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1.6     ! noro        1: @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.5 2000/03/17 02:17:03 noro Exp $
1.3       noro        2: \BJP
1.1       noro        3: @node $BIUO?(B,,, Top
                      4: @appendix $BIUO?(B
1.3       noro        5: \E
                      6: \BEG
                      7: @node Appendix,,, Top
                      8: @appendix Appendix
                      9: \E
1.1       noro       10:
                     11: @menu
1.3       noro       12: \BJP
1.1       noro       13: * $BJ8K!$N>\:Y(B::
                     14: * $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B::
                     15: * $BF~NO%$%s%?%U%'!<%9(B::
1.6     ! noro       16: * $B%i%$%V%i%j%$%s%?%U%'!<%9(B::
1.1       noro       17: * $BJQ99E@(B::
                     18: * $BJ88%(B::
1.3       noro       19: \E
                     20: \BEG
                     21: * Details of syntax::
                     22: * Files of user defined functions::
                     23: * Input interfaces::
1.6     ! noro       24: * Library interfaces::
1.3       noro       25: * Changes::
                     26: * References::
                     27: \E
1.1       noro       28: @end menu
                     29:
1.3       noro       30: \BJP
1.1       noro       31: @node $BJ8K!$N>\:Y(B,,, $BIUO?(B
                     32: @section $BJ8K!$N>\:Y(B
1.3       noro       33: \E
                     34: \BEG
                     35: @node Details of syntax,,, Appendix
                     36: @section Details of syntax
                     37: \E
1.1       noro       38:
                     39: @example
1.3       noro       40: \BJP
                     41: <$B<0(B>:
1.1       noro       42:     @samp{(}<$B<0(B>@samp{)}
                     43:     <$B<0(B> <$BFs9`1i;;;R(B> <$B<0(B>
                     44:     @samp{+} <$B<0(B>
                     45:     @samp{-} <$B<0(B>
                     46:     <$B:8JUCM(B>
                     47:     <$B:8JUCM(B> <$BBeF~1i;;;R(B> <$B<0(B>
                     48:     <$B:8JUCM(B> @samp{++}
                     49:     <$B:8JUCM(B> @samp{--}
                     50:     @samp{++} <$B:8JUCM(B>
                     51:     @samp{--} <$B:8JUCM(B>
                     52:     @samp{!} <$B<0(B>
                     53:     <$B<0(B> @samp{?} <$B<0(B> @samp{:} <$B<0(B>
                     54:     <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)}
1.2       noro       55:     <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{|} <$B%*%W%7%g%sJB$S(B> @samp{)}
1.1       noro       56:     <$BJ8;zNs(B>
                     57:     <$B;X?t%Y%/%H%k(B>
                     58:     <$B%"%H%`(B>
                     59:     <$B%j%9%H(B>
1.3       noro       60: \E
                     61: \BEG
                     62: <expression>:
                     63:     @samp{(}<expression>@samp{)}
                     64:     <expression> <binary operator> <expression>
                     65:     @samp{+} <expression>
                     66:     @samp{-} <expression>
                     67:     <left value>
                     68:     <left value> <assignment operator> <expression>
                     69:     <left value> @samp{++}
                     70:     <left value> @samp{--}
                     71:     @samp{++} <left value>
                     72:     @samp{--} <left value>
                     73:     @samp{!} <expression>
                     74:     <expression> @samp{?} <expression> @samp{:} <expression>
                     75:     <function> @samp{(} <expr list> @samp{)}
                     76:     <function> @samp{(} <expr list> @samp{|} <option list> @samp{)}
                     77:     <string>
                     78:     <exponent vector>
                     79:     <atom>
                     80:     <list>
                     81: \E
1.1       noro       82: @end example
1.3       noro       83: \JP (@xref{$B$5$^$6$^$J<0(B})
                     84: \EG (@xref{various expressions})
1.1       noro       85:
                     86: @example
1.3       noro       87: \BJP
1.1       noro       88: <$B:8JUCM(B>:
                     89:     <$BJQ?t(B> [@samp{[}<$B<0(B>@samp{]}]*
1.3       noro       90: \E
                     91: \BEG
                     92: <left value>:
                     93:     <program variable> [@samp{[}<expression>@samp{]}]*
                     94: \E
1.1       noro       95: @end example
                     96:
                     97: @example
1.3       noro       98: \BJP
1.1       noro       99: <$BFs9`1i;;;R(B>:
                    100:     @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}($BQQ(B)
1.3       noro      101: \E
                    102: \BEG
                    103: <binary operator>:
                    104:     @samp{+} @samp{-} @samp{*} @samp{/} @samp{%} @samp{^}(exponentiation)
                    105:     @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
                    106: \E
1.1       noro      107:     @samp{==} @samp{!=} @samp{<} @samp{>} @samp{<=} @samp{>=} @samp{&&} @samp{||}
                    108: @end example
                    109:
                    110: @example
1.3       noro      111: \JP <$BBeF~1i;;;R(B>:
                    112: \EG <assignment operator>:
1.1       noro      113:     @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{%=} @samp{^=}
                    114: @end example
                    115:
                    116: @example
1.3       noro      117: \BJP
1.1       noro      118: <$B<0JB$S(B>:
                    119:     <$B6u(B>
                    120:     <$B<0(B> [@samp{,} <$B<0(B>]*
1.3       noro      121: \E
                    122: \BEG
                    123: <expr list>:
                    124:     <empty>
                    125:     <expression> [@samp{,} <expression>]*
                    126: \E
1.1       noro      127: @end example
1.2       noro      128:
                    129: @example
1.3       noro      130: \BJP
1.2       noro      131: <$B%*%W%7%g%s(B>:
1.3       noro      132:     alphabet $B$G;O$^$kJ8;zNs(B @samp{=} <$B<0(B>
                    133: \E
                    134: \BEG
                    135: <option>:
                    136:     Character sequence beginning with an alphabetical letter @samp{=} <expression>
                    137: \E
1.2       noro      138: @end example
                    139:
                    140: @example
1.3       noro      141: \BJP
1.2       noro      142: <$B%*%W%7%g%sJB$S(B>:
                    143:     <$B%*%W%7%g%s(B>
                    144:     <$B%*%W%7%g%s(B> [@samp{,} <$B%*%W%7%g%s(B>]*
1.3       noro      145: \E
                    146: \BEG
                    147: <option list>:
                    148:     <option>
                    149:     <option> [@samp{,} <option>]*
                    150: \E
1.2       noro      151: @end example
                    152:
1.1       noro      153:
                    154: @example
1.3       noro      155: \BJP
1.1       noro      156: <$B%j%9%H(B>:
                    157:     @samp{[} <$B<0JB$S(B> @samp{]}
1.3       noro      158: \E
                    159: \BEG
                    160: <list>:
                    161:     @samp{[} <expr list> @samp{]}
                    162: \E
1.1       noro      163: @end example
                    164:
                    165: @example
1.3       noro      166: \BJP
                    167: <$BJQ?t(B>:
1.1       noro      168:     $BBgJ8;z$G;O$^$kJ8;zNs(B (X,Y,Japan $B$J$I(B)
1.3       noro      169: \E
                    170: \BEG
                    171: <program variable>:
                    172:    Sequence of alphabetical letters or numeric digits or @code{_}
                    173:    that begins with a capital alphabetical letter
                    174:    (X,Y,Japan etc.)
                    175: \E
1.1       noro      176: @end example
1.3       noro      177: \JP (@xref{$BJQ?t$*$h$SITDj85(B})
                    178: \EG (@xref{variables and indeterminates})
1.1       noro      179:
                    180: @example
1.3       noro      181: \BJP
1.1       noro      182: <$BH!?t(B>:
                    183:    $B>.J8;z$G;O$^$kJ8;zNs(B (fctr,gcd $B$J$I(B)
1.3       noro      184: \E
                    185: \BEG
                    186: <function>:
                    187:    Sequence of alphabetical letters or numeric digits or @code{_}
                    188:    that begins with a small alphabetical letter
                    189:    (fctr,gcd etc.)
                    190: \E
1.1       noro      191: @end example
                    192:
                    193: @example
1.3       noro      194: \BJP
1.1       noro      195: <$B%"%H%`(B>:
                    196:    <$BITDj85(B>
                    197:    <$B?t(B>
1.3       noro      198: \E
                    199: \BEG
                    200: <atom>:
                    201:    <indeterminate>
                    202:    <number>
                    203: \E
1.1       noro      204: @end example
                    205:
                    206: @example
1.3       noro      207: \BJP
                    208: <$BITDj85(B>:
1.1       noro      209:    $B>.J8;z$G;O$^$kJ8;zNs(B (a,bCD,c1_2 $B$J$I(B)
1.3       noro      210: \E
                    211: \BEG
                    212: <indeterminate>:
                    213:    Sequence of alphabetical letters or numeric digits or @code{_}
                    214:    that begin with a small alphabetical letter
                    215:    (a,bCD,c1_2 etc.)
                    216: \E
1.1       noro      217: @end example
1.3       noro      218: \JP (@xref{$BJQ?t$*$h$SITDj85(B})
                    219: \EG (@xref{variables and indeterminates})
1.1       noro      220:
                    221: @example
1.3       noro      222: \BJP
                    223: <$B?t(B>:
1.1       noro      224:    <$BM-M}?t(B>
                    225:    <$BIbF0>.?t(B>
                    226:    <$BBe?tE*?t(B>
                    227:    <$BJ#AG?t(B>
1.3       noro      228: \E
                    229: \BEG
                    230: <number>:
                    231:    <rational number>
                    232:    <floating point number>
                    233:    <algebraic number>
                    234:    <complex number>
                    235: \E
1.1       noro      236: @end example
1.3       noro      237: \JP (@xref{$B?t$N7?(B})
                    238: \EG (@xref{Types of numbers})
1.1       noro      239:
                    240: @example
1.3       noro      241: \JP <$BM-M}?t(B>:
                    242: \EG <rational number>:
1.1       noro      243:    0, 1, -2, 3/4
                    244: @end example
                    245:
                    246: @example
1.3       noro      247: \JP <$BIbF0>.?t(B>:
                    248: \EG <floating point number>:
1.1       noro      249:    0.0, 1.2e10
                    250: @end example
                    251:
                    252: @example
1.3       noro      253: \JP <$BBe?tE*?t(B>:
                    254: \EG <algebraic number>:
1.1       noro      255:    newalg(x^2+1), alg(0)^2+1
                    256: @end example
1.3       noro      257: \JP (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
                    258: \EG (@xref{Algebraic numbers})
1.1       noro      259:
                    260: @example
1.3       noro      261: \JP <$BJ#AG?t(B>:
                    262: \EG <complex number>:
1.1       noro      263:    1+@code{@@i}, 2.3*@code{@@i}
                    264: @end example
                    265:
                    266: @example
1.3       noro      267: \BJP
1.1       noro      268: <$BJ8;zNs(B>:
                    269:    @samp{"} $B$G0O$^$l$?J8;zNs(B
1.3       noro      270: \E
                    271: \BEG
                    272: <string>:
                    273:    character sequence enclosed by two @samp{"}'s.
                    274: \E
1.1       noro      275: @end example
                    276:
                    277: @example
1.3       noro      278: \BJP
                    279: <$B;X?t%Y%/%H%k(B>:
1.1       noro      280:    @samp{<<} <$B<0JB$S(B> @samp{>>}
1.3       noro      281: \E
                    282: \BEG
                    283: <exponent vector>:
                    284:    @samp{<<} <expr list> @samp{>>}
                    285: \E
1.1       noro      286: @end example
1.3       noro      287: \JP (@xref{$B%0%l%V%J4pDl$N7W;;(B})
                    288: \EG (@xref{Groebner basis computation})
1.1       noro      289:
                    290: @example
1.3       noro      291: \BJP
                    292: <$BJ8(B>:
1.1       noro      293:     <$B<0(B> <$B=*C<(B>
                    294:     <$BJ#J8(B>
                    295:     @samp{break} <$B=*C<(B>
                    296:     @samp{continue} <$B=*C<(B>
                    297:     @samp{return} <$B=*C<(B>
                    298:     @samp{return} <$B<0(B> <$B=*C<(B>
                    299:     @samp{if} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>
                    300:     @samp{if} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B> @samp{else} <$BJ8(B>
                    301:     @samp{for} @samp{(} <$B<0JB$S(B> @samp{;} <$B<0JB$S(B> @samp{;} <$B<0JB$S(B> @samp{)} <$BJ8(B>
                    302:     @samp{do} <$BJ8(B> @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$B=*C<(B>
                    303:     @samp{while} @samp{(} <$B<0JB$S(B> @samp{)} <$BJ8(B>
                    304:     @samp{def} <$BH!?t(B> @samp{(} <$B<0JB$S(B> @samp{)} @samp{@{} <$BJQ?t@k8@(B> <$BJ8JB$S(B> @samp{@}}
                    305:     @samp{end(quit)} <$B=*C<(B>
1.3       noro      306: \E
                    307: \BEG
                    308: <statement>:
                    309:     <expression> <terminator>
                    310:     <compound statement>
                    311:     @samp{break} <terminator>
                    312:     @samp{continue} <terminator>
                    313:     @samp{return} <terminator>
                    314:     @samp{return} <expression> <terminator>
                    315:     @samp{if} @samp{(} <expr list> @samp{)} <statement>
                    316:     @samp{if} @samp{(} <expr list> @samp{)} <statement> @samp{else} <statement>
                    317:     @samp{for} @samp{(} <expr list> @samp{;} <expr list> @samp{;} <expr list> @samp{)} <statement>
                    318:     @samp{do} <statement> @samp{while} @samp{(} <expr list> @samp{)} <terminator>
                    319:     @samp{while} @samp{(} <expr list> @samp{)} <statement>
                    320:     @samp{def} <function> @samp{(} <expr list> @samp{)} @samp{@{} <variable declaration> <stat list> @samp{@}}
                    321:     @samp{end(quit)} <terminator>
                    322: \E
1.1       noro      323: @end example
1.3       noro      324: \JP (@xref{$BJ8(B})
                    325: \EG (@xref{statements})
1.1       noro      326:
                    327: @example
1.3       noro      328: \JP <$B=*C<(B>:
                    329: \EG <terminator>:
1.1       noro      330:     @samp{;} @samp{$}
                    331: @end example
                    332:
                    333: @example
1.3       noro      334: \BJP
1.1       noro      335: <$BJQ?t@k8@(B>:
                    336:     [@samp{extern} <$BJQ?t(B> [@samp{,} <$BJQ?t(B>]* <$B=*C<(B>]*
1.3       noro      337: \E
                    338: \BEG
                    339: <variable declaration>:
                    340:     [@samp{extern} <program variable> [@samp{,} <program variable>]* <terminator>]*
                    341: \E
1.1       noro      342: @end example
                    343:
                    344: @example
1.3       noro      345: \BJP
1.1       noro      346: <$BJ#J8(B>:
                    347:     @samp{@{} <$BJ8JB$S(B> @samp{@}}
1.3       noro      348: \E
                    349: \BEG
                    350: <compound statement>:
                    351:     @samp{@{} <stat list> @samp{@}}
                    352: \E
1.1       noro      353: @end example
                    354:
                    355: @example
1.3       noro      356: \BJP
1.1       noro      357: <$BJ8JB$S(B>:
                    358:     [<$BJ8(B>]*
1.3       noro      359: \E
                    360: \BEG
                    361: <stat list>:
                    362:     [<statement>]*
                    363: \E
1.1       noro      364: @end example
                    365:
1.3       noro      366: \BJP
1.1       noro      367: @node $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B,,, $BIUO?(B
                    368: @section $BE:IU$N%f!<%6Dj5AH!?t%U%!%$%k(B
1.3       noro      369: \E
                    370: \BEG
                    371: @node Files of user defined functions,,, Appendix
                    372: @section Files of user defined functions
                    373: \E
1.1       noro      374:
                    375: @noindent
1.3       noro      376: \BJP
1.1       noro      377: $BI8=`%i%$%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
                    378: $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$$$F(B
                    379: $B@bL@$9$k(B.
1.3       noro      380: \E
                    381: \BEG
                    382: There are several files of user defined functions under the standard
                    383: library directory. (@samp{/usr/local/lib/asir} by default.)
                    384: Here, we explain some of them.
                    385: \E
1.1       noro      386:
                    387: @table @samp
                    388: @item fff
1.3       noro      389: \JP $BBgI8?tAGBN$*$h$SI8?t(B 2 $B$NM-8BBN>e$N0lJQ?tB?9`<00x?tJ,2r(B (@xref{$BM-8BBN$K4X$9$k1i;;(B})
                    390: \EG Univariate factorizer over large finite fields (@xref{Finite fields})
1.1       noro      391: @item gr
1.3       noro      392: \JP $B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B.  (@xref{$B%0%l%V%J4pDl$N7W;;(B})
                    393: \EG Groebner basis package.  (@xref{Groebner basis computation})
1.1       noro      394: @item sp
1.3       noro      395: \JP $BBe?tE*?t$N1i;;$*$h$S0x?tJ,2r(B, $B:G>.J,2rBN(B. (@xref{$BBe?tE*?t$K4X$9$k1i;;(B})
                    396: \EG Operations over algebraic numbers and factorization, Splitting fields. (@xref{Algebraic numbers})
1.1       noro      397: @item alpi
                    398: @itemx bgk
                    399: @itemx cyclic
                    400: @itemx katsura
                    401: @itemx kimura
1.3       noro      402: \JP $B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B.
                    403: \EG Example polynomial sets for benchmarks of Groebner basis computation.
1.1       noro      404: (@xref{katsura hkatsura cyclic hcyclic})
                    405: @item defs.h
1.3       noro      406: \JP $B$$$/$D$+$N%^%/%mDj5A(B. (@xref{$B%W%j%W%m%;%C%5(B})
                    407: \EG Macro definitions. (@xref{preprocessor})
1.1       noro      408: @item fctrtest
1.3       noro      409: \BJP
1.1       noro      410: $B@0?t>e$NB?9`<0$N0x?tJ,2r$N%F%9%H(B. REDUCE $B$N(B @samp{factor.tst} $B$*$h$S(B
                    411: $B=EJ#EY$NBg$-$$$$$/$D$+$NNc$r4^$`(B. $B$3$l$O(B, @code{load()} $B$9$k$H(B
                    412: $BD>$A$K7W;;$,;O$^$k(B. $BF~<j$7$?(B @b{Asir} $B$,@5$7$/F0:n$7$F$$$k$+$N(B
                    413: $B%F%9%H$K$b;H$&$3$H$,$G$-$k(B.
1.3       noro      414: \E
                    415: \BEG
                    416: Test program of factorization of integral polynomials.
                    417: It includes  @samp{factor.tst} of REDUCE and several examples
                    418: for large multiplicity factors.  If this file is @code{load()}'ed,
                    419: computation will begin immediately.
                    420: You may use it as a first test whether @b{Asir} at you hand runs
                    421: correctly.
                    422: \E
1.1       noro      423: @item fctrdata
1.3       noro      424: \BJP
1.1       noro      425: @samp{fctrtest} $B$G;H$o$l$F$$$kNc$r4^$`(B, $B0x?tJ,2r%F%9%HMQ$NNc(B.
1.5       noro      426: @code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@xref{asq af af_noalg}) $BMQ$NNc$G$"$k(B.
1.3       noro      427: \E
                    428: \BEG
                    429: This contains example polynomials for factorization.  It includes
                    430: polynomials used in @samp{fctrtest}.
                    431: Polynomials contained in vector @code{Alg[]} is for the algebraic
1.5       noro      432: factorization @code{af()} (@xref{asq af af_noalg}).
1.3       noro      433: \E
1.1       noro      434: @example
                    435: [45] load("sp")$
                    436: [84] load("fctrdata")$
                    437: [175] cputime(1)$
                    438: 0msec
                    439: [176] Alg[5];
                    440: x^9-15*x^6-87*x^3-125
                    441: 0msec
                    442: [177] af(Alg[5],[newalg(Alg[5])]);
                    443: [[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
                    444: [75*x^2+(-10*#0^7+175*#0^4+395*#0)*x+(3*#0^8-45*#0^5-261*#0^2),1],
                    445: [25*x^2+(25*#0)*x+(#0^8-15*#0^5-87*#0^2),1],[x^2+(#0)*x+(#0^2),1],
                    446: [x+(-#0),1]]
                    447: 3.600sec + gc : 1.040sec
                    448: @end example
                    449: @item ifplot
1.3       noro      450: \BJP
1.1       noro      451: $BIA2h(B (@xref{ifplot conplot plot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
                    452: $B6J@~$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,
                    453: $B%9%Z!<%I(B ($B$i$7$-(B) $B6J@~$NNc$,F~$C$F$$$k(B.
1.3       noro      454: \E
                    455: \BEG
                    456: Examples for plotting (@xref{ifplot conplot plot plotover}).
                    457: Vector @code{IS[]} contains several famous algebraic curves.
                    458: Variables @code{H, D, C, S} contains something like the suits
                    459: (Heart, Diamond, Club, and Spade) of cards.
                    460: \E
1.1       noro      461: @item num
1.3       noro      462: \JP $B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
                    463: \EG Examples of simple operations on numbers.
1.1       noro      464: @item mat
1.3       noro      465: \JP $B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
                    466: \EG Examples of simple operations on matrices.
1.1       noro      467: @item ratint
1.3       noro      468: \BJP
1.1       noro      469: $BM-M}H!?t$NITDj@QJ,(B. @samp{sp}, @samp{gr} $B$,I,MW(B. @code{ratint()} $B$H$$$&(B
                    470: $BH!?t$,Dj5A$5$l$F$$$k$,(B, $B$=$NJV$97k2L$O$d$dJ#;($G$"$k(B. $BNc$G@bL@$9$k(B.
1.3       noro      471: \E
                    472: \BEG
                    473: Indefinite integration of rational functions.  For this,
                    474: files @samp{sp} and @samp{gr} is necessary.  A function @code{ratint()}
                    475: is defined.  Its returns a rather complex result.
                    476: \E
1.1       noro      477: @example
                    478: [0] load("gr")$
                    479: [45] load("sp")$
                    480: [84] load("ratint")$
                    481: [102] ratint(x^6/(x^5+x+1),x);
                    482: [1/2*x^2,
                    483: [[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)),161*t#2^3-23*t#2^2+15*t#2-1],
                    484: [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
                    485: @end example
1.3       noro      486: \BJP
1.1       noro      487: $B$3$NNc$G$O(B, @code{x^6/(x^5+x+1)} $B$NITDj@QJ,$N7W;;$r9T$C$F$$$k(B.
                    488: $B7k2L$O(B 2 $B$D$NMWAG$+$i$J$k%j%9%H$G(B, $BBh(B 1 $BMWAG$OITDj@QJ,$NM-M}ItJ,(B,
                    489: $BBh(B 2 $BMWAG$OBP?tItJ,$rI=$9(B. $BBP?tItJ,$O99$K%j%9%H$H$J$C$F$$$F(B, $B3FMWAG$O(B,
                    490: @code{[root*log(poly),defpoly]} $B$H$$$&7A$r$7$F$$$k(B. $B$3$l$O(B, $BITDj@QJ,$K(B
                    491: $B$*$$$F$O(B, @code{defpoly} $B$NA4$F$N:,(B @code{root} $B$KBP$7$F(B @code{root*log(poly)}
                    492: $B$r:n$j$=$l$i$rB-$79g$o$;$k$H$$$&0UL#$G$"$k(B. $B$3$3$G(B @code{poly} $B$O(B
                    493: @code{root} $B$r4^$s$G$$$F(B, @code{root} $B$rF~$lBX$($k>l9g$K$O(B @code{poly}
                    494: $B$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
                    495: $B3F@.J,$KBP$7$F9T$C$F(B, $BA4$F$rB-$79g$o$;$?$b$N$,BP?tItJ,$H$J$k(B.
1.3       noro      496: \E
                    497: \BEG
                    498: In this example, indefinite integral of the rational function
                    499:  @code{x^6/(x^5+x+1)} is computed.
                    500: The result is a list which comprises two elements:
                    501: The first element is the rational part of the integral;
                    502: The second part is the logarithmic part of the integral.
                    503: The logarithmic part is again a list which comprises finite number of
                    504: elements, each of which is of form @code{[root*log(poly),defpoly]}.
                    505: This pair should be interpreted to sum up
                    506: the expression @code{root*log(poly)}
                    507: through all @b{root}'s @code{root}'s of the @code{defpoly}.
                    508: Here, @code{poly} contains @code{root}, and substitution for @code{root}
                    509: is equally applied to @code{poly}.
                    510: The logarithmic part in total is obtained by applying such
                    511: interpretation to all element pairs in the second element of the
                    512: result and then summing them up all.
                    513: \E
1.1       noro      514: @item primdec
1.3       noro      515: \BJP
1.1       noro      516: $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
1.4       noro      517: (@pxref{primadec primedec}).
1.3       noro      518: \E
                    519: \BEG
                    520: Primary ideal decomposition of polynomial ideals and prime compotision
1.4       noro      521: of radicals (@pxref{primadec primedec}).
                    522: \E
1.1       noro      523: @end table
                    524:
1.3       noro      525: \BJP
1.1       noro      526: @node $BF~NO%$%s%?%U%'!<%9(B,,, $BIUO?(B
                    527: @section $BF~NO%$%s%?%U%'!<%9(B
1.3       noro      528: \E
                    529: \BEG
                    530: @node Input interfaces,,, Appendix
                    531: @section Input interfaces
                    532: \E
1.1       noro      533:
1.3       noro      534: \BJP
1.1       noro      535: $B4{$K=R$Y$?$h$&$K(B, DOS $BHG(B, Windows $BHG(B, Macintosh $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B
                    536: $B$7$F%3%^%s%I%i%$%sJT=8$*$h$S%R%9%H%jCV$-49$($,AH$_9~$^$l$F$$$k(B. UNIX $BHG$G$O(B
                    537: $B$3$N$h$&$J5!G=$OAH$_9~$^$l$F$$$J$$$,(B, $B0J2<$G=R$Y$k$h$&$JF~NO%$%s%?%U%'!<%9(B
                    538: $B$,MQ0U$5$l$F$$$k(B. $B$3$l$i$O(B @b{Asir} $B%P%$%J%j$H$H$b$K(B ftp $B2DG=$G$"$k(B.
                    539: ftp server $B$K4X$7$F$O(B @xref{$BF~<jJ}K!(B}.
1.3       noro      540: \E
                    541: \BEG
                    542: As already mentioned a command line editing facility and a history
                    543: substitution facility are built-in for DOS, Windows Macintosh version
                    544: of @b{Asir}. UNIX versions of @b{Asir} do not have such built-in facilites.
                    545: Instead, the following input interfaces are prepared. This are also available
                    546: from our ftp server. As for our ftp server @xref{How to get Risa/Asir}.
                    547: \E
1.1       noro      548:
                    549: @menu
                    550: * fep::
                    551: * asir.el::
                    552: @end menu
                    553:
1.3       noro      554: \JP @node fep,,, $BF~NO%$%s%?%U%'!<%9(B
                    555: \EG @node fep,,, Input interfaces
1.1       noro      556: @subsection fep
                    557:
                    558: @noindent
1.3       noro      559: \BJP
1.1       noro      560: 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
                    561: $BMQ$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
                    562: $B$3$H$K$h$j(B vi $B$"$k$$$O(B emacs $BIw$N%3%^%s%I%i%$%sJT=8$*$h$S(B csh $BIw$N%R%9%H%j(B
                    563: $BCV$-49$($,2DG=$K$J$k(B.
1.3       noro      564: \E
                    565: \BEG
                    566: Fep is a general purpose front end processor. The author is
                    567: K. Utashiro (SRA Inc.).
                    568:
                    569: Under fep,
                    570: emacs- or vi-like command line editing and csh-like history substitution are
                    571: available for UNIX commands, including @samp{asir}.
                    572: \E
1.1       noro      573: @example
                    574: % fep asir
                    575: ...
                    576: [0] fctr(x^5-1);
                    577: [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
                    578: [1] !!                              /* !!+Return                      */
1.3       noro      579: \BJP
1.1       noro      580: fctr(x^5-1);                        /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */
                    581: ...                                 /* $BJT=8(B+Return                    */
1.3       noro      582: \E
                    583: \BEG
                    584: fctr(x^5-1);                        /* The last input appears.        */
                    585: ...                                 /* Edit+Return                    */
                    586: \E
1.1       noro      587: fctr(x^5+1);
                    588: [[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]
                    589: @end example
                    590:
                    591: @noindent
1.3       noro      592: \BJP
1.1       noro      593: fep $B$O%U%j!<%=%U%H$G%=!<%9$,F~<j2DG=$G$"$k$,(B, $B%*%j%8%J%k$N$b$N$O(B make $B$G$-$k(B
                    594: $B5!<o(B (OS) $B$,8B$i$l$F$$$k(B. $B$$$/$D$+$N5!<o>e$GF0:n$9$k$h$&$K2f!9$,2~B$$7$?$b$N(B
                    595: $B$,(B, ftp $B$GF~<j2DG=$G$"$k(B.
1.3       noro      596: \E
                    597: \BEG
                    598: Fep is a free software and the source is available. However
                    599: machines or operating systems on which the original one can run are limited.
                    600: The modified version by us running on several unsupported environments
                    601: is available from our ftp server.
                    602: \E
1.1       noro      603:
1.3       noro      604: \JP @node asir.el,,, $BF~NO%$%s%?%U%'!<%9(B
                    605: \EG @node asir.el,,, Input interfaces
1.1       noro      606: @subsection asir.el
                    607:
                    608: @noindent
1.3       noro      609: \BJP
1.1       noro      610: @samp{asir.el} $B$O(B, @b{Asir} $B$N(B GNU Emacs $B%$%s%?%U%'!<%9$G$"$k(B ($BCx<T$O(B
                    611: $B5\Eh8w<#;a(B (@code{YVE25250@@pcvan.or.jp}).  @samp{asir.el} $B$K$*$$$F$O(B,
                    612: $BDL>o$N(B emacs $B$G2DG=$JJT=85!G=$NB>$K(B, $B%U%!%$%kL>(B, $B%3%^%s%IL>$N(B completion
                    613: $B$,<B8=$5$l$F$$$k(B.
1.3       noro      614: \E
                    615: \BEG
                    616: @samp{asir.el} is a GNU Emacs interface for @b{Asir}.
                    617: The author is Koji Miyajima (@code{YVE25250@@pcvan.or.jp}).
                    618: In @samp{asir.el}, completion of file names and command names is
                    619: realized other than the ordinary editing functions
                    620: which are available on Emacs.
                    621: \E
1.1       noro      622:
                    623: @noindent
1.3       noro      624: \BJP
1.1       noro      625: @samp{asir.el} $B$O(B PC-VAN $B$G(B
                    626: $B4{$K8x3+$5$l$F$$$k$,(B, $B:#2s$N2~D{$KH<$&JQ99$r9T$C$?$b$N$,(B, $B$d$O$j(B ftp $B$G(B
                    627: $BF~<j2DG=$G$"$k(B.
1.3       noro      628: \E
                    629: \BEG
                    630: @samp{asir.el} is distributed on PC-VAN. The version where several
                    631: changes have been made according to the current version of @b{Asir}
                    632: is available via ftp.
                    633: \E
1.1       noro      634:
                    635: @noindent
1.3       noro      636: \JP $B%;%C%H%"%C%W(B, $B;HMQJ}K!$O(B, @samp{asir.el} $B$N@hF,$K5-=R$5$l$F$$$k(B.
                    637: \BEG
                    638: The way of setting up and the usage can be found at the top of
                    639: @samp{asir.el}.
                    640: \E
1.6     ! noro      641:
        !           642: \BJP
        !           643: @node $B%i%$%V%i%j%$%s%?%U%'!<%9(B,,, $BIUO?(B
        !           644: @section $B%i%$%V%i%j%$%s%?%U%'!<%9(B
        !           645: \E
        !           646: \BEG
        !           647: @node Library interfaces,,, Appendix
        !           648: @section Library interfaces
        !           649: \E
        !           650:
        !           651: \BJP
        !           652: @b{Asir} $B$NDs6!$9$k5!G=$rB>$N%W%m%0%i%`$+$i;HMQ$9$kJ}K!$H$7$F(B, @b{OpenXM} $B$K$h$k(B
        !           653: $BB>$K(B, $B%i%$%V%i%j$ND>@\%j%s%/$K$h$kJ}K!$,2DG=$G$"$k(B. $B%i%$%V%i%j$O(B,
        !           654: GC $B%i%$%V%i%j$G$"$k(B @samp{libasir-gc.a} $B$H$H$b$K(B @b{OpenXM}
        !           655: distribution (@code{http://www.math.kobe-u.ac.jp/OpenXM}) $B$K4^$^$l$k(B.
        !           656: $B8=>u$G$O(B@b{OpenXM} $B%$%s%?%U%'!<%9$N$_$,8x3+$5$l$F$$$k$?$a(B, $B0J2<$G$O(B
        !           657: @b{OpenXM} $B$,%$%s%9%H!<%k$5$l$F$$$k$H2>Dj$9$k(B. @b{OpenXM} root $B%G%#%l%/%H%j$r(B
        !           658: @code{$OpenXM_HOME}$B$H=q$/(B. $B%i%$%V%i%j%U%!%$%k$OA4$F(B @samp{$OpenXM_HOME/lib}
        !           659: $B$K$*$+$l$F$$$k(B. $B%i%$%V%i%j$K$O0J2<$N(B 3 $B<oN`$,$"$k(B.
        !           660: \E
        !           661: \BEG
        !           662: It is possible to link an @b{Asir} library to use the functionalities of
        !           663: @b{Asir} from other programs.
        !           664: The necessary libraries are included in the @b{OpenXM} distribution
        !           665: (@code{http://www.math.kobe-u.ac.jp/OpenXM}).
        !           666: At present only the @b{OpenXM} interfaces are available. Here we assume
        !           667: that @b{OpenXM} is already installed. In the following
        !           668: @code{$OpenXM_HOME} denotes the @b{OpenXM} root directory.
        !           669: All the library files are placed in @samp{$OpenXM_HOME/lib}.
        !           670: There are three kinds of libraries as follows.
        !           671: \E
        !           672: @itemize @bullet
        !           673: @item @samp{libasir.a}
        !           674: @*
        !           675: \BJP
        !           676: @b{PARI}, @b{X11} $B4XO"$N5!G=$r4^$^$J$$(B.
        !           677: $B%j%s%/$K$O(B @samp{libasir-gc.a} $B$N$_$,I,MW(B.
        !           678: \E
        !           679: \BEG
        !           680: It does not contain the functionalities related to @b{PARI} and @b{X11}.
        !           681: Only @samp{libasir-gc.a} is necessary for linking.
        !           682: \E
        !           683:
        !           684: @item @samp{libasir_pari.a}
        !           685: @*
        !           686: \BJP
        !           687: @b{X11} $B4XO"$N5!G=$r4^$^$J$$(B. $B%j%s%/$K$O(B @samp{libasir-gc.a},
        !           688: @samp{libpari.a} $B$,I,MW(B.
        !           689: \E
        !           690: \BEG
        !           691: It does not contain the functionalities related to @b{X11}.
        !           692: @samp{libasir-gc.a}, @samp{libpari.a} are necessary for linking.
        !           693: \E
        !           694:
        !           695: @item @samp{libasir_pari_X.a}
        !           696: @*
        !           697: \BJP
        !           698: $BA4$F$N5!G=$r4^$`(B. $B%j%s%/$K$O(B @samp{libasir-gc.a}, @samp{libpari.a}
        !           699: $B$*$h$S(B @b{X11} $B4XO"$N%i%$%V%i%j;XDj$,I,MW(B.
        !           700: \E
        !           701: \BEG
        !           702: All the functionalities are included. @samp{libasir-gc.a}, @samp{libpari.a}
        !           703: and libraries related to @b{X11} are necessary for linking.
        !           704: \E
        !           705: @end itemize
        !           706: \BJP
        !           707: $BDs6!$5$l$F$$$k4X?t$O0J2<$NDL$j$G$"$k(B.
        !           708: \E
        !           709: @itemize @bullet
        !           710: @item @code{int asir_ox_init(int @var{byteorder})}
        !           711: @*
        !           712: \BJP
        !           713: $B%i%$%V%i%j$N=i4|2=(B. @var{byteorder} $B$O%a%b%j>e$X$N%P%$%J%j(B CMO $B%G!<%?(B
        !           714: $B$X$NE83+J}K!$r;XDj$9$k(B. @var{byteorder} $B$,(B 0 $B$N$H$-%^%7%s8GM-$N(B byteorder
        !           715: $B$rMQ$$$k(B. 1 $B$N$H$-(B network byteorder $B$rMQ$$$k(B. $B=i4|2=$K@.8y$7$?>l9g(B 0,
        !           716: $B<:GT$N;~(B -1 $B$rJV$9(B.
        !           717: \E
        !           718: \BEG
        !           719: It initializes the library.
        !           720: @var{byteorder} specifies the format of binary CMO data on the memory.
        !           721: If @var{byteorder} is 0, the byteorder native to the machine is used.
        !           722: If @var{byteorder} is 1, the network byteorder is used. It returns
        !           723: 0 if the initialization is successful, -1 otherwise.
        !           724: \E
        !           725:
        !           726: @item @code{void asir_ox_push_cmo(void *@var{cmo})}
        !           727: @*
        !           728: \BJP
        !           729: $B%a%b%j>e$KCV$+$l$?(B CMO $B%G!<%?$r(B @b{Asir} $B$NFbIt7A<0$KJQ49$7$F%9%?%C%/$K(B
        !           730: push $B$9$k(B.
        !           731: \E
        !           732: \BJP
        !           733: It converts CMO data pointed by @var{cmo} into an @b{Asir} object and
        !           734: it pushes the object onto the stack.
        !           735: \E
        !           736:
        !           737: @item @code{int asir_ox_peek_cmo_size()}
        !           738: @*
        !           739: \BJP
        !           740: $B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B CMO $B$KJQ49$7$?$H$-$N%5%$%:$rJV$9(B.
        !           741: $BJQ49ITG=$J>l9g$K$O(B -1 $B$rJV$9(B.
        !           742: \E
        !           743: \BEG
        !           744: It returns the size of the object at the top of the stack as CMO object.
        !           745: It returns -1 if the object cannot be converted into CMO object.
        !           746: \E
        !           747:
        !           748: @item @code{int asir_ox_pop_cmo(void *@var{cmo}, int @var{limit})}
        !           749: @*
        !           750: \BJP
        !           751: $B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B pop $B$7(B, CMO $B$KJQ49$7$F(B @var{cmo}$B$G(B
        !           752: $B;X$5$l$kG[Ns$K=q$-(B, CMO $B$N%5%$%:$rJV$9(B. $B$3$N$H$-(B, CMO $B$N%5%$%:$,(B
        !           753: @var{limit} $B$h$jBg$-$$>l9g$K$O(B -1 $B$rJV$9(B. @var{cmo} $B$OD9$5$,>/$J$/$H$b(B
        !           754: @var{limit}$B%P%$%H$NG[Ns$r;X$9I,MW$,$"$k(B. $BJQ49$5$l$?(B CMO $B$r<}MF$G$-$k(B
        !           755: $BG[Ns$ND9$5$rCN$k$?$a$K(B, @code{asir_ox_peek_cmo_size} $B$rMQ$$$k(B.
        !           756: \E
        !           757: \BEG
        !           758: It pops an @b{Asir} object at the top of the stack and it converts
        !           759: the object into CMO data. If the size of the CMO data is not greater
        !           760: than @var{limit}, then the data is written in @var{cmo} and the size
        !           761: is returned. Otherwise -1 is returned. The size of the array pointed
        !           762: by @var{cmo} must be at least @var{limit}. In order to know the size
        !           763: of converted CMO data in advance @code{asir_ox_peek_cmo_size} is called.
        !           764: \E
        !           765:
        !           766: @item @code{void asir_ox_push_cmd(int @var{cmd})}
        !           767: @*
        !           768: \BJP
        !           769: $B%9%?%C%/%^%7%s%3%^%s%I(B @var{cmd} $B$r<B9T$9$k(B.
        !           770: \E
        !           771: \BEG
        !           772: It executes a stack machine command @var{cmd}.
        !           773: \E
        !           774:
        !           775: @item @code{void asir_ox_execute_string(char *@var{str})}
        !           776: @*
        !           777: \BJP
        !           778: @b{Asir} $B$,<B9T2DG=$JJ8;zNs(B @var{str} $B$r<B9T$7(B, $B$=$N7k2L$r%9%?%C%/$K(B push $B$9$k(B.
        !           779: \E
        !           780: \BEG
        !           781: It evaluates @var{str} as a string written in the @b{Asir} user language.
        !           782: The result is pushed onto the stack.
        !           783: \E
        !           784: @end itemize
        !           785:
        !           786: \BJP
        !           787: include $B$9$Y$-(B header file $B$O(B @samp{$OpenXM_HOME/include/asir/ox.h} $B$G$"$k(B.
        !           788: $B$3$N(B header file $B$K$O(B, @b{OpenXM} $B$K4X$9$kA4$F$N(B tag, command $B$NDj5A$,4^$^$l$F(B
        !           789: $B$$$k(B.
        !           790: $B<!$NNc(B (@samp{$OpenXM_HOME/doc/oxlib/test3.c}) $B$O>e5-4X?t$N;HMQ(B
        !           791: $BK!$r<($9(B.
        !           792: \E
        !           793: \BEG
        !           794: A program calling the above functions should include
        !           795: @samp{$OpenXM_HOME/include/asir/ox.h}.
        !           796: In this file all the definitions of @b{OpenXM} tags and commands.
        !           797: The following example
        !           798: (@samp{$OpenXM_HOME/doc/oxlib/test3.c}) illustrates the usage of
        !           799: the above functions.
        !           800: \E
        !           801:
        !           802: @example
        !           803: #include <asir/ox.h>
        !           804: #include <signal.h>
        !           805:
        !           806: main(int argc, char **argv)
        !           807: @{
        !           808:   char buf[BUFSIZ+1];
        !           809:   int c;
        !           810:   unsigned char sendbuf[BUFSIZ+10];
        !           811:   unsigned char *result;
        !           812:   unsigned char h[3];
        !           813:   int len,i,j;
        !           814:   static int result_len = 0;
        !           815:   char *kwd,*bdy;
        !           816:   unsigned int cmd;
        !           817:
        !           818:   signal(SIGINT,SIG_IGN);
        !           819:   asir_ox_init(1); /* 1: network byte order; 0: native byte order */
        !           820:   result_len = BUFSIZ;
        !           821:   result = (void *)malloc(BUFSIZ);
        !           822:   while ( 1 ) @{
        !           823:     printf("Input>"); fflush(stdout);
        !           824:     fgets(buf,BUFSIZ,stdin);
        !           825:     for ( i = 0; buf[i] && isspace(buf[i]); i++ );
        !           826:     if ( !buf[i] )
        !           827:       continue;
        !           828:     kwd = buf+i;
        !           829:     for ( ; buf[i] && !isspace(buf[i]); i++ );
        !           830:     buf[i] = 0;
        !           831:     bdy = buf+i+1;
        !           832:     if ( !strcmp(kwd,"asir") ) @{
        !           833:       sprintf(sendbuf,"%s;",bdy);
        !           834:       asir_ox_execute_string(sendbuf);
        !           835:     @} else if ( !strcmp(kwd,"push") ) @{
        !           836:       h[0] = 0;
        !           837:       h[2] = 0;
        !           838:       j = 0;
        !           839:       while ( 1 ) @{
        !           840:         for ( ; (c= *bdy) && isspace(c); bdy++ );
        !           841:         if ( !c )
        !           842:           break;
        !           843:         else if ( h[0] ) @{
        !           844:           h[1] = c;
        !           845:           sendbuf[j++] = strtoul(h,0,16);
        !           846:           h[0] = 0;
        !           847:         @} else
        !           848:           h[0] = c;
        !           849:         bdy++;
        !           850:       @}
        !           851:       if ( h[0] )
        !           852:         fprintf(stderr,"Number of characters is odd.\n");
        !           853:       else @{
        !           854:         sendbuf[j] = 0;
        !           855:         asir_ox_push_cmo(sendbuf);
        !           856:       @}
        !           857:     @} else if ( !strcmp(kwd,"cmd") ) @{
        !           858:       cmd = atoi(bdy);
        !           859:       asir_ox_push_cmd(cmd);
        !           860:     @} else if ( !strcmp(kwd,"pop") ) @{
        !           861:       len = asir_ox_peek_cmo_size();
        !           862:       if ( !len )
        !           863:         continue;
        !           864:       if ( len > result_len ) @{
        !           865:         result = (char *)realloc(result,len);
        !           866:         result_len = len;
        !           867:       @}
        !           868:       asir_ox_pop_cmo(result,len);
        !           869:       printf("Output>"); fflush(stdout);
        !           870:       printf("\n");
        !           871:       for ( i = 0; i < len; ) @{
        !           872:         printf("%02x ",result[i]);
        !           873:         i++;
        !           874:         if ( !(i%16) )
        !           875:           printf("\n");
        !           876:       @}
        !           877:       printf("\n");
        !           878:     @}
        !           879:   @}
        !           880: @}
        !           881: @end example
        !           882: \BJP
        !           883: $B$3$N%W%m%0%i%`$O(B, @var{keyword} @var{body} $B$J$k(B 1 $B9T$rF~NO$H$7$F<u$1<h$j(B
        !           884: @var{keyword} $B$K1~$8$F<!$N$h$&$JF0:n$r9T$&(B.
        !           885: \E
        !           886: \BEG
        !           887: This program receives a line in the form of @var{keyword} @var{body}
        !           888: as an input and it executes the following operations according to
        !           889: @var{keyword}.
        !           890: \E
        !           891: @itemize @bullet
        !           892: @item @code{asir} @var{body}
        !           893: @*
        !           894: \BJP
        !           895: @var{body} $B$r(B @b{Asir} $B8@8l$G=q$+$l$?<0$H$_$J$7(B, $B<B9T7k2L$r%9%?%C%/$K(B push $B$9$k(B.
        !           896: @code{asir_ox_execute_string()} $B$,MQ$$$i$l$k(B.
        !           897: \E
        !           898: \BEG
        !           899: @var{body} is regarded as an expression written in the @b{Asir} user language.
        !           900: The expression is evaluated and the result is pushed onto the stack.
        !           901: @code{asir_ox_execute_string()} is called.
        !           902: \E
        !           903:
        !           904: @item @code{push} @var{body}
        !           905: @*
        !           906: \BJP
        !           907: @var{body} $B$r(B 16 $B?J?t$GI=<($5$l$?(B CMO $B%G!<%?$H$_$J$7(B, @b{Asir} $B%*%V%8%'%/%H$KJQ49(B
        !           908: $B$7$F%9%?%C%/$K(B push $B$9$k(B. @code{asir_ox_push_cmo()} $B$,MQ$$$i$l$k(B.
        !           909: \E
        !           910: \BEG
        !           911: @var{body} is regarded as a CMO object in the hexadecimal form.
        !           912: The CMO object is converted into an @b{Asir} object and is pushed onto the stack.
        !           913: @code{asir_ox_push_cmo()} is called.
        !           914: \E
        !           915:
        !           916: @item @code{pop}
        !           917: @*
        !           918: \BJP
        !           919: $B%9%?%C%/:G>e0L$N%*%V%8%'%/%H$r(B CMO $B$KJQ49$7(B, 16 $B?J?t$GI=<($9$k(B.
        !           920: @code{asir_ox_peek_cmo_size()} $B$*$h$S(B @code{asir_ox_pop_cmo()} $B$,MQ$$$i$l$k(B.
        !           921: \E
        !           922: \BEG
        !           923: The object at the top of the stack is converted into a CMO object
        !           924: and it is displayed in the hexadecimal form.
        !           925: @code{asir_ox_peek_cmo_size()} and @code{asir_ox_pop_cmo()} are called.
        !           926: \E
        !           927:
        !           928: @item @code{cmd} @var{body}
        !           929: @*
        !           930: \BJP
        !           931: @var{body} $B$r(B SM $B%3%^%s%I$H$_$J$7(B, $B<B9T$9$k(B.
        !           932: @code{asir_ox_push_cmd()} $B$,MQ$$$i$l$k(B.
        !           933: \E
        !           934: \BEG
        !           935: @var{body} is regarded as an SM command and the command is executed.
        !           936: @code{asir_ox_push_cmd()} is called.
        !           937: \E
        !           938: @end itemize
1.1       noro      939:
1.3       noro      940: \BJP
1.1       noro      941: @node $BJQ99E@(B,,, $BIUO?(B
                    942: @section $BJQ99E@(B
1.3       noro      943: \E
                    944: \BEG
                    945: @node Changes,,, Appendix
                    946: @section Appendix
                    947: \E
1.1       noro      948:
                    949: @menu
                    950: * Version 990831::
                    951: * Version 950831::
                    952: * Version 940420::
                    953: @end menu
                    954:
1.3       noro      955: \JP @node Version 990831,,, $BJQ99E@(B
                    956: \EG @node Version 990831,,, Changes
1.1       noro      957: @subsection Version 990831
                    958:
1.3       noro      959: \BJP
1.1       noro      960: 4 $BG/$V$j$NBg2~D{(B. $B@0?t$N(B 32bit $B2=B>(B, $BCf?H$O$:$$$V$sJQ$o$C$F$$$k$b$N$N(B,
                    961: $B8+3]$1$O$=$l$[$IJQ$o$C$F$$$k$h$&$K$O8+$($J$$(B. $B$`$7$m(B, Windows $BHG$J$I$O(B,
                    962: plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B.
                    963:
                    964: $B5lHG$N%f!<%6$,$b$C$H$bCm0U$9$Y$-E@$O(B, $B5lHG$G:n$C$?(B bsave file $B$rFI$_9~$`(B
                    965: $B>l9g$O(B @code{bload27} $B$r;H$&I,MW$,$"$k(B, $B$H$$$&E@$G$"$k(B.
1.3       noro      966: \E
                    967:
                    968: \BEG
                    969: Four years have passed since the last distribution.
                    970: Though the look and feel seem unchanged, internally there are
                    971: several changes such as 32-bit representation of bignums.
                    972: Plotting facilities are not available on Windows.
                    973:
                    974: If you have files created by @code{bsave} on the older version,
                    975: you have to use @code{bload27} to read such files.
                    976: \E
1.1       noro      977:
1.3       noro      978: \JP @node Version 950831,,, $BJQ99E@(B
                    979: \EG @node Version 950831,,, Changes
1.1       noro      980: @subsection Version 950831
                    981:
                    982: @menu
1.3       noro      983: \BJP
1.1       noro      984: * $B%G%P%C%,(B($BJQ99(B)::
                    985: * $BAH$_9~$_H!?t(B($BJQ99(B)::
                    986: * $B%0%l%V%J4pDl(B($BJQ99(B)::
                    987: * $B$=$NB>(B($BJQ99(B)::
1.3       noro      988: \E
                    989: \BEG
                    990: * Debugger(Changes)::
                    991: * Built-in functions(Changes)::
                    992: * Groebner basis computation(Changes)::
                    993: * Others(Changes)::
                    994: \E
1.1       noro      995: @end menu
                    996:
1.3       noro      997: \BJP
1.1       noro      998: @node $B%G%P%C%,(B($BJQ99(B),,, Version 950831
                    999: @subsubsection $B%G%P%C%,(B
1.3       noro     1000: \E
                   1001: \BEG
                   1002: @node Debugger(Changes),,, Version 950831
                   1003: @subsubsection Debugger
                   1004: \E
1.1       noro     1005:
                   1006: @itemize @bullet
                   1007: @item
1.3       noro     1008: \JP $BG$0U$N;~E@$K%G%P%C%0%b!<%I$KF~$l$k(B.
                   1009: \EG One can enter the debug mode anytime.
1.1       noro     1010: @item
1.3       noro     1011: \JP @code{finish} $B%3%^%s%I$NDI2C(B.
                   1012: \EG A command @code{finish} has been appended.
1.1       noro     1013: @item
1.3       noro     1014: \BJP
1.1       noro     1015: @code{up}, @code{down}, @code{frame} $B%3%^%s%I$K$h$k(B, $BG$0U$N%9%?%C%/%U%l!<%`(B
1.3       noro     1016: $B$N;2>H(B.
                   1017: \E
                   1018: \EG One can examine any stack frame with @code{up}, @code{down} and @code{frame}.
1.1       noro     1019: @item
1.3       noro     1020: \JP @code{trace} $B%3%^%s%I$NDI2C(B.
                   1021: \EG A command @code{trace} has been appended.
1.1       noro     1022: @end itemize
                   1023:
1.3       noro     1024: \BJP
1.1       noro     1025: @node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831
                   1026: @subsubsection $BAH$_9~$_H!?t(B
1.3       noro     1027: \E
                   1028: \BEG
                   1029: @node Built-in functions(Changes),,, Version 950831
                   1030: @subsubsection Built-in functions
                   1031: \E
1.1       noro     1032:
                   1033: @itemize @bullet
1.3       noro     1034: \BJP
1.1       noro     1035: @item
                   1036: @code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B.
                   1037: @item
                   1038: @code{sdivm()} $B$J$I(B, $BM-8BBN>e$G$NB?9`<0=|;;$NDI2C(B.
                   1039: @item
                   1040: @code{det()}, @code{res()} $B$J$I$K$*$1$k(B, $BM-8BBN>e$G$N7W;;$N%5%]!<%H(B
                   1041: @item
                   1042: @code{vtol()} ($B%Y%/%H%k$+$i%j%9%H$X$NJQ49(B) $B$NDI2C(B.
                   1043: @item
                   1044: @code{map()} $B$NDI2C(B.
1.3       noro     1045: \E
                   1046: \BEG
                   1047: @item
                   1048: One can specify a main variable for @code{sdiv()} etc.
                   1049: @item
                   1050: Functions for polynomial division over finite fields
                   1051: such as @code{sdivm()} have been appended.
                   1052: @item
                   1053: @code{det()}, @code{res()} can produce results over finite fields.
                   1054: @item
                   1055: @code{vtol()}, conversion from a vector to a list has been appended.
                   1056: @item
                   1057: @code{map()} has been appended.
                   1058: \E
1.1       noro     1059: @end itemize
                   1060:
1.3       noro     1061: \BJP
1.1       noro     1062: @node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831
                   1063: @subsubsection $B%0%l%V%J4pDl(B
1.3       noro     1064: \E
                   1065: \BEG
                   1066: @node Groebner basis computation(Changes),,, Version 950831
                   1067: @subsubsection Groebner basis computation
                   1068: \E
1.1       noro     1069:
                   1070: @itemize @bullet
1.3       noro     1071: \BJP
1.1       noro     1072: @item
                   1073: $B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B.
                   1074: @item
                   1075: @code{grm()}, @code{hgrm()} $B$,(B @code{gr()}, @code{hgr()} $B$KJQ99(B.
                   1076: @item
                   1077: @code{gr()}, @code{hgr()} $B$K$*$$$F(B, $B9`=g=x$N;XDj$,I,MW$K$J$C$?(B.
                   1078: @item
                   1079: $B9`=g=x$N;XDjJ}K!$,3HD%$5$l$?(B.
                   1080: @item
                   1081: $BM-8BBN>e$N%0%l%V%J4pDl7W;;$N%5%]!<%H(B.
                   1082: @item
                   1083: $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl7W;;$N%5%]!<%H(B.
                   1084: @item
                   1085: $B$$$/$D$+$N?7$7$$AH$_9~$_H!?t$NDs6!(B.
1.3       noro     1086: \E
                   1087: \BEG
                   1088: @item Functions for Groebner basis computation have been implemented
                   1089: as built-in functions.
                   1090: @item
                   1091: @code{grm()} and @code{hgrm()} have been changed to @code{gr()} and
                   1092: @code{hgr()} respectively.
                   1093: @item
                   1094: @code{gr()} and @code{hgr()} requires explicit specification of
                   1095: an ordering type.
                   1096: @item
                   1097: Extension of specification of a term ordering type.
                   1098: @item
                   1099: Groebner basis computations over finite fields.
                   1100: @item
                   1101: Lex order Groebner basis computation via a modular change of ordering algorithm.
                   1102: @item
                   1103: Several new built-in functions.
                   1104: \E
1.1       noro     1105: @end itemize
                   1106:
1.3       noro     1107: \BJP
1.1       noro     1108: @node $B$=$NB>(B($BJQ99(B),,, Version 950831
                   1109: @subsubsection $B$=$NB>(B
1.3       noro     1110: \E
                   1111: \BEG
                   1112: @node Others(Changes),,, Version 950831
                   1113: @subsubsection Others
                   1114: \E
1.1       noro     1115:
                   1116: @itemize @bullet
1.3       noro     1117: \BJP
1.1       noro     1118: @item
                   1119: $BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.
                   1120: @item
                   1121: $BBe?tBN>e$N(B GCD $B7W;;$K$*$1$k%b%8%e%i7W;;$N1~MQ(B.
                   1122: @item
                   1123: $B%$%G%"%k$N=`AGJ,2r$N%5%]!<%H(B.
                   1124: @item
                   1125: Windows $B$X$N0\?"(B.
1.3       noro     1126: \E
                   1127: \BEG
                   1128: @item
                   1129: Implementation of tools for distributed computation.
                   1130: @item
                   1131: Application of modular computation for GCD computation over algebraic number
                   1132: fields.
                   1133: @item
                   1134: Implementation of primary decompostion of ideals.
                   1135: @item
                   1136: Porting to Windows.
                   1137: \E
1.1       noro     1138: @end itemize
                   1139:
1.3       noro     1140: \JP @node Version 940420,,, $BJQ99E@(B
                   1141: \EG @node Version 940420,,, Changes
1.1       noro     1142: @subsection Version 940420
                   1143:
                   1144: @noindent
1.3       noro     1145: \JP $B:G=i$N8x3+HG(B.
                   1146: \EG The first public verion.
1.1       noro     1147:
1.3       noro     1148: \BJP
1.1       noro     1149: @node $BJ88%(B,,, $BIUO?(B
                   1150: @section $BJ88%(B
1.3       noro     1151: \E
                   1152: \BEG
                   1153: @node References,,, Appendix
                   1154: @section References
                   1155: \E
1.1       noro     1156: @table @code
                   1157: @item [Batut et al.]
                   1158: Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",
                   1159: 1993.
                   1160: @item [Becker,Weispfenning]
                   1161: Becker, T., Weispfenning, V., "Groebner Bases", Graduate Texts in Math. 141,
                   1162: Springer-Verlag, 1993.
                   1163: @item [Boehm,Weiser]
                   1164: Boehm, H., Weiser, M., "Garbage Collection in an Uncooperative
                   1165: Environment", Software Practice & Experience, September 1988, 807-820.
                   1166: @item [Gebauer,Moeller]
                   1167: Gebauer, R., Moeller, H. M., "An installation of Buchberger's algorithm",
                   1168: J. of Symbolic Computation 6, 275-286.
                   1169: @item [Giovini et al.]
                   1170: Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C.,
                   1171: ""One sugar cube, please" OR Selection strategies in the Buchberger algorithm",
                   1172: Proc. ISSAC'91, 49-54.
                   1173: @item [Noro,Takeshima]
                   1174: Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",
                   1175: Proc. ISSAC'92, 387-396.
                   1176: @item [Noro,Yokoyama]
1.3       noro     1177: Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate
                   1178: Representation of Zero-Dimensional Ideals",
                   1179: J. Symb. Comp. 28/1 (1999), 243-263.
1.1       noro     1180: @item [Shimoyama,Yokoyama]
                   1181: Shimoyama, T., Yokoyama, K.,
                   1182: "Localization and primary decomposition of polynomial ideals",
1.3       noro     1183: J. Symb. Comp. 22 (1996), 247-277.
                   1184: @item [Shoup]
                   1185: Shoup, V., "A new polynomial factorization algorithm and its implementation",
                   1186: J. Symb. Comp. 20 (1995), 364-397.
1.1       noro     1187: @item [Traverso]
                   1188: Traverso, C., "Groebner trace algorithms", Proc. ISSAC '88(LNCS 358), 125-138.
1.3       noro     1189: @item [Weber]
                   1190: Weber, K., "The accelerated Integer GCD Algorithm", ACM TOMS, 21, 1(1995), 111-122.
1.1       noro     1191: @end table
                   1192: