Annotation of OpenXM/src/asir-doc/parts/builtin/num.texi, Revision 1.12
1.12 ! noro 1: @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.11 2016/03/22 07:25:14 noro Exp $
1.2 noro 2: \BJP
1.1 noro 3: @node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B
4: @section $B?t$N1i;;(B
1.2 noro 5: \E
6: \BEG
7: @node Numbers,,, Built-in Function
8: @section Numbers
9: \E
1.1 noro 10:
11: @menu
12: * idiv irem::
13: * fac::
14: * igcd igcdcntl::
15: * ilcm::
1.10 ohara 16: * isqrt::
1.1 noro 17: * inv::
18: * prime lprime::
19: * random::
20: * mt_save mt_load::
21: * nm dn::
22: * conj real imag::
1.4 noro 23: * eval deval::
1.1 noro 24: * pari::
1.12 ! noro 25: * setbprec setprec::
1.1 noro 26: * setmod::
27: * lrandom::
1.3 noro 28: * ntoint32 int32ton::
1.12 ! noro 29: * setround::
1.1 noro 30: @end menu
31:
1.2 noro 32: \JP @node idiv irem,,, $B?t$N1i;;(B
33: \EG @node idiv irem,,, Numbers
1.1 noro 34: @subsection @code{idiv}, @code{irem}
35: @findex idiv
36: @findex irem
37:
38: @table @t
39: @item idiv(@var{i1},@var{i2})
1.2 noro 40: \JP :: $B@0?t=|;;$K$h$k>&(B.
41: \EG :: Integer quotient of @var{i1} divided by @var{i2}.
1.1 noro 42: @item irem(@var{i1},@var{i2})
1.2 noro 43: \JP :: $B@0?t=|;;$K$h$k>jM>(B.
44: \EG :: Integer remainder of @var{i1} divided by @var{i2}.
1.1 noro 45: @end table
46:
47: @table @var
48: @item return
1.2 noro 49: \JP $B@0?t(B
50: \EG integer
1.8 noro 51: @item i1 i2
1.2 noro 52: \JP $B@0?t(B
53: \EG integer
1.1 noro 54: @end table
55:
56: @itemize @bullet
1.2 noro 57: \BJP
1.1 noro 58: @item
59: @var{i1} $B$N(B @var{i2} $B$K$h$k@0?t=|;;$K$h$k>&(B, $B>jM>$r5a$a$k(B.
60: @item
61: @var{i2} $B$O(B 0 $B$G$"$C$F$O$J$i$J$$(B.
62: @item
63: $BHo=|?t$,Ii$N>l9g(B, $B@dBPCM$KBP$9$kCM$K%^%$%J%9$r$D$1$?CM$rJV$9(B.
64: @item
65: @var{i1} @code{%} @var{i2} $B$O(B, $B7k2L$,@5$K@55,2=$5$l$k$3$H$r=|$1$P(B
66: @code{irem()} $B$NBe$o$j$KMQ$$$k$3$H$,$G$-$k(B.
67: @item
68: $BB?9`<0$N>l9g$O(B @code{sdiv}, @code{srem} $B$rMQ$$$k(B.
1.2 noro 69: \E
70: \BEG
71: @item
72: Integer quotient and remainder of @var{i1} divided by @var{i2}.
73: @item
74: @var{i2} must not be 0.
75: @item
76: If the dividend is negative, the results are obtained by changing the
77: sign of the results for absolute values of the dividend.
78: @item
79: One can use
80: @var{i1} @code{%} @var{i2}
81: for replacement of @code{irem()} which only differs in the point that
82: the result is always normalized to non-negative values.
83: @item
84: Use @code{sdiv()}, @code{srem()} for polynomial quotient.
85: \E
1.1 noro 86: @end itemize
87:
88: @example
89: [0] idiv(100,7);
90: 14
91: [0] idiv(-100,7);
92: -14
93: [1] irem(100,7);
94: 2
95: [1] irem(-100,7);
96: -2
97: @end example
98:
99: @table @t
1.2 noro 100: \JP @item $B;2>H(B
101: \EG @item References
1.1 noro 102: @fref{sdiv sdivm srem sremm sqr sqrm}, @fref{%}.
103: @end table
104:
1.2 noro 105: \JP @node fac,,, $B?t$N1i;;(B
106: \EG @node fac,,, Numbers
1.1 noro 107: @subsection @code{fac}
108: @findex fac
109:
110: @table @t
111: @item fac(@var{i})
1.2 noro 112: \JP :: @var{i} $B$N3,>h(B.
113: \EG :: The factorial of @var{i}.
1.1 noro 114: @end table
115:
116: @table @var
117: @item return
1.2 noro 118: \JP $B@0?t(B
119: \EG integer
1.1 noro 120: @item i
1.2 noro 121: \JP $B@0?t(B
122: \EG integer
1.1 noro 123: @end table
124:
125: @itemize @bullet
1.2 noro 126: \BJP
1.1 noro 127: @item
128: @var{i} $B$N3,>h$r7W;;$9$k(B.
129: @item
130: @var{i} $B$,Ii$N>l9g$O(B 0 $B$rJV$9(B.
1.2 noro 131: \E
132: \BEG
133: @item
134: The factorial of @var{i}.
135: @item
136: Returns 0 if the argument @var{i} is negative.
137: \E
1.1 noro 138: @end itemize
139:
140: @example
141: [0] fac(50);
142: 30414093201713378043612608166064768844377641568960512000000000000
143: @end example
144:
1.2 noro 145: \JP @node igcd igcdcntl,,, $B?t$N1i;;(B
146: \EG @node igcd igcdcntl,,, Numbers
1.1 noro 147: @subsection @code{igcd},@code{igcdcntl}
148: @findex igcd
149: @findex igcdcntl
150:
151: @table @t
152: @item igcd(@var{i1},@var{i2})
1.2 noro 153: \JP :: $B@0?t$N(B GCD ($B:GBg8xLs?t(B)
154: \EG :: The integer greatest common divisor of @var{i1} and @var{i2}.
1.1 noro 155: @item igcdcntl([@var{i}])
1.2 noro 156: \JP :: $B@0?t(B GCD$B$N%"%k%4%j%:%`A*Br(B
157: \EG :: Selects an algorithm for integer GCD.
1.1 noro 158: @end table
159:
160: @table @var
161: @item return
1.2 noro 162: \JP $B@0?t(B
163: \EG integer
1.8 noro 164: @item i1 i2 i
1.2 noro 165: \JP $B@0?t(B
166: \EG integer
1.1 noro 167: @end table
168:
169: @itemize @bullet
1.2 noro 170: \BJP
1.1 noro 171: @item
172: @code{igcd} $B$O(B @var{i1} $B$H(B @var{i2} $B$N(B GCD $B$r5a$a$k(B.
173: @item
174: $B0z?t$,@0?t$G$J$$>l9g$O(B, $B%(%i!<$^$?$OL50UL#$J7k2L$rJV$9(B.
175: @item
176: $BB?9`<0$N>l9g$O(B, @code{gcd}, @code{gcdz} $B$rMQ$$$k(B.
177: @item
178: $B@0?t(B GCD $B$K$O$5$^$6$^$JJ}K!$,$"$j(B, @code{igcdcntl} $B$G@_Dj$G$-$k(B.
179:
180: @table @code
181: @item 0
182: Euclid $B8_=|K!(B (default)
183: @item 1
184: binary GCD
185: @item 2
186: bmod GCD
187: @item 3
188: accelerated integer GCD
189: @end table
1.2 noro 190: @code{2}, @code{3} $B$O(B @code{[Weber]} $B$K$h$k(B.
1.1 noro 191:
1.2 noro 192: $B$*$*$`$M(B @code{3} $B$,9bB.$@$,(B, $BNc30$b$"$k(B.
193: \E
194: \BEG
195: @item
196: Function @code{igcd()} returns the integer greatest common divisor of
197: the given two integers.
198: @item
199: An error will result if the argument is not an integer; the result is
200: not valid even if one is returned.
201: @item
202: Use @code{gcd()}, @code{gcdz()} for polynomial GCD.
203:
204: @item
205: Various method of integer GCD computation are implemented
206: and they can be selected by @code{igcdcntl}.
207:
208: @table @code
209: @item 0
210: Euclid algorithm (default)
211: @item 1
212: binary GCD
213: @item 2
214: bmod GCD
215: @item 3
216: accelerated integer GCD
217: @end table
218: @code{2}, @code{3} are due to @code{[Weber]}.
219:
220: In most cases @code{3} is the fastest, but there are exceptions.
221: \E
1.1 noro 222: @end itemize
223:
224: @example
225: [0] A=lrandom(10^4)$
226: [1] B=lrandom(10^4)$
227: [2] C=lrandom(10^4)$
228: [3] D=A*C$
229: [4] E=A*B$
230: [5] cputime(1)$
231: [6] igcd(D,E)$
232: 0.6sec + gc : 1.93sec(2.531sec)
233: [7] igcdcntl(1)$
234: [8] igcd(D,E)$
235: 0.27sec(0.2635sec)
236: [9] igcdcntl(2)$
237: [10] igcd(D,E)$
238: 0.19sec(0.1928sec)
239: [11] igcdcntl(3)$
240: [12] igcd(D,E)$
241: 0.08sec(0.08023sec)
242: @end example
243:
244: @table @t
1.2 noro 245: \JP @item $B;2>H(B
246: \EG @item References
1.1 noro 247: @fref{gcd gcdz}.
248: @end table
249:
1.2 noro 250: \JP @node ilcm,,, $B?t$N1i;;(B
251: \EG @node ilcm,,, Numbers
1.1 noro 252: @subsection @code{ilcm}
253: @findex ilcm
254:
255: @table @t
256: @item ilcm(@var{i1},@var{i2})
1.2 noro 257: \JP :: $B:G>.8xG\?t$r5a$a$k(B.
258: \EG :: The integer least common multiple of @var{i1} and @var{i2}.
1.1 noro 259: @end table
260:
261: @table @var
262: @item return
1.2 noro 263: \JP $B@0?t(B
264: \EG integer
1.8 noro 265: @item i1 i2
1.2 noro 266: \JP $B@0?t(B
267: \EG integer
1.1 noro 268: @end table
269:
270: @itemize @bullet
1.2 noro 271: \BJP
1.1 noro 272: @item
273: $B@0?t(B @var{i1}, @var{i2} $B$N:G>.8xG\?t$r5a$a$k(B.
274: @item
275: $B0lJ}$,(B 0 $B$N>l9g(B 0 $B$rJV$9(B.
1.2 noro 276: \E
277: \BEG
1.1 noro 278: @item
1.2 noro 279: This function computes the integer least common multiple of
280: @var{i1}, @var{i2}.
281: @item
282: If one of argument is equal to 0, the return 0.
283: \E
1.1 noro 284: @end itemize
285:
286: @table @t
1.2 noro 287: \JP @item $B;2>H(B
288: \EG @item References
1.1 noro 289: @fref{igcd igcdcntl}, @fref{mt_save mt_load}.
1.9 ohara 290: @end table
291:
292: \JP @node isqrt,,, $B?t$N1i;;(B
293: \EG @node isqrt,,, Numbers
294: @subsection @code{isqrt}
295: @findex isqrt
296:
297: @table @t
298: @item isqrt(@var{n})
299: \JP :: $BJ?J}:,$r1[$($J$$:GBg$N@0?t$r5a$a$k(B.
300: \EG :: The integer square root of @var{n}.
301: @end table
302:
303: @table @var
304: @item return
305: \JP $BHsIi@0?t(B
306: \EG non-negative integer
307: @item n
308: \JP $BHsIi@0?t(B
309: \EG non-negative integer
1.1 noro 310: @end table
1.2 noro 311:
312: \JP @node inv,,, $B?t$N1i;;(B
313: \EG @node inv,,, Numbers
1.1 noro 314: @subsection @code{inv}
315: @findex inv
316:
317: @table @t
318: @item inv(@var{i},@var{m})
1.2 noro 319: \JP :: @var{m} $B$rK!$H$9$k(B @var{i} $B$N5U?t(B
320: \EG :: the inverse (reciprocal) of @var{i} modulo @var{m}.
1.1 noro 321: @end table
322:
323: @table @var
324: @item return
1.2 noro 325: \JP $B@0?t(B
326: \EG integer
1.8 noro 327: @item i m
1.2 noro 328: \JP $B@0?t(B
329: \EG integer
1.1 noro 330: @end table
331:
332: @itemize @bullet
1.2 noro 333: \BJP
1.1 noro 334: @item
335: @var{ia} @equiv{} 1 mod (@var{m}) $B$J$k@0?t(B @var{a} $B$r5a$a$k(B.
336: @item
337: @var{i} $B$H(B @var{m} $B$O8_$$$KAG$G$J$1$l$P$J$i$J$$$,(B, @code{inv()} $B$O(B
338: $B$=$N%A%'%C%/$O9T$o$J$$(B.
1.2 noro 339: \E
340: \BEG
341: @item
342: This function computes an integer such that
343: @var{ia} @equiv{} 1 mod (@var{m}).
344: @item
345: The integer @var{i} and @var{m} must be mutually prime.
346: However, @code{inv()} does not check it.
347: \E
1.1 noro 348: @end itemize
349:
350: @example
351: [71] igcd(1234,4321);
352: 1
353: [72] inv(1234,4321);
354: 3239
355: [73] irem(3239*1234,4321);
356: 1
357: @end example
358:
359: @table @t
1.2 noro 360: \JP @item $B;2>H(B
361: \EG @item References
1.1 noro 362: @fref{igcd igcdcntl}.
363: @end table
364:
1.2 noro 365: \JP @node prime lprime,,, $B?t$N1i;;(B
366: \EG @node prime lprime,,, Numbers
1.1 noro 367: @subsection @code{prime}, @code{lprime}
368: @findex prime
369: @findex lprime
370:
371: @table @t
372: @item prime(@var{index})
373: @item lprime(@var{index})
1.2 noro 374: \JP :: $BAG?t$rJV$9(B
375: \EG :: Returns a prime number.
1.1 noro 376: @end table
377:
378: @table @var
379: @item return
1.2 noro 380: \JP $B@0?t(B
381: \EG integer
1.1 noro 382: @item index
1.2 noro 383: \JP $B@0?t(B
384: \EG integer
1.1 noro 385: @end table
386:
387: @itemize @bullet
1.2 noro 388: \BJP
1.1 noro 389: @item
390: @code{prime()}, @code{lprime()} $B$$$:$l$b%7%9%F%`$,FbIt$K;}$D(B
391: $BAG?tI=$NMWAG$rJV$9(B. @code{index} $B$O(B 0 $B0J>e$N@0?t$G(B, $BAG?tI=(B
392: $B$N%$%s%G%C%/%9$KMQ$$$i$l$k(B. @code{prime()} $B$O(B 16381 $B$^$G(B
393: $B$NAG?t$r>.$5$$=g$K(B 1900 $B8D(B, @code{lprime()} $B$O(B, 10 $B?J(B 8 $B7e$G:GBg$N(B
394: $BAG?t$+$iBg$-$$=g$K(B 999 $B8DJV$9(B. $B$=$l0J30$N%$%s%G%C%/%9$KBP$7$F$O(B
395: 0 $B$rJV$9(B.
396: @item
1.2 noro 397: $B$h$j0lHLE*$JAG?t@8@.H!?t$H$7$F$O(B,
398: @code{pari(nextprime,@var{number})}
1.1 noro 399: $B$,$"$k(B.
1.2 noro 400: \E
401: \BEG
402: @item
403: The two functions, @code{prime()} and @code{lprime()}, returns
404: an element stored in the system table of prime numbers.
405: Here, @code{index} is a non-negative integer and be used as an index
406: for the prime tables.
407: The function @code{prime()} can return one of 1900 primes
408: up to 16381 indexed so that the smaller one has smaller
409: index. The function @code{lprime()} can return one of 999 primes which
410: are 8 digit sized and indexed so that the larger one has the smaller
411: index.
412: The two function always returns 0 for other indices.
413: @item
414: For more general function for prime generation, there is a @code{PARI}
415: function
416:
417: @code{pari(nextprime,@var{number})}.
418: \E
1.1 noro 419: @end itemize
420:
421: @example
422: [95] prime(0);
423: 2
424: [96] prime(1228);
425: 9973
426: [97] lprime(0);
427: 99999989
428: [98] lprime(999);
429: 0
430: @end example
431:
432: @table @t
1.2 noro 433: \JP @item $B;2>H(B
434: \EG @item References
1.1 noro 435: @fref{pari}.
436: @end table
437:
1.2 noro 438: \JP @node random,,, $B?t$N1i;;(B
439: \EG @node random,,, Numbers
1.1 noro 440: @subsection @code{random}
441: @findex random
442:
443: @table @t
1.5 takayama 444: @item random([@var{seed}])
1.2 noro 445: \JP :: $BMp?t$r@8@.$9$k(B.
1.1 noro 446: @end table
447:
448: @table @var
449: @item seed
1.2 noro 450: @itemx return
451: \JP $B<+A3?t(B
452: \EG non-negative integer
1.1 noro 453: @end table
454:
455: @itemize @bullet
1.2 noro 456: \BJP
1.1 noro 457: @item
458: $B:GBg(B 2^32-1 $B$NHsIi@0?t$NMp?t$r@8@.$9$k(B.
459: @item
460: 0 $B$G$J$$0z?t$,$"$k;~(B, $B$=$NCM$r(B seed $B$H$7$F@_Dj$7$F$+$i(B, $BMp?t$r@8@.$9$k(B.
461: @item
462: default $B$N(B seed $B$O8GDj$N$?$a(B, $B<o$r@_Dj$7$J$1$l$P(B, $B@8@.$5$l$kMp?t$N(B
463: $B7ONs$O5/F0Kh$K0lDj$G$"$k(B.
464: @item
465: $B>>K\bC(B-$B@>B<Bs;N$K$h$k(B Mersenne Twister (http://www.math.keio.ac.jp/matsumoto/mt.html) $B%"%k%4%j%:%`$N(B, $BH`$i<+?H$K$h$k<BAu$rMQ$$$F$$$k(B.
466: @item
467: $B<~4|$O(B 2^19937-1 $B$HHs>o$KD9$$(B.
468: @item
469: @code{mt_save} $B$K$h$j(B state $B$r%U%!%$%k$K(B save $B$G$-$k(B. $B$3$l$r(B @code{mt_load}
470: $B$GFI$_9~$`$3$H$K$h$j(B, $B0[$k(B Asir $B%;%C%7%g%s4V$G0l$D$NMp?t$N7ONs$rC)$k$3$H$,(B
471: $B$G$-$k(B.
1.2 noro 472: \E
473: \BEG
474: @item
475: Generates a random number which is a non-negative integer less than 2^32.
476: @item
477: If a non zero argument is specified, then after setting it as a random seed,
478: a random number is generated.
479: @item
480: As the default seed is fixed, the sequence of the random numbers is
481: always the same if a seed is not set.
482: @item
483: The algorithm is Mersenne Twister
484: (http://www.math.keio.ac.jp/matsumoto/mt.html) by M. Matsumoto and
485: T. Nishimura. The implementation is done also by themselves.
486: @item
487: The period of the random number sequence is 2^19937-1.
488: @item
489: One can save the state of the random number generator with @code{mt_save}.
490: By loading the state file with @code{mt_load},
491: one can trace a single random number sequence arcoss multiple sessions.
492: \E
1.1 noro 493: @end itemize
494:
495: @table @t
1.2 noro 496: \JP @item $B;2>H(B
497: \EG @item References
1.1 noro 498: @fref{lrandom}, @fref{mt_save mt_load}.
499: @end table
500:
1.2 noro 501: \JP @node lrandom,,, $B?t$N1i;;(B
502: \EG @node lrandom,,, Numbers
1.1 noro 503: @subsection @code{lrandom}
504: @findex lrandom
505:
506: @table @t
1.5 takayama 507: @item lrandom(@var{bit})
1.2 noro 508: \JP :: $BB?G\D9Mp?t$r@8@.$9$k(B.
509: \EG :: Generates a long random number.
1.1 noro 510: @end table
511:
512: @table @var
513: @item bit
514: @item return
1.2 noro 515: \JP $B<+A3?t(B
516: \EG integer
1.1 noro 517: @end table
518:
519: @itemize @bullet
1.2 noro 520: \BJP
1.1 noro 521: @item
522: $B9b!9(B @var{bit} $B$NHsIi@0?t$NMp?t$r@8@.$9$k(B.
523: @item
524: @code{random} $B$rJ#?t2s8F$S=P$7$F7k9g$7(B, $B;XDj$N(B bit $BD9$K%^%9%/$7$F$$$k(B.
1.2 noro 525: \E
526: \BEG
527: @item
528: Generates a non-negative integer of at most @var{bit} bits.
529: @item
530: The result is a concatination of outputs of @code{random}.
531: \E
1.1 noro 532: @end itemize
533:
534: @table @t
1.2 noro 535: \JP @item $B;2>H(B
536: \EG @item References
1.1 noro 537: @fref{random}, @fref{mt_save mt_load}.
538: @end table
539:
1.2 noro 540: \JP @node mt_save mt_load,,, $B?t$N1i;;(B
541: \EG @node mt_save mt_load,,, Numbers
1.1 noro 542: @subsection @code{mt_save}, @code{mt_load}
543: @findex mt_save
544: @findex mt_load
545:
546: @table @t
547: @item mt_save(@var{fname})
1.2 noro 548: \JP :: $BMp?t@8@.4o$N8=:_$N>uBV$r%U%!%$%k$K%;!<%V$9$k(B.
549: \EG :: Saves the state of the random number generator.
1.1 noro 550: @item mt_load(@var{fname})
1.2 noro 551: \JP :: $B%U%!%$%k$K%;!<%V$5$l$?Mp?t@8@.4o$N>uBV$r%m!<%I$9$k(B.
552: \EG :: Loads a saved state of the random number generator.
1.1 noro 553: @end table
554:
555: @table @var
556: @item return
1.2 noro 557: \JP 0 $B$^$?$O(B 1
558: \EG 0 or 1
1.1 noro 559: @item fname
1.2 noro 560: \JP $BJ8;zNs(B
561: \EG string
1.1 noro 562: @end table
563:
564: @itemize @bullet
1.2 noro 565: \BJP
566: @item
567: $B$"$k>uBV$r%;!<%V$7(B, $B$=$N>uBV$r%m!<%I$9$k$3$H$G(B,
1.1 noro 568: $B0l$D$N5?;wMp?t7ONs$r(B, $B?75,$N(B Asir $B%;%C%7%g%s$GB3$1$F$?$I$k$3$H$,(B
569: $B$G$-$k(B.
1.2 noro 570: \E
571: \BEG
572: @item
573: One can save the state of the random number generator with @code{mt_save}.
574: By loading the state file with @code{mt_load},
575: one can trace a single random number sequence arcoss multiple
576: @b{Asir} sessions.
577: \E
1.1 noro 578: @end itemize
579:
580: @example
581: [340] random();
582: 3510405877
583: [341] mt_save("/tmp/mt_state");
584: 1
585: [342] random();
586: 4290933890
587: [343] quit;
588: % asir
589: This is Asir, Version 991108.
590: Copyright (C) FUJITSU LABORATORIES LIMITED.
591: 3 March 1994. All rights reserved.
592: [340] mt_load("/tmp/mt_state");
593: 1
594: [341] random();
595: 4290933890
596: @end example
597:
598: @table @t
1.2 noro 599: \JP @item $B;2>H(B
600: \EG @item References
1.1 noro 601: @fref{random}, @fref{lrandom}.
602: @end table
603:
1.2 noro 604: \JP @node nm dn,,, $B?t$N1i;;(B
605: \EG @node nm dn,,, Numbers
1.1 noro 606: @subsection @code{nm}, @code{dn}
607: @findex nm
608: @findex dn
609:
610: @table @t
611: @item nm(@var{rat})
1.2 noro 612: \JP :: @var{rat} $B$NJ,;R(B.
613: \EG :: Numerator of @var{rat}.
1.1 noro 614: @item dn(@var{rat})
1.2 noro 615: \JP :: @var{rat} $B$NJ,Jl(B.
616: \EG :: Denominator of @var{rat}.
1.1 noro 617: @end table
618:
619: @table @var
620: @item return
1.2 noro 621: \JP $B@0?t$^$?$OB?9`<0(B
622: \EG integer or polynomial
1.1 noro 623: @item rat
1.2 noro 624: \JP $BM-M}?t$^$?$OM-M}<0(B
625: \EG rational number or rational expression
1.1 noro 626: @end table
627:
628: @itemize @bullet
1.2 noro 629: \BJP
1.1 noro 630: @item
631: $BM?$($i$l$?M-M}?t$^$?M-M}<0$NJ,;R5Z$SJ,Jl$rJV$9(B.
632: @item
633: $BM-M}?t$N>l9g(B, $BJ,Jl$O>o$K@5$G(B, $BId9f$OJ,;R$,;}$D(B.
634: @item
635: $BM-M}<0$N>l9g(B, $BC1$KJ,Jl(B, $BJ,;R$r<h$j=P$9$@$1$G$"$k(B.
636: $BM-M}<0$KBP$7$F$O(B, $BLsJ,$O<+F0E*$K$O9T$o$l$J$$(B. @code{red()}
637: $B$rL@<(E*$K8F$S=P$9I,MW$,$"$k(B.
1.2 noro 638: \E
639: \BEG
640: @item
641: Numerator and denominator of a given rational expression.
642: @item
643: For a rational number, they return its numerator and denominator,
644: respectively. For a rational expression whose numerator and denominator
645: may contain rational numbers, they do not separate those rational
646: coefficients to numerators and denominators.
647: @item
648: For a rational number, the denominator is always kept positive, and
649: the sign is contained in the numerator.
650: @item
651: @b{Risa/Asir} does not cancel the common divisors unless otherwise explicitly
652: specified by the user.
653: Therefore, @code{nm()} and @code{dn()} return the numerator and the
654: denominator as it is, respectively.
655: \E
1.1 noro 656: @end itemize
657:
658: @example
659: [2] [nm(-43/8),dn(-43/8)];
660: [-43,8]
661: [3] dn((x*z)/(x*y));
662: y*x
663: [3] dn(red((x*z)/(x*y)));
664: y
665: @end example
666:
667: @table @t
1.2 noro 668: \JP @item $B;2>H(B
669: \EG @item References
1.1 noro 670: @fref{red}.
671: @end table
672:
1.2 noro 673: \JP @node conj real imag,,, $B?t$N1i;;(B
674: \EG @node conj real imag,,, Numbers
1.1 noro 675: @subsection @code{conj}, @code{real}, @code{imag}
676: @findex conj
677:
678: @table @t
679: @item real(@var{comp})
1.2 noro 680: \JP :: @var{comp} $B$N<B?tItJ,(B.
681: \EG :: Real part of @var{comp}.
1.1 noro 682: @item imag(@var{comp})
1.2 noro 683: \JP :: @var{comp} $B$N5u?tItJ,(B.
684: \EG :: Imaginary part of @var{comp}.
1.1 noro 685: @item conj(@var{comp})
1.2 noro 686: \JP :: @var{comp} $B$N6&LrJ#AG?t(B.
687: \EG :: Complex conjugate of @var{comp}.
1.1 noro 688: @end table
689:
690: @table @var
691: @item return comp
1.2 noro 692: \JP $BJ#AG?t(B
693: \EG complex number
1.1 noro 694: @end table
695:
696: @itemize @bullet
1.2 noro 697: \BJP
1.1 noro 698: @item
699: $BJ#AG?t$KBP$7(B, $B<BIt(B, $B5uIt(B, $B6&Lr$r5a$a$k(B.
700: @item
701: $B$3$l$i$O(B, $BB?9`<0$KBP$7$F$bF/$/(B.
1.2 noro 702: \E
703: \BEG
704: @item
705: Basic operations for complex numbers.
706: @item
707: These functions works also for polynomials with complex coefficients.
708: \E
1.1 noro 709: @end itemize
710:
711: @example
712: [111] A=(2+@@i)^3;
713: (2+11*@@i)
714: [112] [real(A),imag(A),conj(A)];
715: [2,11,(2-11*@@i)]
716: @end example
717:
1.4 noro 718: \JP @node eval deval ,,, $B?t$N1i;;(B
719: \EG @node eval deval,,, Numbers
720: @subsection @code{eval}, @code{deval}
1.1 noro 721: @findex eval
1.4 noro 722: @findex deval
1.1 noro 723: @cindex PARI
724:
725: @table @t
726: @item eval(@var{obj}[,@var{prec}])
1.4 noro 727: @item deval(@var{obj})
1.2 noro 728: \JP :: @var{obj} $B$NCM$NI>2A(B.
729: \EG :: Evaluate @var{obj} numerically.
1.1 noro 730: @end table
731:
732: @table @var
733: @item return
1.2 noro 734: \JP $B?t$"$k$$$O<0(B
735: \EG number or expression
1.1 noro 736: @item obj
1.2 noro 737: \JP $B0lHL$N<0(B
738: \EG general expression
1.1 noro 739: @item prec
1.2 noro 740: \JP $B@0?t(B
741: \EG integer
1.1 noro 742: @end table
743:
744: @itemize @bullet
1.2 noro 745: \BJP
1.1 noro 746: @item
747: @var{obj} $B$K4^$^$l$kH!?t$NCM$r2DG=$J8B$jI>2A$9$k(B.
748: @item
1.4 noro 749: @code{deval} $B$OG\@:EYIbF0>.?t$r7k2L$H$7$F(B
750: @code{eval} $B$N>l9g(B, $BM-M}?t$O$=$N$^$^;D$k(B.
1.1 noro 751: @item
1.11 noro 752: @code{eval} $B$K$*$$$F$O(B, $B7W;;$O(B @b{MPFR} $B%i%$%V%i%j$,9T$&(B.
1.4 noro 753: @code{deval} $B$K$*$$$F$O(B, $B7W;;$O(B C $B?t3X%i%$%V%i%j$N4X?t$rMQ$$$F9T$&(B.
754: @item
755: @code{deval} $B$OJ#AG?t$O07$($J$$(B.
756: @item
757: @code{eval} $B$K$*$$$F$O(B,
1.1 noro 758: @var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B.
759: @var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B.
1.12 ! noro 760: (@xref{setbprec setprec}.)
1.1 noro 761: @item
762: @table @t
763: @item $B07$($kH!?t$O(B, $B<!$NDL$j(B.
764: @code{sin}, @code{cos}, @code{tan},
765:
766: @code{asin}, @code{acos}, @code{atan},
767:
768: @code{sinh}, @code{cosh}, @code{tanh},
769:
770: @code{asinh}, @code{acosh}, @code{atanh},
771:
772: @code{exp}, @code{log}, @code{pow(a,b) (a^b)}
773: @end table
774: @item
1.4 noro 775: $B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B. $B$?$@$7(B @code{@@i} $B$r07$($k$N$O(B
776: @code{eval}, @code{deval} $B$N$_$G$"$k(B.
1.1 noro 777: @table @t
778: @item @@i
779: $B5u?tC10L(B
780: @item @@pi
781: $B1_<~N((B
782: @item @@e
783: $B<+A3BP?t$NDl(B
784: @end table
1.2 noro 785: \E
786: \BEG
787: @item
788: Evaluates the value of the functions contained in @var{obj} as far as
789: possible.
790: @item
1.4 noro 791: @code{deval} returns
792: double float. Rational numbers remain unchanged in results from @code{eval}.
793: @item
794: In @code{eval} the computation is done
1.11 noro 795: by @b{MPFR} library. In @code{deval} the computation is
1.4 noro 796: done by the C math library.
797: @item
798: @code{deval} cannot handle complex numbers.
1.2 noro 799: @item
800: When @var{prec} is specified, computation will be performed with a
801: precision of about @var{prec}-digits.
802: If @var{prec} is not specified, computation is performed with the
1.12 ! noro 803: precision set currently. (@xref{setbprec setprec}.)
1.2 noro 804: @item
805: Currently available numerical functions are listed below.
806:
807: @table @t
808: @code{sin}, @code{cos}, @code{tan},
809:
810: @code{asin}, @code{acos}, @code{atan},
811:
812: @code{sinh}, @code{cosh}, @code{tanh},
813: @code{asinh}, @code{acosh}, @code{atanh},
814:
815: @code{exp}, @code{log}, @code{pow(a,b) (a^b)}
816: @end table
817: @item
1.4 noro 818: Symbols for special values are as the followings. Note that
819: @code{@@i} cannot be handled by @code{deval}.
1.2 noro 820: @table @t
821: @item @@i
822: unit of imaginary number
823: @item @@pi
824: the number pi,
825: the ratio of circumference to diameter
826: @item @@e
827: Napier's number (@t{exp}(1))
828: @end table
829: \E
1.1 noro 830: @end itemize
831:
832: @example
833: [118] eval(exp(@@pi*@@i));
834: -1.0000000000000000000000000000
835: [119] eval(2^(1/2));
836: 1.414213562373095048763788073031
837: [120] eval(sin(@@pi/3));
838: 0.86602540378443864674620506632
839: [121] eval(sin(@@pi/3)-3^(1/2)/2,50);
840: -2.78791084448179148471 E-58
1.4 noro 841: [122] eval(1/2);
842: 1/2
843: [123] deval(sin(1)^2+cos(1)^2);
844: 1
1.1 noro 845: @end example
846:
847: @table @t
1.2 noro 848: \JP @item $B;2>H(B
849: \EG @item References
1.12 ! noro 850: @fref{ctrl}, @fref{setbprec setprec}.
1.1 noro 851: @end table
852:
1.2 noro 853: \JP @node pari,,, $B?t$N1i;;(B
854: \EG @node pari,,, Numbers
1.1 noro 855: @subsection @code{pari}
856: @findex pari
857: @cindex PARI
858:
859: @table @t
860: @item pari(@var{func},@var{arg},@var{prec})
1.2 noro 861: \JP :: @b{PARI} $B$NH!?t(B @var{func} $B$r8F$S=P$9(B.
862: \EG :: Call @b{PARI} function @var{func}.
1.1 noro 863: @end table
864:
865: @table @var
866: @item return
1.2 noro 867: \JP @var{func} $BKh$K0[$J$k(B.
868: \EG Depends on @var{func}.
1.1 noro 869: @item func
1.2 noro 870: \JP @b{PARI} $B$NH!?tL>(B
871: \EG Function name of @b{PARI}.
1.1 noro 872: @item arg
1.2 noro 873: \JP @var{func} $B$N0z?t(B
874: \EG Arguments of @var{func}.
1.1 noro 875: @item prec
1.2 noro 876: \JP $B@0?t(B
877: \EG integer
1.1 noro 878: @end table
879:
880: @itemize @bullet
1.2 noro 881: \BJP
1.1 noro 882: @item
883: @b{PARI} $B$NH!?t$r8F$S=P$9(B.
884:
885: @item
886: @b{PARI} @code{[Batut et al.]} $B$O(B Bordeaux $BBg3X$G3+H/$5$l%U(B
887: $B%j!<%=%U%H%&%'%"$H$7$F8x3+$5$l$F$$$k(B. @b{PARI} $B$O?t<0=hM}E*$J5!G=$rM-(B
888: $B$7$F$O$$$k$,(B, $B<g$J%?!<%2%C%H$O@0?tO@$K4XO"$7$??t(B (@b{bignum},
889: @b{bigfloat}) $B$N1i;;$G(B, $B;MB'1i;;$K8B$i$:(B@b{bigfloat} $B$K$h$k$5$^$6$^$J(B
890: $BH!?tCM$NI>2A$r9bB.$K9T$&$3$H$,$G$-$k(B. @b{PARI} $B$OB>$N%W%m%0%i%`$+$i(B
891: $B%5%V%k!<%A%s%i%$%V%i%j$H$7$FMQ$$$k$3$H$,$G$-(B, $B$^$?(B, @samp{gp} $B$H$$$&(B
892: @b{PARI}$B%i%$%V%i%j$N%$%s%?%U%'!<%9$K$h$j(B UNIX $B$N%"%W%j%1!<%7%g%s$H$7$F(B
1.11 noro 893: $BMxMQ$9$k$3$H$b$G$-$k(B.
1.1 noro 894: @item
895: $B:G8e$N0z?t(B @var{prec} $B$G7W;;@:EY$r;XDj$G$-$k(B.
896: @var{prec} $B$r>JN,$7$?>l9g(B @code{setprec()} $B$G;XDj$7$?@:EY$H$J$k(B.
897: @item
898: $B8=;~E@$G<B9T$G$-$k(B @b{PARI} $B$NH!?t$O<!$NDL$j$G$"$k(B. $B$$$:$l$b(B
899: 1 $B0z?t$G(B @b{Asir} $B$,BP1~$G$-$k7?$N0z?t$r$H$kH!?t$G$"$k(B.
900: $B$J$*3F!9$N5!G=$K$D$$$F$O(B @b{PARI} $B$N%^%K%e%"%k$r;2>H$N$3$H(B.
1.2 noro 901: \E
902: \BEG
903: @item
904: This command connects @b{Asir} to @b{PARI} system so that several
905: functions of @b{PARI} can be conveniently used from @b{Risa/Asir}.
906: @item
907: @b{PARI} @code{[Batut et al.]} is developed at Bordeaux University, and
908: distributed as a free software. Though it has a certain facility to computer
909: algebra, its major target is the operation of numbers (@b{bignum},
910: @b{bigfloat}) related to the number theory. It facilitates various
911: function evaluations as well as arithmetic operations at a remarkable
912: speed. It can also be used from other external programs as a library.
913: It provides a language interface named @samp{gp} to its library, which
914: enables a user to use @b{PARI} as a calculator which runs on UNIX.
915: @item
916: The last argument (optional) @var{int} specifies the precision in digits
917: for bigfloat operation.
918: If the precision is not explicitly specified, operation will be performed
919: with the precision set by @code{setprec()}.
920: @item
921: Currently available functions of @b{PARI} system are as follows.
922: Note these are only a part of functions in @b{PARI} system.
923: For details of individual functions, refer to the @b{PARI} manual.
924: (Some of them can be seen in the following example.)
925: \E
1.1 noro 926:
927: @code{abs},
928: @code{adj},
929: @code{arg},
930: @code{bigomega},
931: @code{binary},
932: @code{ceil},
933: @code{centerlift},
934: @code{cf},
935: @code{classno},
936: @code{classno2},
937: @code{conj},
938: @code{content},
939: @code{denom},
940: @code{det},
941: @code{det2},
942: @code{detr},
943: @code{dilog},
944: @code{disc},
945: @code{discf},
946: @code{divisors},
947: @code{eigen},
948: @code{eintg1},
949: @code{erfc},
950: @code{eta},
951: @code{floor},
952: @code{frac},
953: @code{galois},
954: @code{galoisconj},
955: @code{gamh},
956: @code{gamma},
957: @code{hclassno},
958: @code{hermite},
959: @code{hess},
960: @code{imag},
961: @code{image},
962: @code{image2},
963: @code{indexrank},
964: @code{indsort},
965: @code{initalg},
966: @code{isfund},
967: @code{isprime},
968: @code{ispsp},
969: @code{isqrt},
970: @code{issqfree},
971: @code{issquare},
972: @code{jacobi},
973: @code{jell},
974: @code{ker},
975: @code{keri},
976: @code{kerint},
977: @code{kerintg1},
978: @code{kerint2},
979: @code{kerr},
980: @code{length},
981: @code{lexsort},
982: @code{lift},
983: @code{lindep},
984: @code{lll},
985: @code{lllg1},
986: @code{lllgen},
987: @code{lllgram},
988: @code{lllgramg1},
989: @code{lllgramgen},
990: @code{lllgramint},
991: @code{lllgramkerim},
992: @iftex
993: @break
994: @end iftex
995: @code{lllgramkerimgen},
996: @code{lllint},
997: @code{lllkerim},
998: @code{lllkerimgen},
999: @code{lllrat},
1000: @code{lngamma},
1001: @code{logagm},
1002: @code{mat},
1003: @code{matrixqz2},
1004: @code{matrixqz3},
1005: @code{matsize},
1006: @code{modreverse},
1007: @code{mu},
1008: @code{nextprime},
1009: @code{norm},
1010: @code{norml2},
1011: @code{numdiv},
1012: @code{numer},
1013: @code{omega},
1014: @code{order},
1015: @code{ordred},
1016: @code{phi},
1017: @code{pnqn},
1018: @code{polred},
1019: @code{polred2},
1020: @code{primroot},
1021: @code{psi},
1022: @code{quadgen},
1023: @code{quadpoly},
1024: @code{real},
1025: @code{recip},
1026: @code{redcomp},
1027: @code{redreal},
1028: @code{regula},
1029: @code{reorder},
1030: @code{reverse},
1031: @code{rhoreal},
1032: @code{roots},
1033: @code{rootslong},
1034: @code{round},
1035: @code{sigma},
1036: @code{signat},
1037: @code{simplify},
1038: @code{smalldiscf},
1039: @code{smallfact},
1040: @code{smallpolred},
1041: @code{smallpolred2},
1042: @code{smith},
1043: @code{smith2},
1044: @code{sort},
1045: @code{sqr},
1046: @code{sqred},
1047: @code{sqrt},
1048: @code{supplement},
1049: @code{trace},
1050: @code{trans},
1051: @code{trunc},
1052: @code{type},
1053: @code{unit},
1054: @code{vec},
1055: @code{wf},
1056: @code{wf2},
1057: @code{zeta}
1058:
1.2 noro 1059: \BJP
1.1 noro 1060: @item
1.11 noro 1061: @b{Asir} $B$GMQ$$$F$$$k$N$O(B @b{PARI} $B$N$[$s$N0lIt$N5!G=$G$"$k(B.
1.2 noro 1062: \E
1063: \BEG
1064: @item
1065: @b{Asir} currently uses only a very small subset of @b{PARI}.
1066: \E
1.1 noro 1067: @end itemize
1068:
1069: @example
1.2 noro 1070: \JP /* $B9TNs$N8GM-%Y%/%H%k$r5a$a$k(B. */
1071: \EG /* Eigen vectors of a numerical matrix */
1.1 noro 1072: [0] pari(eigen,newmat(2,2,[[1,1],[1,2]]));
1073: [ -1.61803398874989484819771921990 0.61803398874989484826 ]
1074: [ 1 1 ]
1.2 noro 1075: \JP /* 1 $BJQ?tB?9`<0$N:,$r5a$a$k(B. */
1076: \EG /* Roots of a polynomial */
1.1 noro 1077: [1] pari(roots,t^2-2);
1078: [ -1.41421356237309504876 1.41421356237309504876 ]
1079: @end example
1080:
1081: @table @t
1.2 noro 1082: \JP @item $B;2>H(B
1083: \EG @item References
1.12 ! noro 1084: @fref{setbprec setprec}.
1.1 noro 1085: @end table
1086:
1.11 noro 1087: \JP @node setbprec setprec,,, $B?t$N1i;;(B
1088: \EG @node setbprec setprec,,, Numbers
1089: @subsection @code{setbprec}, @code{setprec}
1090: @findex setbprec
1.1 noro 1091: @findex setprec
1092:
1093: @table @t
1.11 noro 1094: @item setbprec([@var{n}])
1095: @itemx setprec([@var{n}])
1096: \JP :: @b{setbprec}, @b{setprec} $B$O(B @b{bigfloat} $B$N@:EY$r$=$l$>$l(B 2 $B?J(B, 10$B?J(B @var{n} $B7e$K@_Dj$9$k(B.
1097: \EG :: @b{setbprec}, @b{setprec} set the precision for @b{bigfloat} operations to @var{n} bits, @var{n} digits respectively.
1.1 noro 1098: @end table
1099:
1100: @table @var
1101: @item return
1.2 noro 1102: \JP $B@0?t(B
1103: \EG integer
1.1 noro 1104: @item n
1.2 noro 1105: \JP $B@0?t(B
1106: \EG integer
1.1 noro 1107: @end table
1108:
1109: @itemize @bullet
1.2 noro 1110: \BJP
1.1 noro 1111: @item
1112: $B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B.
1113: $B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B.
1114: @item
1.11 noro 1115: @b{bigfloat} $B$N7W;;$O(B @b{MPFR} $B%i%$%V%i%j$K$h$C$F9T$o$l$k(B.
1.1 noro 1116: @item
1117: @b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B.
1118: @b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B.
1119: @item
1120: $B@_Dj$G$-$k7e?t$K>e8B$O$J$$$,(B, $B;XDj$7$?7e?t$K@_Dj$5$l$k$H$O(B
1121: $B8B$i$J$$(B. $BBg$-$a$NCM$r@_Dj$9$k$N$,0BA4$G$"$k(B.
1.2 noro 1122: \E
1123: \BEG
1124: @item
1.11 noro 1125: When an argument @var{n} is given, these functions
1126: set the precision for @b{bigfloat} operations to @var{n} bits or @var{n} digits.
1127: The return value is always the previous precision regardless of
1.2 noro 1128: the existence of an argument.
1129:
1130: @item
1.11 noro 1131: @b{Bigfloat} operations are done by @b{MPFR} library.
1.2 noro 1132: @item
1133: This is effective for computations in @b{bigfloat}.
1134: Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.'
1135: @item
1136: There is no upper limit for precision digits.
1137: It sets the precision to some digits around the specified precision.
1138: Therefore, it is safe to specify a larger value.
1139: \E
1.1 noro 1140: @end itemize
1141:
1142: @example
1143: [1] setprec();
1.11 noro 1144: 15
1145: [2] setprec(100);
1146: 15
1147: [3] setprec(100);
1148: 99
1149: [4] setbprec();
1150: 332
1151: @end example
1152:
1153: @table @t
1154: \JP @item $B;2>H(B
1155: @fref{ctrl}, @fref{eval deval}.
1156: @end table
1157:
1158: \JP @node setround,,, $B?t$N1i;;(B
1159: \EG @node setround,,, Numbers
1160: @subsection @code{setround}
1161: @findex setround
1162:
1163: @table @t
1164: @item setround([@var{mode}])
1165: \JP :: @b{bigfloat} $B$N4]$a%b!<%I$r(B @var{mode} $B$K@_Dj$9$k(B.
1166: \EG :: Sets the rounding mode @var{mode}.
1167: @end table
1168:
1169: @table @var
1170: @item return
1171: \JP $B@0?t(B
1172: \EG integer
1173: @item mode
1174: \JP $B@0?t(B
1175: \EG integer
1176: @end table
1177:
1178: @itemize @bullet
1179: \BJP
1180: @item
1181: $B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N4]$a%b!<%I$r(B @var{mode} $B$K@_Dj$9$k(B.
1182: $B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B.
1183: $B4]$a%b!<%I$N0UL#$O<!$N$H$*$j(B.
1184: @table @code
1185: @item 0
1186: Round to nearest
1187: @item 1
1188: Round toward 0
1189: @item 2
1190: Round toward +infinity
1191: @item 3
1192: Round toward -infinity
1193: @end table
1194: @item
1195: @b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B.
1196: @b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B.
1197: \E
1198: \BEG
1199: @item
1200: When an argument @var{mode} is given, these functions
1201: set the rounding mode for @b{bigfloat} operations to @var{mode}.
1202: The return value is always the previous rounding mode regardless of
1203: the existence of an argument.
1204: The meanings of rounding modes are as follows
1205: @table @code
1206: @item 0
1207: Round to nearest
1208: @item 1
1209: Round toward 0
1210: @item 2
1211: Round toward +infinity
1212: @item 3
1213: Round toward -infinity
1214: @end table
1215:
1216: @item
1217: This is effective for computations in @b{bigfloat}.
1218: Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.'
1219: \E
1220: @end itemize
1221:
1222: @example
1223: [1] setprec();
1224: 15
1.1 noro 1225: [2] setprec(100);
1.11 noro 1226: 15
1.1 noro 1227: [3] setprec(100);
1.11 noro 1228: 99
1229: [4] setbprec();
1230: 332
1.1 noro 1231: @end example
1232:
1233: @table @t
1.2 noro 1234: \JP @item $B;2>H(B
1.11 noro 1235: @fref{ctrl}, @fref{eval deval}.
1.1 noro 1236: @end table
1237:
1.11 noro 1238:
1.2 noro 1239: \JP @node setmod,,, $B?t$N1i;;(B
1240: \EG @node setmod,,, Numbers
1.1 noro 1241: @subsection @code{setmod}
1242: @findex setmod
1243:
1244: @table @t
1245: @item setmod([@var{p}])
1.2 noro 1246: \JP :: $BM-8BBN$r(B GF(@var{p}) $B$K@_Dj$9$k(B.
1247: \EG :: Sets the ground field to GF(@var{p}).
1.1 noro 1248: @end table
1249:
1250: @table @var
1251: @item return
1.2 noro 1252: \JP $B@0?t(B
1253: \EG integer
1.1 noro 1254: @item n
1.2 noro 1255: \JP 2^27 $BL$K~$NAG?t(B
1256: \EG prime less than 2^27
1.1 noro 1257: @end table
1258:
1259: @itemize @bullet
1.2 noro 1260: \BJP
1.1 noro 1261: @item
1262: $BM-8BBN$r(B GF(@var{p}) $B$K@_Dj$9$k(B. $B@_DjCM$rJV$9(B.
1263: @item
1264: $BM-8BBN$N85$N7?$r;}$D?t$O(B, $B$=$l<+?H$O$I$NM-8BBN$KB0$9$k$+$N>pJs$r;}$?$:(B,
1265: $B8=:_@_Dj$5$l$F$$$kAG?t(B @var{p} $B$K$h$j(B GF(@var{p}) $B>e$G$N1i;;$,E,MQ$5$l$k(B.
1.2 noro 1266: @item
1267: $B0L?t$NBg$-$JM-8BBN$K4X$7$F$O(B @pxref{$BM-8BBN$K4X$9$k1i;;(B}.
1268: \E
1269: \BEG
1270: @item
1271: Sets the ground field to GF(@var{p}) and returns the value @var{p}.
1272: @item
1273: A member of a finite field does not have any information
1274: about the field and the arithmetic operations over GF(@var{p}) are applied
1275: with @var{p} set at the time.
1276: @item
1277: As for large finite fields, @pxref{Finite fields}.
1278: \E
1.1 noro 1279: @end itemize
1280:
1281: @example
1282: [0] A=dp_mod(dp_ptod(2*x,[x]),3,[]);
1283: (2)*<<1>>
1284: [1] A+A;
1285: addmi : invalid modulus
1286: return to toplevel
1287: [1] setmod(3);
1288: 3
1289: [2] A+A;
1290: (1)*<<1>>
1291: @end example
1292:
1293: @table @t
1.2 noro 1294: \JP @item $B;2>H(B
1295: \EG @item References
1296: \JP @fref{dp_mod dp_rat}, @fref{$B?t$N7?(B}.
1297: \EG @fref{dp_mod dp_rat}, @fref{Types of numbers}.
1.1 noro 1298: @end table
1299:
1.3 noro 1300: \JP @node ntoint32 int32ton,,, $B?t$N1i;;(B
1301: \EG @node ntoint32 int32ton,,, Numbers
1302: @subsection @code{ntoint32}, @code{int32ton}
1303: @findex ntoint32
1304: @findex int32ton
1305:
1306: @table @t
1307: @item ntoint32(@var{n})
1308: @itemx int32ton(@var{int32})
1309: \JP :: $BHsIi@0?t$HId9f$J$7(B 32bit $B@0?t$N4V$N7?JQ49(B.
1310: \EG :: Type-conversion between a non-negative integer and an unsigned 32bit integer.
1311: @end table
1312:
1313: @table @var
1314: @item return
1315: \JP $BId9f$J$7(B 32bit $B@0?t$^$?$OHsIi@0?t(B
1316: \EG unsigned 32bit integer or non-negative integer
1317: @item n
1318: \JP 2^32 $BL$K~$NHsIi@0?t(B
1319: \EG non-negative interger less than 2^32
1320: @item int32
1321: \JP $BId9f$J$7(B 32bit $B@0?t(B
1322: \EG unsigned 32bit integer
1323: @end table
1324:
1325: @itemize @bullet
1326: \BJP
1327: @item $BHsIi@0?t(B ($B<1JL;R(B 1) $B$NId9f$J$7(B 32bit $B@0?t(B ($B<1JL;R(B 10) $B$X$NJQ49(B,
1328: $B$^$?$O$=$N5UJQ49$r9T$&(B.
1329: @item 32bit $B@0?t$O(B @b{OpenXM} $B$N4pK\9=@.MWAG$G$"$j(B, $B@0?t$r$=$N7?$GAw?.(B
1330: $B$9$kI,MW$,$"$k>l9g$KMQ$$$k(B.
1331: \E
1332: \BEG
1333: @item These functions do conversions between non-negative
1334: integers (the type id 1) and unsigned 32bit integers (the type id 10).
1335: @item An unsigned 32bit integer is a fundamental construct of @b{OpenXM}
1336: and one often has to send an integer to a server as an unsigned 32bit
1337: integer. These functions are used in such a case.
1338: \E
1339: @end itemize
1340:
1341: @table @t
1342: \JP @item $B;2>H(B
1343: \EG @item References
1344: \JP @fref{$BJ,;67W;;(B}, @fref{$B?t$N7?(B}.
1345: \EG @fref{Distributed computation}, @fref{Types of numbers}.
1346: @end table
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