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.

@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

\BEG

@node References,,, Appendix

@section References

@table @code

@item [Batut et al.]

Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",

Line 447 Proc. ISSAC'91, 49-54.

Line 903 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

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]

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.

@end table

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