Annotation of OpenXM/src/asir-doc/parts/builtin/num.texi, Revision 1.1.1.1
1.1 noro 1: @node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B
2: @section $B?t$N1i;;(B
3:
4: @menu
5: * idiv irem::
6: * fac::
7: * igcd igcdcntl::
8: * ilcm::
9: * inv::
10: * prime lprime::
11: * random::
12: * mt_save mt_load::
13: * nm dn::
14: * conj real imag::
15: * eval::
16: * pari::
17: * setprec::
18: * setmod::
19: * lrandom::
20: @end menu
21:
22: @node idiv irem,,, $B?t$N1i;;(B
23: @subsection @code{idiv}, @code{irem}
24: @findex idiv
25: @findex irem
26:
27: @table @t
28: @item idiv(@var{i1},@var{i2})
29: :: $B@0?t=|;;$K$h$k>&(B.
30: @item irem(@var{i1},@var{i2})
31: :: $B@0?t=|;;$K$h$k>jM>(B.
32: @end table
33:
34: @table @var
35: @item return
36: $B@0?t(B
37: @item i1,i2
38: $B@0?t(B
39: @end table
40:
41: @itemize @bullet
42: @item
43: @var{i1} $B$N(B @var{i2} $B$K$h$k@0?t=|;;$K$h$k>&(B, $B>jM>$r5a$a$k(B.
44: @item
45: @var{i2} $B$O(B 0 $B$G$"$C$F$O$J$i$J$$(B.
46: @item
47: $BHo=|?t$,Ii$N>l9g(B, $B@dBPCM$KBP$9$kCM$K%^%$%J%9$r$D$1$?CM$rJV$9(B.
48: @item
49: @var{i1} @code{%} @var{i2} $B$O(B, $B7k2L$,@5$K@55,2=$5$l$k$3$H$r=|$1$P(B
50: @code{irem()} $B$NBe$o$j$KMQ$$$k$3$H$,$G$-$k(B.
51: @item
52: $BB?9`<0$N>l9g$O(B @code{sdiv}, @code{srem} $B$rMQ$$$k(B.
53: @end itemize
54:
55: @example
56: [0] idiv(100,7);
57: 14
58: [0] idiv(-100,7);
59: -14
60: [1] irem(100,7);
61: 2
62: [1] irem(-100,7);
63: -2
64: @end example
65:
66: @table @t
67: @item $B;2>H(B
68: @fref{sdiv sdivm srem sremm sqr sqrm}, @fref{%}.
69: @end table
70:
71: @node fac,,, $B?t$N1i;;(B
72: @subsection @code{fac}
73: @findex fac
74:
75: @table @t
76: @item fac(@var{i})
77: :: @var{i} $B$N3,>h(B.
78: @end table
79:
80: @table @var
81: @item return
82: $B@0?t(B
83: @item i
84: $B@0?t(B
85: @end table
86:
87: @itemize @bullet
88: @item
89: @var{i} $B$N3,>h$r7W;;$9$k(B.
90: @item
91: @var{i} $B$,Ii$N>l9g$O(B 0 $B$rJV$9(B.
92: @end itemize
93:
94: @example
95: [0] fac(50);
96: 30414093201713378043612608166064768844377641568960512000000000000
97: @end example
98:
99: @node igcd igcdcntl,,, $B?t$N1i;;(B
100: @subsection @code{igcd},@code{igcdcntl}
101: @findex igcd
102: @findex igcdcntl
103:
104: @table @t
105: @item igcd(@var{i1},@var{i2})
106: :: $B@0?t$N(B GCD ($B:GBg8xLs?t(B)
107: @item igcdcntl([@var{i}])
108: :: $B@0?t(B GCD$B$N%"%k%4%j%:%`A*Br(B
109: @end table
110:
111: @table @var
112: @item return
113: $B@0?t(B
114: @item i1,i2,i
115: $B@0?t(B
116: @end table
117:
118: @itemize @bullet
119: @item
120: @code{igcd} $B$O(B @var{i1} $B$H(B @var{i2} $B$N(B GCD $B$r5a$a$k(B.
121: @item
122: $B0z?t$,@0?t$G$J$$>l9g$O(B, $B%(%i!<$^$?$OL50UL#$J7k2L$rJV$9(B.
123: @item
124: $BB?9`<0$N>l9g$O(B, @code{gcd}, @code{gcdz} $B$rMQ$$$k(B.
125: @item
126: $B@0?t(B GCD $B$K$O$5$^$6$^$JJ}K!$,$"$j(B, @code{igcdcntl} $B$G@_Dj$G$-$k(B.
127:
128: @table @code
129: @item 0
130: Euclid $B8_=|K!(B (default)
131: @item 1
132: binary GCD
133: @item 2
134: bmod GCD
135: @item 3
136: accelerated integer GCD
137: @end table
138: 2, 3 $B$O(B K. Weber, ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122 $B$K$h$k(B.
139:
140: $B$*$*$`$M(B 3 $B$,9bB.$@$,(B, $BNc30$b$"$k(B.
141: @end itemize
142:
143: @example
144: [0] A=lrandom(10^4)$
145: [1] B=lrandom(10^4)$
146: [2] C=lrandom(10^4)$
147: [3] D=A*C$
148: [4] E=A*B$
149: [5] cputime(1)$
150: [6] igcd(D,E)$
151: 0.6sec + gc : 1.93sec(2.531sec)
152: [7] igcdcntl(1)$
153: [8] igcd(D,E)$
154: 0.27sec(0.2635sec)
155: [9] igcdcntl(2)$
156: [10] igcd(D,E)$
157: 0.19sec(0.1928sec)
158: [11] igcdcntl(3)$
159: [12] igcd(D,E)$
160: 0.08sec(0.08023sec)
161: @end example
162:
163: @table @t
164: @item $B;2>H(B
165: @fref{gcd gcdz}.
166: @end table
167:
168: @node ilcm,,, $B?t$N1i;;(B
169: @subsection @code{ilcm}
170: @findex ilcm
171:
172: @table @t
173: @item ilcm(@var{i1},@var{i2})
174: :: $B:G>.8xG\?t$r5a$a$k(B.
175: @end table
176:
177: @table @var
178: @item return
179: $B@0?t(B
180: @item i1,i2
181: $B@0?t(B
182: @end table
183:
184: @itemize @bullet
185: @item
186: $B@0?t(B @var{i1}, @var{i2} $B$N:G>.8xG\?t$r5a$a$k(B.
187: @item
188: $B0lJ}$,(B 0 $B$N>l9g(B 0 $B$rJV$9(B.
189: @item
190:
191: @end itemize
192:
193: @table @t
194: @item $B;2>H(B
195: @fref{igcd igcdcntl}, @fref{mt_save mt_load}.
196: @end table
197: @node inv,,, $B?t$N1i;;(B
198: @subsection @code{inv}
199: @findex inv
200:
201: @table @t
202: @item inv(@var{i},@var{m})
203: :: @var{m} $B$rK!$H$9$k(B @var{i} $B$N5U?t(B
204: @end table
205:
206: @table @var
207: @item return
208: $B@0?t(B
209: @item i,m
210: $B@0?t(B
211: @end table
212:
213: @itemize @bullet
214: @item
215: @var{ia} @equiv{} 1 mod (@var{m}) $B$J$k@0?t(B @var{a} $B$r5a$a$k(B.
216: @item
217: @var{i} $B$H(B @var{m} $B$O8_$$$KAG$G$J$1$l$P$J$i$J$$$,(B, @code{inv()} $B$O(B
218: $B$=$N%A%'%C%/$O9T$o$J$$(B.
219: @end itemize
220:
221: @example
222: [71] igcd(1234,4321);
223: 1
224: [72] inv(1234,4321);
225: 3239
226: [73] irem(3239*1234,4321);
227: 1
228: @end example
229:
230: @table @t
231: @item $B;2>H(B
232: @fref{igcd igcdcntl}.
233: @end table
234:
235: @node prime lprime,,, $B?t$N1i;;(B
236: @subsection @code{prime}, @code{lprime}
237: @findex prime
238: @findex lprime
239:
240: @table @t
241: @item prime(@var{index})
242: @item lprime(@var{index})
243: :: $BAG?t$rJV$9(B
244: @end table
245:
246: @table @var
247: @item return
248: $B@0?t(B
249: @item index
250: $B@0?t(B
251: @end table
252:
253: @itemize @bullet
254: @item
255: @code{prime()}, @code{lprime()} $B$$$:$l$b%7%9%F%`$,FbIt$K;}$D(B
256: $BAG?tI=$NMWAG$rJV$9(B. @code{index} $B$O(B 0 $B0J>e$N@0?t$G(B, $BAG?tI=(B
257: $B$N%$%s%G%C%/%9$KMQ$$$i$l$k(B. @code{prime()} $B$O(B 16381 $B$^$G(B
258: $B$NAG?t$r>.$5$$=g$K(B 1900 $B8D(B, @code{lprime()} $B$O(B, 10 $B?J(B 8 $B7e$G:GBg$N(B
259: $BAG?t$+$iBg$-$$=g$K(B 999 $B8DJV$9(B. $B$=$l0J30$N%$%s%G%C%/%9$KBP$7$F$O(B
260: 0 $B$rJV$9(B.
261: @item
262: $B$h$j0lHLE*$JAG?t@8@.H!?t$H$7$F$O(B, @code{pari(nextprime,@var{number})}
263: $B$,$"$k(B.
264: @end itemize
265:
266: @example
267: [95] prime(0);
268: 2
269: [96] prime(1228);
270: 9973
271: [97] lprime(0);
272: 99999989
273: [98] lprime(999);
274: 0
275: @end example
276:
277: @table @t
278: @item $B;2>H(B
279: @fref{pari}.
280: @end table
281:
282: @node random,,, $B?t$N1i;;(B
283: @subsection @code{random}
284: @findex random
285:
286: @table @t
287: @item radom([@var{seed}])
288: :: $BMp?t$r@8@.$9$k(B.
289: @end table
290:
291: @table @var
292: @item seed
293: @item return
294: $B<+A3?t(B
295: @end table
296:
297: @itemize @bullet
298: @item
299: $B:GBg(B 2^32-1 $B$NHsIi@0?t$NMp?t$r@8@.$9$k(B.
300: @item
301: 0 $B$G$J$$0z?t$,$"$k;~(B, $B$=$NCM$r(B seed $B$H$7$F@_Dj$7$F$+$i(B, $BMp?t$r@8@.$9$k(B.
302: @item
303: default $B$N(B seed $B$O8GDj$N$?$a(B, $B<o$r@_Dj$7$J$1$l$P(B, $B@8@.$5$l$kMp?t$N(B
304: $B7ONs$O5/F0Kh$K0lDj$G$"$k(B.
305: @item
306: $B>>K\bC(B-$B@>B<Bs;N$K$h$k(B Mersenne Twister (http://www.math.keio.ac.jp/matsumoto/mt.html) $B%"%k%4%j%:%`$N(B, $BH`$i<+?H$K$h$k<BAu$rMQ$$$F$$$k(B.
307: @item
308: $B<~4|$O(B 2^19937-1 $B$HHs>o$KD9$$(B.
309: @item
310: @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}
311: $B$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
312: $B$G$-$k(B.
313: @end itemize
314:
315: @table @t
316: @item $B;2>H(B
317: @fref{lrandom}, @fref{mt_save mt_load}.
318: @end table
319:
320: @node lrandom,,, $B?t$N1i;;(B
321: @subsection @code{lrandom}
322: @findex lrandom
323:
324: @table @t
325: @item lradom(@var{bit})
326: :: $BB?G\D9Mp?t$r@8@.$9$k(B.
327: @end table
328:
329: @table @var
330: @item bit
331: @item return
332: $B<+A3?t(B
333: @end table
334:
335: @itemize @bullet
336: @item
337: $B9b!9(B @var{bit} $B$NHsIi@0?t$NMp?t$r@8@.$9$k(B.
338: @item
339: @code{random} $B$rJ#?t2s8F$S=P$7$F7k9g$7(B, $B;XDj$N(B bit $BD9$K%^%9%/$7$F$$$k(B.
340: @end itemize
341:
342: @table @t
343: @item $B;2>H(B
344: @fref{random}, @fref{mt_save mt_load}.
345: @end table
346:
347: @node mt_save mt_load,,, $B?t$N1i;;(B
348: @subsection @code{mt_save}, @code{mt_load}
349: @findex mt_save
350: @findex mt_load
351:
352: @table @t
353: @item mt_save(@var{fname})
354: :: $BMp?t@8@.4o$N8=:_$N>uBV$r%U%!%$%k$K%;!<%V$9$k(B.
355: @item mt_load(@var{fname})
356: :: $B%U%!%$%k$K%;!<%V$5$l$?Mp?t@8@.4o$N>uBV$r%m!<%I$9$k(B.
357: @end table
358:
359: @table @var
360: @item return
361: 0 $B$^$?$O(B 1
362: @item fname
363: $BJ8;zNs(B
364: @end table
365:
366: @itemize @bullet
367: @item $B$"$k>uBV$r%;!<%V$7(B, $B$=$N>uBV$r%m!<%I$9$k$3$H$G(B,
368: $B0l$D$N5?;wMp?t7ONs$r(B, $B?75,$N(B Asir $B%;%C%7%g%s$GB3$1$F$?$I$k$3$H$,(B
369: $B$G$-$k(B.
370: @end itemize
371:
372: @example
373: [340] random();
374: 3510405877
375: [341] mt_save("/tmp/mt_state");
376: 1
377: [342] random();
378: 4290933890
379: [343] quit;
380: % asir
381: This is Asir, Version 991108.
382: Copyright (C) FUJITSU LABORATORIES LIMITED.
383: 3 March 1994. All rights reserved.
384: [340] mt_load("/tmp/mt_state");
385: 1
386: [341] random();
387: 4290933890
388: @end example
389:
390: @table @t
391: @item $B;2>H(B
392: @fref{random}, @fref{lrandom}.
393: @end table
394:
395: @node nm dn,,, $B?t$N1i;;(B
396: @subsection @code{nm}, @code{dn}
397: @findex nm
398: @findex dn
399:
400: @table @t
401: @item nm(@var{rat})
402: :: @var{rat} $B$NJ,;R(B.
403: @item dn(@var{rat})
404: :: @var{rat} $B$NJ,Jl(B.
405: @end table
406:
407: @table @var
408: @item return
409: $B@0?t$^$?$OB?9`<0(B
410: @item rat
411: $BM-M}?t$^$?$OM-M}<0(B
412: @end table
413:
414: @itemize @bullet
415: @item
416: $BM?$($i$l$?M-M}?t$^$?M-M}<0$NJ,;R5Z$SJ,Jl$rJV$9(B.
417: @item
418: $BM-M}?t$N>l9g(B, $BJ,Jl$O>o$K@5$G(B, $BId9f$OJ,;R$,;}$D(B.
419: @item
420: $BM-M}<0$N>l9g(B, $BC1$KJ,Jl(B, $BJ,;R$r<h$j=P$9$@$1$G$"$k(B.
421: $BM-M}<0$KBP$7$F$O(B, $BLsJ,$O<+F0E*$K$O9T$o$l$J$$(B. @code{red()}
422: $B$rL@<(E*$K8F$S=P$9I,MW$,$"$k(B.
423: @end itemize
424:
425: @example
426: [2] [nm(-43/8),dn(-43/8)];
427: [-43,8]
428: [3] dn((x*z)/(x*y));
429: y*x
430: [3] dn(red((x*z)/(x*y)));
431: y
432: @end example
433:
434: @table @t
435: @item $B;2>H(B
436: @fref{red}.
437: @end table
438:
439: @node conj real imag,,, $B?t$N1i;;(B
440: @subsection @code{conj}, @code{real}, @code{imag}
441: @findex conj
442:
443: @table @t
444: @item real(@var{comp})
445: :: @var{comp} $B$N<B?tItJ,(B.
446: @item imag(@var{comp})
447: :: @var{comp} $B$N5u?tItJ,(B.
448: @item conj(@var{comp})
449: :: @var{comp} $B$N6&LrJ#AG?t(B.
450: @end table
451:
452: @table @var
453: @item return comp
454: $BJ#AG?t(B
455: @end table
456:
457: @itemize @bullet
458: @item
459: $BJ#AG?t$KBP$7(B, $B<BIt(B, $B5uIt(B, $B6&Lr$r5a$a$k(B.
460: @item
461: $B$3$l$i$O(B, $BB?9`<0$KBP$7$F$bF/$/(B.
462: @end itemize
463:
464: @example
465: [111] A=(2+@@i)^3;
466: (2+11*@@i)
467: [112] [real(A),imag(A),conj(A)];
468: [2,11,(2-11*@@i)]
469: @end example
470:
471: @node eval,,, $B?t$N1i;;(B
472: @subsection @code{eval}
473: @findex eval
474: @cindex PARI
475:
476: @table @t
477: @item eval(@var{obj}[,@var{prec}])
478: :: @var{obj} $B$NCM$NI>2A(B.
479: @end table
480:
481: @table @var
482: @item return
483: $B?t$"$k$$$O<0(B
484: @item obj
485: $B0lHL$N<0(B
486: @item prec
487: $B@0?t(B
488: @end table
489:
490: @itemize @bullet
491: @item
492: @var{obj} $B$K4^$^$l$kH!?t$NCM$r2DG=$J8B$jI>2A$9$k(B.
493: @item
494: $B7W;;$O(B @b{PARI} (@xref{pari}) $B$,9T$&(B.
495: @item
496: @var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B.
497: @var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B.
498: (@xref{setprec})
499: @item
500: @table @t
501: @item $B07$($kH!?t$O(B, $B<!$NDL$j(B.
502: @code{sin}, @code{cos}, @code{tan},
503:
504: @code{asin}, @code{acos}, @code{atan},
505:
506: @code{sinh}, @code{cosh}, @code{tanh},
507:
508: @code{asinh}, @code{acosh}, @code{atanh},
509:
510: @code{exp}, @code{log}, @code{pow(a,b) (a^b)}
511: @end table
512: @item
513: $B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B.
514: @table @t
515: @item @@i
516: $B5u?tC10L(B
517: @item @@pi
518: $B1_<~N((B
519: @item @@e
520: $B<+A3BP?t$NDl(B
521: @end table
522: @end itemize
523:
524: @example
525: [118] eval(exp(@@pi*@@i));
526: -1.0000000000000000000000000000
527: [119] eval(2^(1/2));
528: 1.414213562373095048763788073031
529: [120] eval(sin(@@pi/3));
530: 0.86602540378443864674620506632
531: [121] eval(sin(@@pi/3)-3^(1/2)/2,50);
532: -2.78791084448179148471 E-58
533: @end example
534:
535: @table @t
536: @item $B;2>H(B
537: @fref{ctrl}, @fref{setprec}, @fref{pari}.
538: @end table
539:
540: @node pari,,, $B?t$N1i;;(B
541: @subsection @code{pari}
542: @findex pari
543: @cindex PARI
544:
545: @table @t
546: @item pari(@var{func},@var{arg},@var{prec})
547: :: @b{PARI} $B$NH!?t(B @var{func} $B$r8F$S=P$9(B.
548: @end table
549:
550: @table @var
551: @item return
552: @var{func} $BKh$K0[$J$k(B.
553: @item func
554: @b{PARI} $B$NH!?tL>(B
555: @item arg
556: @var{func} $B$N0z?t(B
557: @item prec
558: $B@0?t(B
559: @end table
560:
561: @itemize @bullet
562: @item
563: @b{PARI} $B$NH!?t$r8F$S=P$9(B.
564:
565: @item
566: @b{PARI} @code{[Batut et al.]} $B$O(B Bordeaux $BBg3X$G3+H/$5$l%U(B
567: $B%j!<%=%U%H%&%'%"$H$7$F8x3+$5$l$F$$$k(B. @b{PARI} $B$O?t<0=hM}E*$J5!G=$rM-(B
568: $B$7$F$O$$$k$,(B, $B<g$J%?!<%2%C%H$O@0?tO@$K4XO"$7$??t(B (@b{bignum},
569: @b{bigfloat}) $B$N1i;;$G(B, $B;MB'1i;;$K8B$i$:(B@b{bigfloat} $B$K$h$k$5$^$6$^$J(B
570: $BH!?tCM$NI>2A$r9bB.$K9T$&$3$H$,$G$-$k(B. @b{PARI} $B$OB>$N%W%m%0%i%`$+$i(B
571: $B%5%V%k!<%A%s%i%$%V%i%j$H$7$FMQ$$$k$3$H$,$G$-(B, $B$^$?(B, @samp{gp} $B$H$$$&(B
572: @b{PARI}$B%i%$%V%i%j$N%$%s%?%U%'!<%9$K$h$j(B UNIX $B$N%"%W%j%1!<%7%g%s$H$7$F(B
573: $BMxMQ$9$k$3$H$b$G$-$k(B. $B8=:_$N%P!<%8%g%s$O(B @b{1.39} $B$G$$$/$D$+$N(B ftp
574: site ($B$?$H$($P(B @code{math.ucla.edu:/pub/pari})
575: $B$+$i(B anonymous ftp $B$G$-$k(B.
576: @item
577: $B:G8e$N0z?t(B @var{prec} $B$G7W;;@:EY$r;XDj$G$-$k(B.
578: @var{prec} $B$r>JN,$7$?>l9g(B @code{setprec()} $B$G;XDj$7$?@:EY$H$J$k(B.
579: @item
580: $B8=;~E@$G<B9T$G$-$k(B @b{PARI} $B$NH!?t$O<!$NDL$j$G$"$k(B. $B$$$:$l$b(B
581: 1 $B0z?t$G(B @b{Asir} $B$,BP1~$G$-$k7?$N0z?t$r$H$kH!?t$G$"$k(B.
582: $B$J$*3F!9$N5!G=$K$D$$$F$O(B @b{PARI} $B$N%^%K%e%"%k$r;2>H$N$3$H(B.
583:
584: @code{abs},
585: @code{adj},
586: @code{arg},
587: @code{bigomega},
588: @code{binary},
589: @code{ceil},
590: @code{centerlift},
591: @code{cf},
592: @code{classno},
593: @code{classno2},
594: @code{conj},
595: @code{content},
596: @code{denom},
597: @code{det},
598: @code{det2},
599: @code{detr},
600: @code{dilog},
601: @code{disc},
602: @code{discf},
603: @code{divisors},
604: @code{eigen},
605: @code{eintg1},
606: @code{erfc},
607: @code{eta},
608: @code{floor},
609: @code{frac},
610: @code{galois},
611: @code{galoisconj},
612: @code{gamh},
613: @code{gamma},
614: @code{hclassno},
615: @code{hermite},
616: @code{hess},
617: @code{imag},
618: @code{image},
619: @code{image2},
620: @code{indexrank},
621: @code{indsort},
622: @code{initalg},
623: @code{isfund},
624: @code{isprime},
625: @code{ispsp},
626: @code{isqrt},
627: @code{issqfree},
628: @code{issquare},
629: @code{jacobi},
630: @code{jell},
631: @code{ker},
632: @code{keri},
633: @code{kerint},
634: @code{kerintg1},
635: @code{kerint2},
636: @code{kerr},
637: @code{length},
638: @code{lexsort},
639: @code{lift},
640: @code{lindep},
641: @code{lll},
642: @code{lllg1},
643: @code{lllgen},
644: @code{lllgram},
645: @code{lllgramg1},
646: @code{lllgramgen},
647: @code{lllgramint},
648: @code{lllgramkerim},
649: @iftex
650: @break
651: @end iftex
652: @code{lllgramkerimgen},
653: @code{lllint},
654: @code{lllkerim},
655: @code{lllkerimgen},
656: @code{lllrat},
657: @code{lngamma},
658: @code{logagm},
659: @code{mat},
660: @code{matinvr},
661: @code{matrixqz2},
662: @code{matrixqz3},
663: @code{matsize},
664: @code{modreverse},
665: @code{mu},
666: @code{nextprime},
667: @code{norm},
668: @code{norml2},
669: @code{numdiv},
670: @code{numer},
671: @code{omega},
672: @code{order},
673: @code{ordred},
674: @code{phi},
675: @code{pnqn},
676: @code{polred},
677: @code{polred2},
678: @code{primroot},
679: @code{psi},
680: @code{quadgen},
681: @code{quadpoly},
682: @code{real},
683: @code{recip},
684: @code{redcomp},
685: @code{redreal},
686: @code{regula},
687: @code{reorder},
688: @code{reverse},
689: @code{rhoreal},
690: @code{roots},
691: @code{rootslong},
692: @code{round},
693: @code{sigma},
694: @code{signat},
695: @code{simplify},
696: @code{smalldiscf},
697: @code{smallfact},
698: @code{smallpolred},
699: @code{smallpolred2},
700: @code{smith},
701: @code{smith2},
702: @code{sort},
703: @code{sqr},
704: @code{sqred},
705: @code{sqrt},
706: @code{supplement},
707: @code{trace},
708: @code{trans},
709: @code{trunc},
710: @code{type},
711: @code{unit},
712: @code{vec},
713: @code{wf},
714: @code{wf2},
715: @code{zeta}
716:
717: @item
718: @b{Asir} $B$GMQ$$$F$$$k$N$O(B @b{PARI} $B$N$[$s$N0lIt$N5!G=$G$"$k$,(B, $B:#8e(B
719: $B$h$jB?$/$N5!G=$,MxMQ$G$-$k$h$&2~NI$9$kM=Dj$G$"$k(B.
720: @end itemize
721:
722: @example
723: /* $B9TNs$N8GM-%Y%/%H%k$r5a$a$k(B. */
724: [0] pari(eigen,newmat(2,2,[[1,1],[1,2]]));
725: [ -1.61803398874989484819771921990 0.61803398874989484826 ]
726: [ 1 1 ]
727: /* 1 $BJQ?tB?9`<0$N:,$r5a$a$k(B. */
728: [1] pari(roots,t^2-2);
729: [ -1.41421356237309504876 1.41421356237309504876 ]
730: @end example
731:
732: @table @t
733: @item $B;2>H(B
734: @fref{setprec}.
735: @end table
736:
737: @node setprec,,, $B?t$N1i;;(B
738: @subsection @code{setprec}
739: @findex setprec
740: @cindex PARI
741:
742: @table @t
743: @item setprec([@var{n}])
744: :: @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B.
745: @end table
746:
747: @table @var
748: @item return
749: $B@0?t(B
750: @item n
751: $B@0?t(B
752: @end table
753:
754: @itemize @bullet
755: @item
756: $B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B.
757: $B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B.
758: @item
759: @b{bigfloat} $B$N7W;;$O(B @b{PARI} (@xref{pari}) $B$K$h$C$F9T$o$l$k(B.
760: @item
761: @b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B.
762: @b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B.
763: @item
764: $B@_Dj$G$-$k7e?t$K>e8B$O$J$$$,(B, $B;XDj$7$?7e?t$K@_Dj$5$l$k$H$O(B
765: $B8B$i$J$$(B. $BBg$-$a$NCM$r@_Dj$9$k$N$,0BA4$G$"$k(B.
766: @end itemize
767:
768: @example
769: [1] setprec();
770: 9
771: [2] setprec(100);
772: 9
773: [3] setprec(100);
774: 96
775: @end example
776:
777: @table @t
778: @item $B;2>H(B
779: @fref{ctrl}, @fref{eval}, @fref{pari}.
780: @end table
781:
782: @node setmod,,, $B?t$N1i;;(B
783: @subsection @code{setmod}
784: @findex setmod
785:
786: @table @t
787: @item setmod([@var{p}])
788: :: $BM-8BBN$r(B GF(@var{p}) $B$K@_Dj$9$k(B.
789: @end table
790:
791: @table @var
792: @item return
793: $B@0?t(B
794: @item n
795: 2^27 $BL$K~$NAG?t(B
796: @end table
797:
798: @itemize @bullet
799: @item
800: $BM-8BBN$r(B GF(@var{p}) $B$K@_Dj$9$k(B. $B@_DjCM$rJV$9(B.
801: @item
802: $BM-8BBN$N85$N7?$r;}$D?t$O(B, $B$=$l<+?H$O$I$NM-8BBN$KB0$9$k$+$N>pJs$r;}$?$:(B,
803: $B8=:_@_Dj$5$l$F$$$kAG?t(B @var{p} $B$K$h$j(B GF(@var{p}) $B>e$G$N1i;;$,E,MQ$5$l$k(B.
804: @end itemize
805:
806: @example
807: [0] A=dp_mod(dp_ptod(2*x,[x]),3,[]);
808: (2)*<<1>>
809: [1] A+A;
810: addmi : invalid modulus
811: return to toplevel
812: [1] setmod(3);
813: 3
814: [2] A+A;
815: (1)*<<1>>
816: @end example
817:
818: @table @t
819: @item $B;2>H(B
820: @fref{dp_mod dp_rat}, @fref{$B?t$N7?(B}.
821: @end table
822:
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