¿ô¤Î·¿

0

Í­Íý¿ô
Í­Íý¿ô¤Ï, Ǥ°Õ¿ÇÜĹÀ°¿ô (bignum) ¤Ë¤è¤ê¼Â¸½¤µ¤ì¤Æ¤¤¤ë. Í­Íý¿ô¤Ï¾ï¤Ë ´ûÌóʬ¿ô¤Çɽ¸½¤µ¤ì¤ë.

1

ÇÜÀºÅÙÉâÆ°¾®¿ô
¥Þ¥·¥ó¤ÎÄ󶡤¹¤ëÇÜÀºÅÙÉâÆ°¾®¿ô¤Ç¤¢¤ë. Asir ¤Îµ¯Æ°»þ¤Ë¤Ï, Ä̾ï¤Î·Á¼°¤ÇÆþÎϤµ¤ì¤¿ÉâÆ°¾®¿ô¤Ï¤³¤Î·¿¤ËÊÑ´¹¤µ¤ì¤ë. ¤¿¤À¤·, ctrl() ¤Ë¤è¤ê bigfloat ¤¬ÁªÂò¤µ¤ì¤Æ¤¤¤ë¾ì¹ç¤Ë¤Ï bigfloat ¤ËÊÑ´¹¤µ¤ì¤ë.

[0] 1.2;
1.2
[1] 1.2e-1000; 
0
[2] ctrl("bigfloat",1);
1
[3] 1.2e-1000;         
1.20000000000000000513 E-1000

ÇÜÀºÅÙÉâÆ°¾®¿ô¤ÈÍ­Íý¿ô¤Î±é»»¤Ï, Í­Íý¿ô¤¬ÉâÆ°¾®¿ô¤ËÊÑ´¹¤µ¤ì¤Æ, ÉâÆ°¾®¿ô¤È¤·¤Æ±é»»¤µ¤ì¤ë.

2

Âå¿ôŪ¿ô
See section Âå¿ôŪ¿ô¤Ë´Ø¤¹¤ë±é»».

3

bigfloat
bigfloat ¤Ï, Asir ¤Ç¤Ï PARI ¥é¥¤¥Ö¥é¥ê¤Ë¤è¤ê ¼Â¸½¤µ¤ì¤Æ¤¤¤ë. PARI ¤Ë¤ª¤¤¤Æ¤Ï, bigfloat ¤Ï, ²¾¿ôÉô ¤Î¤ßǤ°Õ¿ÇÜŤÇ, »Ø¿ôÉô¤Ï 1 ¥ï¡¼¥É°ÊÆâ¤ÎÀ°¿ô¤Ë¸Â¤é¤ì¤Æ¤¤¤ë. ctrl() ¤Ç bigfloat ¤òÁªÂò¤¹¤ë¤³¤È¤Ë¤è¤ê, °Ê¸å¤ÎÉâÆ°¾®¿ô ¤ÎÆþÎÏ¤Ï bigfloat ¤È¤·¤Æ°·¤ï¤ì¤ë. ÀºÅ٤ϥǥե©¥ë¥È¤Ç¤Ï 10 ¿Ê 9 ·åÄøÅ٤Ǥ¢¤ë¤¬, setprec() ¤Ë¤è¤ê»ØÄê²Äǽ¤Ç¤¢¤ë.

[0] ctrl("bigfloat",1);
1
[1] eval(2^(1/2));
1.414213562373095048763788073031
[2] setprec(100);      
9
[3] eval(2^(1/2));
1.41421356237309504880168872420969807856967187537694807317654396116148

eval() ¤Ï, °ú¿ô¤Ë´Þ¤Þ¤ì¤ëÈ¡¿ôÃͤò²Äǽ¤Ê¸Â¤ê¿ôÃͲ½¤¹¤ëÈ¡¿ô¤Ç¤¢¤ë. setprec() ¤Ç»ØÄꤵ¤ì¤¿·å¿ô¤Ï, ·ë²Ì¤ÎÀºÅÙ¤òÊݾڤ¹¤ë¤â¤Î¤Ç¤Ï¤Ê¤¯, PARI ÆâÉô¤ÇÍѤ¤¤é¤ì¤ëɽ¸½¤Î¥µ¥¤¥º¤ò¼¨¤¹¤³¤È¤ËÃí°Õ¤¹¤Ù¤­¤Ç¤¢¤ë. (See section eval, deval, section pari.)

4

Ê£ÁÇ¿ô
Ê£ÁÇ¿ô¤Ï, Í­Íý¿ô, ÇÜÀºÅÙÉâÆ°¾®¿ô, bigfloat ¤ò¼ÂÉô, µõÉô¤È¤·¤Æ a+b*@i (@i ¤Ïµõ¿ôñ°Ì) ¤È¤·¤ÆÍ¿¤¨¤é¤ì¤ë¿ô¤Ç¤¢¤ë. ¼ÂÉô, µõÉô¤Ï ¤½¤ì¤¾¤ì real(), imag() ¤Ç¼è¤ê½Ð¤»¤ë.

5

¾®É¸¿ô¤ÎÍ­¸ÂÁÇÂΤθµ
¤³¤³¤Ç¸À¤¦¾®É¸¿ô¤È¤Ï, ɸ¿ô¤¬ 2^27 ̤Ëþ¤Î¤â¤Î¤Î¤³¤È¤Ç¤¢¤ë. ¤³¤Î¤è¤¦¤ÊÍ­¸Â ÂΤÏ, ¸½ºß¤Î¤È¤³¤í¥°¥ì¥Ö¥Ê´ðÄì·×»»¤Ë¤ª¤¤¤ÆÆâÉôŪ¤ËÍѤ¤¤é¤ì, Í­¸ÂÂη¸¿ô¤Î ʬ»¶É½¸½Â¿¹à¼°¤Î·¸¿ô¤ò¼è¤ê½Ð¤¹¤³¤È¤ÇÆÀ¤é¤ì¤ë. ¤½¤ì¼«¿È¤Ï°¤¹¤ëÍ­¸ÂÂÎ¤Ë´Ø ¤¹¤ë¾ðÊó¤Ï»ý¤¿¤º, setmod() ¤ÇÀßÄꤵ¤ì¤Æ¤¤¤ëÁÇ¿ô p ¤òÍѤ¤¤Æ GF(p) ¾å¤Ç¤Î±é»»¤¬Å¬ÍѤµ¤ì¤ë.

6

Âçɸ¿ô¤ÎÍ­¸ÂÁÇÂΤθµ
ɸ¿ô¤È¤·¤ÆǤ°Õ¤ÎÁÇ¿ô¤¬¤È¤ì¤ë. ¤³¤Î·¿¤Î¿ô¤Ï, À°¿ô¤ËÂФ·simp_ff ¤òŬÍѤ¹¤ë¤³¤È¤Ë¤è¤êÆÀ¤é¤ì¤ë.

7

ɸ¿ô 2 ¤ÎÍ­¸ÂÂΤθµ
ɸ¿ô 2 ¤ÎǤ°Õ¤ÎÍ­¸ÂÂΤ赤òɽ¸½¤¹¤ë. ɸ¿ô 2 ¤ÎÍ­¸ÂÂÎ F ¤Ï, ³ÈÂ缡¿ô [F:GF(2)] ¤ò n ¤È¤¹¤ì¤Ð, GF(2) ¾å´ûÌó¤Ê n ¼¡Â¿¹à¼° f(t) ¤Ë¤è¤ê F=GF(2)[t]/(f(t)) ¤È¤¢¤é¤ï¤µ¤ì¤ë. ¤µ¤é¤Ë, GF(2)[t] ¤Î¸µ g ¤Ï, f(t) ¤â´Þ¤á¤Æ¼«Á³¤Ê»ÅÊý¤Ç¥Ó¥Ã¥ÈÎó¤È¤ß¤Ê¤µ¤ì¤ë¤¿¤á, ·Á¼°¾å¤Ï, F ¤Î¸µ g mod f ¤Ï, g, f ¤ò¤¢¤é¤ï¤¹ 2 ¤Ä¤Î¥Ó¥Ã¥ÈÎó¤Çɽ¸½¤¹¤ë¤³¤È¤¬¤Ç¤­¤ë. F ¤Î¸µ¤òÆþÎϤ¹¤ë¤¤¤¯¤Ä¤«¤ÎÊýË¡¤¬ÍÑ°Õ¤µ¤ì¤Æ¤¤¤ë.

• @
@ ¤Ï¤½¤Î¸å¤í¤Ë¿ô»ú, ʸ»ú¤òȼ¤Ã¤Æ, ¥Ò¥¹¥È¥ê¤äÆüì¤Ê¿ô¤ò¤¢¤é¤ï¤¹¤¬, ñÆȤǸ½¤ì¤¿¾ì¹ç¤Ë¤Ï, F=GF(2)[t]/(f(t)) ¤Ë¤ª¤±¤ë t mod f ¤ò¤¢¤é¤ï¤¹. ¤è¤Ã¤Æ, @ ¤Î¿¹à¼°¤È¤·¤Æ F ¤Î¸µ¤òÆþÎϤǤ­¤ë. (@^10+@+1 ¤Ê¤É)
• ptogf2n
  Ǥ°ÕÊÑ¿ô¤Î 1 ÊÑ¿ô¿¹à¼°¤ò, ptogf2n ¤Ë¤è¤êÂбþ¤¹¤ë F ¤Î¸µ¤ËÊÑ´¹¤¹¤ë.
• ntogf2n
  Ǥ°Õ¤Î¼«Á³¿ô¤ò, ¼«Á³¤Ê»ÅÊý¤Ç F ¤Î¸µ¤È¤ß¤Ê¤¹. ¼«Á³¿ô¤È¤·¤Æ¤Ï, 10 ¿Ê, 16 ¿Ê (0x ¤Ç»Ï¤Þ¤ë), 2 ¿Ê (0b ¤Ç»Ï¤Þ¤ë) ¤ÇÆþÎϤ¬²Äǽ¤Ç¤¢¤ë.
• ¤½¤Î¾
  ¿¹à¼°¤Î·¸¿ô¤ò´Ý¤´¤È F ¤Î¸µ¤ËÊÑ´¹¤¹¤ë¤è¤¦¤Ê¾ì¹ç, simp_ff ¤Ë¤è¤êÊÑ´¹¤Ç¤­¤ë.

Âçɸ¿ôÁÇÂΤÎɸ¿ô, ɸ¿ô 2 ¤ÎÍ­¸ÂÂΤÎÄêµÁ¿¹à¼°¤Ï, setmod_ff ¤ÇÀßÄꤹ¤ë. Í­¸ÂÂΤθµ¤É¤¦¤·¤Î±é»»¤Ç¤Ï, setmod_ff ¤Ë¤è¤êÀßÄꤵ¤ì¤Æ¤¤¤ë modulus ¤Ç, °¤¹¤ëÂΤ¬Ê¬¤«¤ê, ¤½¤ÎÃæ¤Ç±é»»¤¬¹Ô¤ï¤ì¤ë. °ìÊý¤¬Í­Íý¿ô¤Î¾ì¹ç¤Ë¤Ï, ¤½¤ÎÍ­Íý¿ô¤Ï¼«Æ°Åª¤Ë¸½ºßÀßÄꤵ¤ì¤Æ¤¤¤ë Í­¸ÂÂΤ赤ËÊÑ´¹¤µ¤ì, ±é»»¤¬¹Ô¤ï¤ì¤ë.

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