Annotation of OpenXM/src/asir-doc/parts/appendix.texi, Revision 1.10
1.10 ! noro 1: @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.9 2002/09/03 01:50:57 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: <$B%j%9%H(B>
1.3 noro 60: \E
61: \BEG
62: <expression>:
63: @samp{(}<expression>@samp{)}
64: <expression> <binary operator> <expression>
65: @samp{+} <expression>
66: @samp{-} <expression>
67: <left value>
68: <left value> <assignment operator> <expression>
69: <left value> @samp{++}
70: <left value> @samp{--}
71: @samp{++} <left value>
72: @samp{--} <left value>
73: @samp{!} <expression>
74: <expression> @samp{?} <expression> @samp{:} <expression>
75: <function> @samp{(} <expr list> @samp{)}
76: <function> @samp{(} <expr list> @samp{|} <option list> @samp{)}
77: <string>
78: <exponent vector>
79: <atom>
80: <list>
81: \E
1.1 noro 82: @end example
1.9 noro 83: \JP (@xref{$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$I(B)
1.3 noro 169: \E
170: \BEG
171: <program variable>:
172: Sequence of alphabetical letters or numeric digits or @code{_}
173: that begins with a capital alphabetical letter
174: (X,Y,Japan etc.)
175: \E
1.1 noro 176: @end example
1.9 noro 177: \JP (@xref{$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$I(B)
1.3 noro 210: \E
211: \BEG
212: <indeterminate>:
213: Sequence of alphabetical letters or numeric digits or @code{_}
214: that begin with a small alphabetical letter
215: (a,bCD,c1_2 etc.)
216: \E
1.1 noro 217: @end example
1.9 noro 218: \JP (@xref{$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
1.9 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 <$BBe?tE*?t(B>:
254: \EG <algebraic number>:
1.1 noro 255: newalg(x^2+1), alg(0)^2+1
256: @end example
1.9 noro 257: \JP (@xref{$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
1.9 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)} <$B=*C<(B>
1.3 noro 306: \E
307: \BEG
308: <statement>:
309: <expression> <terminator>
310: <compound statement>
311: @samp{break} <terminator>
312: @samp{continue} <terminator>
313: @samp{return} <terminator>
314: @samp{return} <expression> <terminator>
315: @samp{if} @samp{(} <expr list> @samp{)} <statement>
316: @samp{if} @samp{(} <expr list> @samp{)} <statement> @samp{else} <statement>
317: @samp{for} @samp{(} <expr list> @samp{;} <expr list> @samp{;} <expr list> @samp{)} <statement>
318: @samp{do} <statement> @samp{while} @samp{(} <expr list> @samp{)} <terminator>
319: @samp{while} @samp{(} <expr list> @samp{)} <statement>
320: @samp{def} <function> @samp{(} <expr list> @samp{)} @samp{@{} <variable declaration> <stat list> @samp{@}}
321: @samp{end(quit)} <terminator>
322: \E
1.1 noro 323: @end example
1.9 noro 324: \JP (@xref{$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$$$F(B
379: $B@bL@$9$k(B.
1.3 noro 380: \E
381: \BEG
382: There are several files of user defined functions under the standard
383: library directory. (@samp{/usr/local/lib/asir} by default.)
384: Here, we explain some of them.
385: \E
1.1 noro 386:
387: @table @samp
388: @item fff
1.9 noro 389: \JP $BBgI8?tAGBN$*$h$SI8?t(B 2 $B$NM-8BBN>e$N0lJQ?tB?9`<00x?tJ,2r(B (@xref{$BM-8BBN$K4X$9$k1i;;(B}.)
390: \EG Univariate factorizer over large finite fields (@xref{Finite fields}.)
1.1 noro 391: @item gr
1.9 noro 392: \JP $B%0%l%V%J4pDl7W;;%Q%C%1!<%8(B. (@xref{$B%0%l%V%J4pDl$N7W;;(B}.)
393: \EG Groebner basis package. (@xref{Groebner basis computation}.)
1.1 noro 394: @item sp
1.9 noro 395: \JP $BBe?tE*?t$N1i;;$*$h$S0x?tJ,2r(B, $B:G>.J,2rBN(B. (@xref{$BBe?tE*?t$K4X$9$k1i;;(B}.)
396: \EG Operations over algebraic numbers and factorization, Splitting fields. (@xref{Algebraic numbers}.)
1.1 noro 397: @item alpi
398: @itemx bgk
399: @itemx cyclic
400: @itemx katsura
401: @itemx kimura
1.3 noro 402: \JP $B%0%l%V%J4pDl7W;;$K$*$$$F(B, $B%Y%s%A%^!<%/$=$NB>$GMQ$$$i$l$kNc(B.
403: \EG Example polynomial sets for benchmarks of Groebner basis computation.
1.9 noro 404: (@xref{katsura hkatsura cyclic hcyclic}.)
1.1 noro 405: @item defs.h
1.9 noro 406: \JP $B$$$/$D$+$N%^%/%mDj5A(B. (@xref{$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$$$kNc$r4^$`(B, $B0x?tJ,2r%F%9%HMQ$NNc(B.
1.9 noro 426: @code{Alg[]} $B$K<}$a$i$l$F$$$kNc$O(B, @code{af()} (@ref{asq af af_noalg}) $BMQ$NNc$G$"$k(B.
1.3 noro 427: \E
428: \BEG
429: This contains example polynomials for factorization. It includes
430: polynomials used in @samp{fctrtest}.
431: Polynomials contained in vector @code{Alg[]} is for the algebraic
1.9 noro 432: factorization @code{af()}. (@xref{asq af af_noalg}.)
1.3 noro 433: \E
1.1 noro 434: @example
435: [45] load("sp")$
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
1.10 ! noro 451: $BIA2h(B (@ref{ifplot conplot plot polarplot plotover}) $B$N$?$a$NNc(B. @code{IS[]} $B$K$OM-L>$J(B
1.1 noro 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$$$k(B.
1.3 noro 454: \E
455: \BEG
1.10 ! noro 456: Examples for plotting. (@xref{ifplot conplot plot polarplot plotover}.)
1.3 noro 457: Vector @code{IS[]} contains several famous algebraic curves.
458: Variables @code{H, D, C, S} contains something like the suits
459: (Heart, Diamond, Club, and Spade) of cards.
460: \E
1.1 noro 461: @item num
1.3 noro 462: \JP $B?t$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
463: \EG Examples of simple operations on numbers.
1.1 noro 464: @item mat
1.3 noro 465: \JP $B9TNs$K4X$9$k4JC1$J1i;;H!?t$NNc(B.
466: \EG Examples of simple operations on matrices.
1.1 noro 467: @item ratint
1.3 noro 468: \BJP
1.1 noro 469: $BM-M}H!?t$NITDj@QJ,(B. @samp{sp}, @samp{gr} $B$,I,MW(B. @code{ratint()} $B$H$$$&(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
1.7 noro 535: DOS $BHG(B, Windows $BHG$G$OF~NO%$%s%?%U%'!<%9$H(B
1.1 noro 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}.
1.7 noro 540:
541: Windows $BHG(B @samp{asirgui.exe} $B$O(B, $BDL>o$N(B Windows $B$K$*$1$k47=,$H$O0[$J$k(B
542: $B7A$N%3%T!<%Z!<%9%H5!G=$rDs6!$7$F$$$k(B. Window $B>e$KI=<($5$l$F$$$kJ8;zNs(B
543: $B$KBP$7%^%&%9:8%\%?%s$r2!$7$J$,$i%I%i%C%0$9$k$HJ8;zNs$,A*Br$5$l$k(B.
544: $B%\%?%s$rN%$9$HH?E>I=<($,85$KLa$k$,(B, $B$=$NJ8;zNs$O%3%T!<%P%C%U%!$K(B
545: $B<h$j9~$^$l$F$$$k(B. $B%^%&%91&%\%?%s$r2!$9$H(B, $B%3%T!<%P%C%U%!Fb$NJ8;zNs$,(B
546: $B8=:_$N%+!<%=%k0LCV$KA^F~$5$l$k(B. $B4{$KI=<($5$l$?ItJ,$O(B readonly
547: $B$G$"$j(B, $B$=$NItJ,$r2~JQ$G$-$J$$$3$H$KCm0U$7$FM_$7$$(B.
1.3 noro 548: \E
549: \BEG
1.7 noro 550: A command line editing facility and a history
551: substitution facility are built-in for DOS, Windows version
1.3 noro 552: of @b{Asir}. UNIX versions of @b{Asir} do not have such built-in facilites.
553: Instead, the following input interfaces are prepared. This are also available
554: from our ftp server. As for our ftp server @xref{How to get Risa/Asir}.
1.7 noro 555:
556: On Windows, @samp{asirgui.exe} has a copy and paste functionality
557: different from Windows convention. Press the left button of the mouse
558: and drag the mouse cursor on a text, then the text is selected and is
559: highlighted. When the button is released, highlighted text returns to
560: the normal state and it is saved in the copy buffer. If the right
561: button is pressed, the text in the copy buffer is inserted at the
562: current text cursor position. Note that the existing text is read-only and
563: one cannot modify it.
1.3 noro 564: \E
1.1 noro 565:
566: @menu
567: * fep::
568: * asir.el::
569: @end menu
570:
1.3 noro 571: \JP @node fep,,, $BF~NO%$%s%?%U%'!<%9(B
572: \EG @node fep,,, Input interfaces
1.1 noro 573: @subsection fep
574:
575: @noindent
1.3 noro 576: \BJP
1.1 noro 577: fep $B$H$O(B, SRA $B$N2NBe;a$K$h$j3+H/$5$l$?%3%^%s%I%i%$%sJT=8(B, $B%R%9%H%jCV$-49$((B
578: $BMQ$NF~NO%U%m%s%H%(%s%I$G$"$k(B. $B$3$N%W%m%0%i%`$N85$G(B @samp{asir} $B$r5/F0$9$k(B
579: $B$3$H$K$h$j(B vi $B$"$k$$$O(B emacs $BIw$N%3%^%s%I%i%$%sJT=8$*$h$S(B csh $BIw$N%R%9%H%j(B
580: $BCV$-49$($,2DG=$K$J$k(B.
1.3 noro 581: \E
582: \BEG
583: Fep is a general purpose front end processor. The author is
584: K. Utashiro (SRA Inc.).
585:
586: Under fep,
587: emacs- or vi-like command line editing and csh-like history substitution are
588: available for UNIX commands, including @samp{asir}.
589: \E
1.1 noro 590: @example
591: % fep asir
592: ...
593: [0] fctr(x^5-1);
594: [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
595: [1] !! /* !!+Return */
1.3 noro 596: \BJP
1.1 noro 597: fctr(x^5-1); /* $BD>A0$NF~NO$,8=$l$k$FJT=8$G$-$k(B */
598: ... /* $BJT=8(B+Return */
1.3 noro 599: \E
600: \BEG
601: fctr(x^5-1); /* The last input appears. */
602: ... /* Edit+Return */
603: \E
1.1 noro 604: fctr(x^5+1);
605: [[1,1],[x+1,1],[x^4-x^3+x^2-x+1,1]]
606: @end example
607:
608: @noindent
1.3 noro 609: \BJP
1.1 noro 610: 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
611: $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$$7$?$b$N(B
612: $B$,(B, ftp $B$GF~<j2DG=$G$"$k(B.
1.3 noro 613: \E
614: \BEG
615: Fep is a free software and the source is available. However
616: machines or operating systems on which the original one can run are limited.
617: The modified version by us running on several unsupported environments
618: is available from our ftp server.
619: \E
1.1 noro 620:
1.3 noro 621: \JP @node asir.el,,, $BF~NO%$%s%?%U%'!<%9(B
622: \EG @node asir.el,,, Input interfaces
1.1 noro 623: @subsection asir.el
624:
625: @noindent
1.3 noro 626: \BJP
1.1 noro 627: @samp{asir.el} $B$O(B, @b{Asir} $B$N(B GNU Emacs $B%$%s%?%U%'!<%9$G$"$k(B ($BCx<T$O(B
628: $B5\Eh8w<#;a(B (@code{YVE25250@@pcvan.or.jp}). @samp{asir.el} $B$K$*$$$F$O(B,
629: $BDL>o$N(B emacs $B$G2DG=$JJT=85!G=$NB>$K(B, $B%U%!%$%kL>(B, $B%3%^%s%IL>$N(B completion
630: $B$,<B8=$5$l$F$$$k(B.
1.3 noro 631: \E
632: \BEG
633: @samp{asir.el} is a GNU Emacs interface for @b{Asir}.
634: The author is Koji Miyajima (@code{YVE25250@@pcvan.or.jp}).
635: In @samp{asir.el}, completion of file names and command names is
636: realized other than the ordinary editing functions
637: which are available on Emacs.
638: \E
1.1 noro 639:
640: @noindent
1.3 noro 641: \BJP
1.1 noro 642: @samp{asir.el} $B$O(B PC-VAN $B$G(B
643: $B4{$K8x3+$5$l$F$$$k$,(B, $B:#2s$N2~D{$KH<$&JQ99$r9T$C$?$b$N$,(B, $B$d$O$j(B ftp $B$G(B
644: $BF~<j2DG=$G$"$k(B.
1.3 noro 645: \E
646: \BEG
647: @samp{asir.el} is distributed on PC-VAN. The version where several
648: changes have been made according to the current version of @b{Asir}
649: is available via ftp.
650: \E
1.1 noro 651:
652: @noindent
1.3 noro 653: \JP $B%;%C%H%"%C%W(B, $B;HMQJ}K!$O(B, @samp{asir.el} $B$N@hF,$K5-=R$5$l$F$$$k(B.
654: \BEG
655: The way of setting up and the usage can be found at the top of
656: @samp{asir.el}.
657: \E
1.6 noro 658:
659: \BJP
660: @node $B%i%$%V%i%j%$%s%?%U%'!<%9(B,,, $BIUO?(B
661: @section $B%i%$%V%i%j%$%s%?%U%'!<%9(B
662: \E
663: \BEG
664: @node Library interfaces,,, Appendix
665: @section Library interfaces
666: \E
667:
668: \BJP
669: @b{Asir} $B$NDs6!$9$k5!G=$rB>$N%W%m%0%i%`$+$i;HMQ$9$kJ}K!$H$7$F(B, @b{OpenXM} $B$K$h$k(B
670: $BB>$K(B, $B%i%$%V%i%j$ND>@\%j%s%/$K$h$kJ}K!$,2DG=$G$"$k(B. $B%i%$%V%i%j$O(B,
671: GC $B%i%$%V%i%j$G$"$k(B @samp{libasir-gc.a} $B$H$H$b$K(B @b{OpenXM}
672: distribution (@code{http://www.math.kobe-u.ac.jp/OpenXM}) $B$K4^$^$l$k(B.
673: $B8=>u$G$O(B@b{OpenXM} $B%$%s%?%U%'!<%9$N$_$,8x3+$5$l$F$$$k$?$a(B, $B0J2<$G$O(B
674: @b{OpenXM} $B$,%$%s%9%H!<%k$5$l$F$$$k$H2>Dj$9$k(B. @b{OpenXM} root $B%G%#%l%/%H%j$r(B
675: @code{$OpenXM_HOME}$B$H=q$/(B. $B%i%$%V%i%j%U%!%$%k$OA4$F(B @samp{$OpenXM_HOME/lib}
676: $B$K$*$+$l$F$$$k(B. $B%i%$%V%i%j$K$O0J2<$N(B 3 $B<oN`$,$"$k(B.
677: \E
678: \BEG
679: It is possible to link an @b{Asir} library to use the functionalities of
680: @b{Asir} from other programs.
681: The necessary libraries are included in the @b{OpenXM} distribution
1.8 noro 682: @ifhtml
683: (<A HREF="http://www.math.kobe-u.ac.jp/OpenXM">OpenXM </A>)
684: @end ifhtml
1.6 noro 685: (@code{http://www.math.kobe-u.ac.jp/OpenXM}).
686: At present only the @b{OpenXM} interfaces are available. Here we assume
687: that @b{OpenXM} is already installed. In the following
688: @code{$OpenXM_HOME} denotes the @b{OpenXM} root directory.
689: All the library files are placed in @samp{$OpenXM_HOME/lib}.
690: There are three kinds of libraries as follows.
691: \E
692: @itemize @bullet
693: @item @samp{libasir.a}
694: @*
695: \BJP
696: @b{PARI}, @b{X11} $B4XO"$N5!G=$r4^$^$J$$(B.
697: $B%j%s%/$K$O(B @samp{libasir-gc.a} $B$N$_$,I,MW(B.
698: \E
699: \BEG
700: It does not contain the functionalities related to @b{PARI} and @b{X11}.
701: Only @samp{libasir-gc.a} is necessary for linking.
702: \E
703:
704: @item @samp{libasir_pari.a}
705: @*
706: \BJP
707: @b{X11} $B4XO"$N5!G=$r4^$^$J$$(B. $B%j%s%/$K$O(B @samp{libasir-gc.a},
708: @samp{libpari.a} $B$,I,MW(B.
709: \E
710: \BEG
711: It does not contain the functionalities related to @b{X11}.
712: @samp{libasir-gc.a}, @samp{libpari.a} are necessary for linking.
713: \E
714:
715: @item @samp{libasir_pari_X.a}
716: @*
717: \BJP
718: $BA4$F$N5!G=$r4^$`(B. $B%j%s%/$K$O(B @samp{libasir-gc.a}, @samp{libpari.a}
719: $B$*$h$S(B @b{X11} $B4XO"$N%i%$%V%i%j;XDj$,I,MW(B.
720: \E
721: \BEG
722: All the functionalities are included. @samp{libasir-gc.a}, @samp{libpari.a}
723: and libraries related to @b{X11} are necessary for linking.
724: \E
725: @end itemize
726: \BJP
727: $BDs6!$5$l$F$$$k4X?t$O0J2<$NDL$j$G$"$k(B.
728: \E
729: @itemize @bullet
730: @item @code{int asir_ox_init(int @var{byteorder})}
731: @*
732: \BJP
733: $B%i%$%V%i%j$N=i4|2=(B. @var{byteorder} $B$O%a%b%j>e$X$N%P%$%J%j(B CMO $B%G!<%?(B
734: $B$X$NE83+J}K!$r;XDj$9$k(B. @var{byteorder} $B$,(B 0 $B$N$H$-%^%7%s8GM-$N(B byteorder
735: $B$rMQ$$$k(B. 1 $B$N$H$-(B network byteorder $B$rMQ$$$k(B. $B=i4|2=$K@.8y$7$?>l9g(B 0,
736: $B<:GT$N;~(B -1 $B$rJV$9(B.
737: \E
738: \BEG
739: It initializes the library.
740: @var{byteorder} specifies the format of binary CMO data on the memory.
741: If @var{byteorder} is 0, the byteorder native to the machine is used.
742: If @var{byteorder} is 1, the network byteorder is used. It returns
743: 0 if the initialization is successful, -1 otherwise.
744: \E
745:
746: @item @code{void asir_ox_push_cmo(void *@var{cmo})}
747: @*
748: \BJP
749: $B%a%b%j>e$KCV$+$l$?(B CMO $B%G!<%?$r(B @b{Asir} $B$NFbIt7A<0$KJQ49$7$F%9%?%C%/$K(B
750: push $B$9$k(B.
751: \E
752: \BJP
753: It converts CMO data pointed by @var{cmo} into an @b{Asir} object and
754: it pushes the object onto the stack.
755: \E
756:
757: @item @code{int asir_ox_peek_cmo_size()}
758: @*
759: \BJP
760: $B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B CMO $B$KJQ49$7$?$H$-$N%5%$%:$rJV$9(B.
761: $BJQ49ITG=$J>l9g$K$O(B -1 $B$rJV$9(B.
762: \E
763: \BEG
764: It returns the size of the object at the top of the stack as CMO object.
765: It returns -1 if the object cannot be converted into CMO object.
766: \E
767:
768: @item @code{int asir_ox_pop_cmo(void *@var{cmo}, int @var{limit})}
769: @*
770: \BJP
771: $B%9%?%C%/$N:G>e0L$K$"$k(B @b{Asir} $B%G!<%?$r(B pop $B$7(B, CMO $B$KJQ49$7$F(B @var{cmo}$B$G(B
772: $B;X$5$l$kG[Ns$K=q$-(B, CMO $B$N%5%$%:$rJV$9(B. $B$3$N$H$-(B, CMO $B$N%5%$%:$,(B
773: @var{limit} $B$h$jBg$-$$>l9g$K$O(B -1 $B$rJV$9(B. @var{cmo} $B$OD9$5$,>/$J$/$H$b(B
774: @var{limit}$B%P%$%H$NG[Ns$r;X$9I,MW$,$"$k(B. $BJQ49$5$l$?(B CMO $B$r<}MF$G$-$k(B
775: $BG[Ns$ND9$5$rCN$k$?$a$K(B, @code{asir_ox_peek_cmo_size} $B$rMQ$$$k(B.
776: \E
777: \BEG
778: It pops an @b{Asir} object at the top of the stack and it converts
779: the object into CMO data. If the size of the CMO data is not greater
780: than @var{limit}, then the data is written in @var{cmo} and the size
781: is returned. Otherwise -1 is returned. The size of the array pointed
782: by @var{cmo} must be at least @var{limit}. In order to know the size
783: of converted CMO data in advance @code{asir_ox_peek_cmo_size} is called.
784: \E
785:
786: @item @code{void asir_ox_push_cmd(int @var{cmd})}
787: @*
788: \BJP
789: $B%9%?%C%/%^%7%s%3%^%s%I(B @var{cmd} $B$r<B9T$9$k(B.
790: \E
791: \BEG
792: It executes a stack machine command @var{cmd}.
793: \E
794:
795: @item @code{void asir_ox_execute_string(char *@var{str})}
796: @*
797: \BJP
798: @b{Asir} $B$,<B9T2DG=$JJ8;zNs(B @var{str} $B$r<B9T$7(B, $B$=$N7k2L$r%9%?%C%/$K(B push $B$9$k(B.
799: \E
800: \BEG
801: It evaluates @var{str} as a string written in the @b{Asir} user language.
802: The result is pushed onto the stack.
803: \E
804: @end itemize
805:
806: \BJP
807: include $B$9$Y$-(B header file $B$O(B @samp{$OpenXM_HOME/include/asir/ox.h} $B$G$"$k(B.
808: $B$3$N(B header file $B$K$O(B, @b{OpenXM} $B$K4X$9$kA4$F$N(B tag, command $B$NDj5A$,4^$^$l$F(B
809: $B$$$k(B.
810: $B<!$NNc(B (@samp{$OpenXM_HOME/doc/oxlib/test3.c}) $B$O>e5-4X?t$N;HMQ(B
811: $BK!$r<($9(B.
812: \E
813: \BEG
814: A program calling the above functions should include
815: @samp{$OpenXM_HOME/include/asir/ox.h}.
816: In this file all the definitions of @b{OpenXM} tags and commands.
817: The following example
818: (@samp{$OpenXM_HOME/doc/oxlib/test3.c}) illustrates the usage of
819: the above functions.
820: \E
821:
822: @example
823: #include <asir/ox.h>
824: #include <signal.h>
825:
826: main(int argc, char **argv)
827: @{
828: char buf[BUFSIZ+1];
829: int c;
830: unsigned char sendbuf[BUFSIZ+10];
831: unsigned char *result;
832: unsigned char h[3];
833: int len,i,j;
834: static int result_len = 0;
835: char *kwd,*bdy;
836: unsigned int cmd;
837:
838: signal(SIGINT,SIG_IGN);
839: asir_ox_init(1); /* 1: network byte order; 0: native byte order */
840: result_len = BUFSIZ;
841: result = (void *)malloc(BUFSIZ);
842: while ( 1 ) @{
843: printf("Input>"); fflush(stdout);
844: fgets(buf,BUFSIZ,stdin);
845: for ( i = 0; buf[i] && isspace(buf[i]); i++ );
846: if ( !buf[i] )
847: continue;
848: kwd = buf+i;
849: for ( ; buf[i] && !isspace(buf[i]); i++ );
850: buf[i] = 0;
851: bdy = buf+i+1;
852: if ( !strcmp(kwd,"asir") ) @{
853: sprintf(sendbuf,"%s;",bdy);
854: asir_ox_execute_string(sendbuf);
855: @} else if ( !strcmp(kwd,"push") ) @{
856: h[0] = 0;
857: h[2] = 0;
858: j = 0;
859: while ( 1 ) @{
860: for ( ; (c= *bdy) && isspace(c); bdy++ );
861: if ( !c )
862: break;
863: else if ( h[0] ) @{
864: h[1] = c;
865: sendbuf[j++] = strtoul(h,0,16);
866: h[0] = 0;
867: @} else
868: h[0] = c;
869: bdy++;
870: @}
871: if ( h[0] )
872: fprintf(stderr,"Number of characters is odd.\n");
873: else @{
874: sendbuf[j] = 0;
875: asir_ox_push_cmo(sendbuf);
876: @}
877: @} else if ( !strcmp(kwd,"cmd") ) @{
878: cmd = atoi(bdy);
879: asir_ox_push_cmd(cmd);
880: @} else if ( !strcmp(kwd,"pop") ) @{
881: len = asir_ox_peek_cmo_size();
882: if ( !len )
883: continue;
884: if ( len > result_len ) @{
885: result = (char *)realloc(result,len);
886: result_len = len;
887: @}
888: asir_ox_pop_cmo(result,len);
889: printf("Output>"); fflush(stdout);
890: printf("\n");
891: for ( i = 0; i < len; ) @{
892: printf("%02x ",result[i]);
893: i++;
894: if ( !(i%16) )
895: printf("\n");
896: @}
897: printf("\n");
898: @}
899: @}
900: @}
901: @end example
902: \BJP
903: $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
904: @var{keyword} $B$K1~$8$F<!$N$h$&$JF0:n$r9T$&(B.
905: \E
906: \BEG
907: This program receives a line in the form of @var{keyword} @var{body}
908: as an input and it executes the following operations according to
909: @var{keyword}.
910: \E
911: @itemize @bullet
912: @item @code{asir} @var{body}
913: @*
914: \BJP
915: @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.
916: @code{asir_ox_execute_string()} $B$,MQ$$$i$l$k(B.
917: \E
918: \BEG
919: @var{body} is regarded as an expression written in the @b{Asir} user language.
920: The expression is evaluated and the result is pushed onto the stack.
921: @code{asir_ox_execute_string()} is called.
922: \E
923:
924: @item @code{push} @var{body}
925: @*
926: \BJP
927: @var{body} $B$r(B 16 $B?J?t$GI=<($5$l$?(B CMO $B%G!<%?$H$_$J$7(B, @b{Asir} $B%*%V%8%'%/%H$KJQ49(B
928: $B$7$F%9%?%C%/$K(B push $B$9$k(B. @code{asir_ox_push_cmo()} $B$,MQ$$$i$l$k(B.
929: \E
930: \BEG
931: @var{body} is regarded as a CMO object in the hexadecimal form.
932: The CMO object is converted into an @b{Asir} object and is pushed onto the stack.
933: @code{asir_ox_push_cmo()} is called.
934: \E
935:
936: @item @code{pop}
937: @*
938: \BJP
939: $B%9%?%C%/:G>e0L$N%*%V%8%'%/%H$r(B CMO $B$KJQ49$7(B, 16 $B?J?t$GI=<($9$k(B.
940: @code{asir_ox_peek_cmo_size()} $B$*$h$S(B @code{asir_ox_pop_cmo()} $B$,MQ$$$i$l$k(B.
941: \E
942: \BEG
943: The object at the top of the stack is converted into a CMO object
944: and it is displayed in the hexadecimal form.
945: @code{asir_ox_peek_cmo_size()} and @code{asir_ox_pop_cmo()} are called.
946: \E
947:
948: @item @code{cmd} @var{body}
949: @*
950: \BJP
951: @var{body} $B$r(B SM $B%3%^%s%I$H$_$J$7(B, $B<B9T$9$k(B.
952: @code{asir_ox_push_cmd()} $B$,MQ$$$i$l$k(B.
953: \E
954: \BEG
955: @var{body} is regarded as an SM command and the command is executed.
956: @code{asir_ox_push_cmd()} is called.
957: \E
958: @end itemize
1.1 noro 959:
1.3 noro 960: \BJP
1.1 noro 961: @node $BJQ99E@(B,,, $BIUO?(B
962: @section $BJQ99E@(B
1.3 noro 963: \E
964: \BEG
965: @node Changes,,, Appendix
966: @section Appendix
967: \E
1.1 noro 968:
969: @menu
970: * Version 990831::
971: * Version 950831::
972: * Version 940420::
973: @end menu
974:
1.3 noro 975: \JP @node Version 990831,,, $BJQ99E@(B
976: \EG @node Version 990831,,, Changes
1.1 noro 977: @subsection Version 990831
978:
1.3 noro 979: \BJP
1.1 noro 980: 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,
981: $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,
982: plot $B$,;H$($J$$$?$a(B, $BB`2=$7$F$$$k(B.
983:
984: $B5lHG$N%f!<%6$,$b$C$H$bCm0U$9$Y$-E@$O(B, $B5lHG$G:n$C$?(B bsave file $B$rFI$_9~$`(B
985: $B>l9g$O(B @code{bload27} $B$r;H$&I,MW$,$"$k(B, $B$H$$$&E@$G$"$k(B.
1.3 noro 986: \E
987:
988: \BEG
989: Four years have passed since the last distribution.
990: Though the look and feel seem unchanged, internally there are
991: several changes such as 32-bit representation of bignums.
992: Plotting facilities are not available on Windows.
993:
994: If you have files created by @code{bsave} on the older version,
995: you have to use @code{bload27} to read such files.
996: \E
1.1 noro 997:
1.3 noro 998: \JP @node Version 950831,,, $BJQ99E@(B
999: \EG @node Version 950831,,, Changes
1.1 noro 1000: @subsection Version 950831
1001:
1002: @menu
1.3 noro 1003: \BJP
1.1 noro 1004: * $B%G%P%C%,(B($BJQ99(B)::
1005: * $BAH$_9~$_H!?t(B($BJQ99(B)::
1006: * $B%0%l%V%J4pDl(B($BJQ99(B)::
1007: * $B$=$NB>(B($BJQ99(B)::
1.3 noro 1008: \E
1009: \BEG
1010: * Debugger(Changes)::
1011: * Built-in functions(Changes)::
1012: * Groebner basis computation(Changes)::
1013: * Others(Changes)::
1014: \E
1.1 noro 1015: @end menu
1016:
1.3 noro 1017: \BJP
1.1 noro 1018: @node $B%G%P%C%,(B($BJQ99(B),,, Version 950831
1019: @subsubsection $B%G%P%C%,(B
1.3 noro 1020: \E
1021: \BEG
1022: @node Debugger(Changes),,, Version 950831
1023: @subsubsection Debugger
1024: \E
1.1 noro 1025:
1026: @itemize @bullet
1027: @item
1.3 noro 1028: \JP $BG$0U$N;~E@$K%G%P%C%0%b!<%I$KF~$l$k(B.
1029: \EG One can enter the debug mode anytime.
1.1 noro 1030: @item
1.3 noro 1031: \JP @code{finish} $B%3%^%s%I$NDI2C(B.
1032: \EG A command @code{finish} has been appended.
1.1 noro 1033: @item
1.3 noro 1034: \BJP
1.1 noro 1035: @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 1036: $B$N;2>H(B.
1037: \E
1038: \EG One can examine any stack frame with @code{up}, @code{down} and @code{frame}.
1.1 noro 1039: @item
1.3 noro 1040: \JP @code{trace} $B%3%^%s%I$NDI2C(B.
1041: \EG A command @code{trace} has been appended.
1.1 noro 1042: @end itemize
1043:
1.3 noro 1044: \BJP
1.1 noro 1045: @node $BAH$_9~$_H!?t(B($BJQ99(B),,, Version 950831
1046: @subsubsection $BAH$_9~$_H!?t(B
1.3 noro 1047: \E
1048: \BEG
1049: @node Built-in functions(Changes),,, Version 950831
1050: @subsubsection Built-in functions
1051: \E
1.1 noro 1052:
1053: @itemize @bullet
1.3 noro 1054: \BJP
1.1 noro 1055: @item
1056: @code{sdiv()} $B$J$I$K$*$1$k(B, $B<gJQ?t$N;XDj$N%5%]!<%H(B.
1057: @item
1058: @code{sdivm()} $B$J$I(B, $BM-8BBN>e$G$NB?9`<0=|;;$NDI2C(B.
1059: @item
1060: @code{det()}, @code{res()} $B$J$I$K$*$1$k(B, $BM-8BBN>e$G$N7W;;$N%5%]!<%H(B
1061: @item
1062: @code{vtol()} ($B%Y%/%H%k$+$i%j%9%H$X$NJQ49(B) $B$NDI2C(B.
1063: @item
1064: @code{map()} $B$NDI2C(B.
1.3 noro 1065: \E
1066: \BEG
1067: @item
1068: One can specify a main variable for @code{sdiv()} etc.
1069: @item
1070: Functions for polynomial division over finite fields
1071: such as @code{sdivm()} have been appended.
1072: @item
1073: @code{det()}, @code{res()} can produce results over finite fields.
1074: @item
1075: @code{vtol()}, conversion from a vector to a list has been appended.
1076: @item
1077: @code{map()} has been appended.
1078: \E
1.1 noro 1079: @end itemize
1080:
1.3 noro 1081: \BJP
1.1 noro 1082: @node $B%0%l%V%J4pDl(B($BJQ99(B),,, Version 950831
1083: @subsubsection $B%0%l%V%J4pDl(B
1.3 noro 1084: \E
1085: \BEG
1086: @node Groebner basis computation(Changes),,, Version 950831
1087: @subsubsection Groebner basis computation
1088: \E
1.1 noro 1089:
1090: @itemize @bullet
1.3 noro 1091: \BJP
1.1 noro 1092: @item
1093: $B%0%l%V%J4pDl7W;;5!G=$NAH$_9~$_H!?t2=(B.
1094: @item
1095: @code{grm()}, @code{hgrm()} $B$,(B @code{gr()}, @code{hgr()} $B$KJQ99(B.
1096: @item
1097: @code{gr()}, @code{hgr()} $B$K$*$$$F(B, $B9`=g=x$N;XDj$,I,MW$K$J$C$?(B.
1098: @item
1099: $B9`=g=x$N;XDjJ}K!$,3HD%$5$l$?(B.
1100: @item
1101: $BM-8BBN>e$N%0%l%V%J4pDl7W;;$N%5%]!<%H(B.
1102: @item
1103: $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl7W;;$N%5%]!<%H(B.
1104: @item
1105: $B$$$/$D$+$N?7$7$$AH$_9~$_H!?t$NDs6!(B.
1.3 noro 1106: \E
1107: \BEG
1108: @item Functions for Groebner basis computation have been implemented
1109: as built-in functions.
1110: @item
1111: @code{grm()} and @code{hgrm()} have been changed to @code{gr()} and
1112: @code{hgr()} respectively.
1113: @item
1114: @code{gr()} and @code{hgr()} requires explicit specification of
1115: an ordering type.
1116: @item
1117: Extension of specification of a term ordering type.
1118: @item
1119: Groebner basis computations over finite fields.
1120: @item
1121: Lex order Groebner basis computation via a modular change of ordering algorithm.
1122: @item
1123: Several new built-in functions.
1124: \E
1.1 noro 1125: @end itemize
1126:
1.3 noro 1127: \BJP
1.1 noro 1128: @node $B$=$NB>(B($BJQ99(B),,, Version 950831
1129: @subsubsection $B$=$NB>(B
1.3 noro 1130: \E
1131: \BEG
1132: @node Others(Changes),,, Version 950831
1133: @subsubsection Others
1134: \E
1.1 noro 1135:
1136: @itemize @bullet
1.3 noro 1137: \BJP
1.1 noro 1138: @item
1139: $BJ,;67W;;MQ%D!<%k(B, $BH!?t$NDI2C(B.
1140: @item
1141: $BBe?tBN>e$N(B GCD $B7W;;$K$*$1$k%b%8%e%i7W;;$N1~MQ(B.
1142: @item
1143: $B%$%G%"%k$N=`AGJ,2r$N%5%]!<%H(B.
1144: @item
1145: Windows $B$X$N0\?"(B.
1.3 noro 1146: \E
1147: \BEG
1148: @item
1149: Implementation of tools for distributed computation.
1150: @item
1151: Application of modular computation for GCD computation over algebraic number
1152: fields.
1153: @item
1154: Implementation of primary decompostion of ideals.
1155: @item
1156: Porting to Windows.
1157: \E
1.1 noro 1158: @end itemize
1159:
1.3 noro 1160: \JP @node Version 940420,,, $BJQ99E@(B
1161: \EG @node Version 940420,,, Changes
1.1 noro 1162: @subsection Version 940420
1163:
1164: @noindent
1.3 noro 1165: \JP $B:G=i$N8x3+HG(B.
1166: \EG The first public verion.
1.1 noro 1167:
1.3 noro 1168: \BJP
1.1 noro 1169: @node $BJ88%(B,,, $BIUO?(B
1170: @section $BJ88%(B
1.3 noro 1171: \E
1172: \BEG
1173: @node References,,, Appendix
1174: @section References
1175: \E
1.1 noro 1176: @table @code
1177: @item [Batut et al.]
1178: Batut, C., Bernardi, D., Cohen, H., Olivier, M., "User's Guide to PARI-GP",
1179: 1993.
1180: @item [Becker,Weispfenning]
1181: Becker, T., Weispfenning, V., "Groebner Bases", Graduate Texts in Math. 141,
1182: Springer-Verlag, 1993.
1183: @item [Boehm,Weiser]
1184: Boehm, H., Weiser, M., "Garbage Collection in an Uncooperative
1185: Environment", Software Practice & Experience, September 1988, 807-820.
1186: @item [Gebauer,Moeller]
1187: Gebauer, R., Moeller, H. M., "An installation of Buchberger's algorithm",
1188: J. of Symbolic Computation 6, 275-286.
1189: @item [Giovini et al.]
1190: Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C.,
1191: ""One sugar cube, please" OR Selection strategies in the Buchberger algorithm",
1192: Proc. ISSAC'91, 49-54.
1193: @item [Noro,Takeshima]
1194: Noro, M., Takeshima, T., "Risa/Asir -- A Computer Algebra System",
1195: Proc. ISSAC'92, 387-396.
1196: @item [Noro,Yokoyama]
1.3 noro 1197: Noro, M., Yokoyama, K., "A Modular Method to Compute the Rational Univariate
1198: Representation of Zero-Dimensional Ideals",
1199: J. Symb. Comp. 28/1 (1999), 243-263.
1.1 noro 1200: @item [Shimoyama,Yokoyama]
1201: Shimoyama, T., Yokoyama, K.,
1202: "Localization and primary decomposition of polynomial ideals",
1.3 noro 1203: J. Symb. Comp. 22 (1996), 247-277.
1204: @item [Shoup]
1205: Shoup, V., "A new polynomial factorization algorithm and its implementation",
1206: J. Symb. Comp. 20 (1995), 364-397.
1.1 noro 1207: @item [Traverso]
1208: Traverso, C., "Groebner trace algorithms", Proc. ISSAC '88(LNCS 358), 125-138.
1.3 noro 1209: @item [Weber]
1210: Weber, K., "The accelerated Integer GCD Algorithm", ACM TOMS, 21, 1(1995), 111-122.
1.1 noro 1211: @end table
1212:
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