기초수학 실습

2028 days 전, khk1741 작성

sage: 1 in ZZ 
       
True
True
sage: I in RR 
       
False
False
sage: RR(sqrt(2)) 
       
1.41421356237310
1.41421356237310
sage: [6,28,496,8128] 
       
[6, 28, 496, 8128]
[6, 28, 496, 8128]
plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]])) 
       
sage: plot(sin, 0, 10, color='purple 
       
sage: 1/2 in ZZ 
       
False
False
1/2 in QQ 
       
True
True
sqrt(2) in RR 
       
True
True
sqrt(2) in QQ 
       
False
False
i^3 
       
-I
-I
I in CC 
       
True
True
QQ(.5) 
       
1/2
1/2
RR(sqrt(2)) 
       
1.41421356237310
1.41421356237310
RR(sqrt(5)) 
       
2.23606797749979
2.23606797749979
(True or False) and False 
       
False
False
not (True or False) == (False and True) 
       
True
True
1 >= 1 
       
True
True
1 + i >= 2 - i 
       
(I + 1) >= (-I + 2)
(I + 1) >= (-I + 2)
((3/2) > 1) or (2/3 < 1) 
       
True
True
((3/2) > 1) ^^ (2/3 < 1) # ^^ xor 배타적 논리합 
       
False
False
x > 1/2 
       
x > (1/2)
x > (1/2)
s=12 
       
       
12
12
t=7 
       
       
7
7
t=t+1 
       
       
8
8
a,b=1,2 
       
a,b 
       
(1, 2)
(1, 2)
a,b,c=2,5,8 
       
a,b,c 
       
(2, 5, 8)
(2, 5, 8)
a=b=1 
       
       
1
1
       
1
1
f(x) = x^2 + x + 1 f(3) 
       
13
13
[6,28,496,8128] 
       
[6, 28, 496, 8128]
[6, 28, 496, 8128]
[1..999] 
       
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21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,
57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122,
123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136,
137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150,
151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178,
179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192,
193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206,
207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,
221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234,
235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248,
249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262,
263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276,
277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290,
291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304,
305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318,
319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332,
333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346,
347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360,
361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374,
375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388,
389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402,
403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416,
417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430,
431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444,
445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458,
459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472,
473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486,
487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500,
501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514,
515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528,
529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542,
543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,
557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570,
571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584,
585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598,
599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612,
613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626,
627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640,
641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654,
655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668,
669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682,
683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696,
697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710,
711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724,
725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738,
739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752,
753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766,
767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780,
781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794,
795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808,
809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822,
823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836,
837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850,
851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864,
865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878,
879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892,
893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906,
907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920,
921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934,
935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948,
949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962,
963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976,
977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990,
991, 992, 993, 994, 995, 996, 997, 998, 999]
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[2.4..240] 
       
[2.40000000000000, 3.40000000000000, 4.40000000000000, 5.40000000000000,
6.40000000000000, 7.40000000000000, 8.40000000000000, 9.40000000000000,
10.4000000000000, 11.4000000000000, 12.4000000000000, 13.4000000000000,
14.4000000000000, 15.4000000000000, 16.4000000000000, 17.4000000000000,
18.4000000000000, 19.4000000000000, 20.4000000000000, 21.4000000000000,
22.4000000000000, 23.4000000000000, 24.4000000000000, 25.4000000000000,
26.4000000000000, 27.4000000000000, 28.4000000000000, 29.4000000000000,
30.4000000000000, 31.4000000000000, 32.4000000000000, 33.4000000000000,
34.4000000000000, 35.4000000000000, 36.4000000000000, 37.4000000000000,
38.4000000000000, 39.4000000000000, 40.4000000000000, 41.4000000000000,
42.4000000000000, 43.4000000000000, 44.4000000000000, 45.4000000000000,
46.4000000000000, 47.4000000000000, 48.4000000000000, 49.4000000000000,
50.4000000000000, 51.4000000000000, 52.4000000000000, 53.4000000000000,
54.4000000000000, 55.4000000000000, 56.4000000000000, 57.4000000000000,
58.4000000000000, 59.4000000000000, 60.4000000000000, 61.4000000000000,
62.4000000000000, 63.4000000000000, 64.4000000000000, 65.4000000000000,
66.4000000000000, 67.4000000000000, 68.4000000000000, 69.4000000000000,
70.4000000000000, 71.4000000000000, 72.4000000000000, 73.4000000000000,
74.4000000000000, 75.4000000000000, 76.4000000000000, 77.4000000000000,
78.4000000000000, 79.4000000000000, 80.4000000000000, 81.4000000000000,
82.4000000000000, 83.4000000000000, 84.4000000000000, 85.4000000000000,
86.4000000000000, 87.4000000000000, 88.4000000000000, 89.4000000000000,
90.4000000000000, 91.4000000000000, 92.4000000000000, 93.4000000000000,
94.4000000000000, 95.4000000000000, 96.4000000000000, 97.4000000000000,
98.4000000000000, 99.4000000000000, 100.400000000000, 101.400000000000,
102.400000000000, 103.400000000000, 104.400000000000, 105.400000000000,
106.400000000000, 107.400000000000, 108.400000000000, 109.400000000000,
110.400000000000, 111.400000000000, 112.400000000000, 113.400000000000,
114.400000000000, 115.400000000000, 116.400000000000, 117.400000000000,
118.400000000000, 119.400000000000, 120.400000000000, 121.400000000000,
122.400000000000, 123.400000000000, 124.400000000000, 125.400000000000,
126.400000000000, 127.400000000000, 128.400000000000, 129.400000000000,
130.400000000000, 131.400000000000, 132.400000000000, 133.400000000000,
134.400000000000, 135.400000000000, 136.400000000000, 137.400000000000,
138.400000000000, 139.400000000000, 140.400000000000, 141.400000000000,
142.400000000000, 143.400000000000, 144.400000000000, 145.400000000000,
146.400000000000, 147.400000000000, 148.400000000000, 149.400000000000,
150.400000000000, 151.400000000000, 152.400000000000, 153.400000000000,
154.400000000000, 155.400000000000, 156.400000000000, 157.400000000000,
158.400000000000, 159.400000000000, 160.400000000000, 161.400000000000,
162.400000000000, 163.400000000000, 164.400000000000, 165.400000000000,
166.400000000000, 167.400000000000, 168.400000000000, 169.400000000000,
170.400000000000, 171.400000000000, 172.400000000000, 173.400000000000,
174.400000000000, 175.400000000000, 176.400000000000, 177.400000000000,
178.400000000000, 179.400000000000, 180.400000000000, 181.400000000000,
182.400000000000, 183.400000000000, 184.400000000000, 185.400000000000,
186.400000000000, 187.400000000000, 188.400000000000, 189.400000000000,
190.400000000000, 191.400000000000, 192.400000000000, 193.400000000000,
194.400000000000, 195.400000000000, 196.400000000000, 197.400000000000,
198.400000000000, 199.400000000000, 200.400000000000, 201.400000000000,
202.400000000000, 203.400000000000, 204.400000000000, 205.400000000000,
206.400000000000, 207.400000000000, 208.400000000000, 209.400000000000,
210.400000000000, 211.400000000000, 212.400000000000, 213.400000000000,
214.400000000000, 215.400000000000, 216.400000000000, 217.400000000000,
218.400000000000, 219.400000000000, 220.400000000000, 221.400000000000,
222.400000000000, 223.400000000000, 224.400000000000, 225.400000000000,
226.400000000000, 227.400000000000, 228.400000000000, 229.400000000000,
230.400000000000, 231.400000000000, 232.400000000000, 233.400000000000,
234.400000000000, 235.400000000000, 236.400000000000, 237.400000000000,
238.400000000000, 239.400000000000]
[2.40000000000000, 3.40000000000000, 4.40000000000000, 5.40000000000000, 6.40000000000000, 7.40000000000000, 8.40000000000000, 9.40000000000000, 10.4000000000000, 11.4000000000000, 12.4000000000000, 13.4000000000000, 14.4000000000000, 15.4000000000000, 16.4000000000000, 17.4000000000000, 18.4000000000000, 19.4000000000000, 20.4000000000000, 21.4000000000000, 22.4000000000000, 23.4000000000000, 24.4000000000000, 25.4000000000000, 26.4000000000000, 27.4000000000000, 28.4000000000000, 29.4000000000000, 30.4000000000000, 31.4000000000000, 32.4000000000000, 33.4000000000000, 34.4000000000000, 35.4000000000000, 36.4000000000000, 37.4000000000000, 38.4000000000000, 39.4000000000000, 40.4000000000000, 41.4000000000000, 42.4000000000000, 43.4000000000000, 44.4000000000000, 45.4000000000000, 46.4000000000000, 47.4000000000000, 48.4000000000000, 49.4000000000000, 50.4000000000000, 51.4000000000000, 52.4000000000000, 53.4000000000000, 54.4000000000000, 55.4000000000000, 56.4000000000000, 57.4000000000000, 58.4000000000000, 59.4000000000000, 60.4000000000000, 61.4000000000000, 62.4000000000000, 63.4000000000000, 64.4000000000000, 65.4000000000000, 66.4000000000000, 67.4000000000000, 68.4000000000000, 69.4000000000000, 70.4000000000000, 71.4000000000000, 72.4000000000000, 73.4000000000000, 74.4000000000000, 75.4000000000000, 76.4000000000000, 77.4000000000000, 78.4000000000000, 79.4000000000000, 80.4000000000000, 81.4000000000000, 82.4000000000000, 83.4000000000000, 84.4000000000000, 85.4000000000000, 86.4000000000000, 87.4000000000000, 88.4000000000000, 89.4000000000000, 90.4000000000000, 91.4000000000000, 92.4000000000000, 93.4000000000000, 94.4000000000000, 95.4000000000000, 96.4000000000000, 97.4000000000000, 98.4000000000000, 99.4000000000000, 100.400000000000, 101.400000000000, 102.400000000000, 103.400000000000, 104.400000000000, 105.400000000000, 106.400000000000, 107.400000000000, 108.400000000000, 109.400000000000, 110.400000000000, 111.400000000000, 112.400000000000, 113.400000000000, 114.400000000000, 115.400000000000, 116.400000000000, 117.400000000000, 118.400000000000, 119.400000000000, 120.400000000000, 121.400000000000, 122.400000000000, 123.400000000000, 124.400000000000, 125.400000000000, 126.400000000000, 127.400000000000, 128.400000000000, 129.400000000000, 130.400000000000, 131.400000000000, 132.400000000000, 133.400000000000, 134.400000000000, 135.400000000000, 136.400000000000, 137.400000000000, 138.400000000000, 139.400000000000, 140.400000000000, 141.400000000000, 142.400000000000, 143.400000000000, 144.400000000000, 145.400000000000, 146.400000000000, 147.400000000000, 148.400000000000, 149.400000000000, 150.400000000000, 151.400000000000, 152.400000000000, 153.400000000000, 154.400000000000, 155.400000000000, 156.400000000000, 157.400000000000, 158.400000000000, 159.400000000000, 160.400000000000, 161.400000000000, 162.400000000000, 163.400000000000, 164.400000000000, 165.400000000000, 166.400000000000, 167.400000000000, 168.400000000000, 169.400000000000, 170.400000000000, 171.400000000000, 172.400000000000, 173.400000000000, 174.400000000000, 175.400000000000, 176.400000000000, 177.400000000000, 178.400000000000, 179.400000000000, 180.400000000000, 181.400000000000, 182.400000000000, 183.400000000000, 184.400000000000, 185.400000000000, 186.400000000000, 187.400000000000, 188.400000000000, 189.400000000000, 190.400000000000, 191.400000000000, 192.400000000000, 193.400000000000, 194.400000000000, 195.400000000000, 196.400000000000, 197.400000000000, 198.400000000000, 199.400000000000, 200.400000000000, 201.400000000000, 202.400000000000, 203.400000000000, 204.400000000000, 205.400000000000, 206.400000000000, 207.400000000000, 208.400000000000, 209.400000000000, 210.400000000000, 211.400000000000, 212.400000000000, 213.400000000000, 214.400000000000, 215.400000000000, 216.400000000000, 217.400000000000, 218.400000000000, 219.400000000000, 220.400000000000, 221.400000000000, 222.400000000000, 223.400000000000, 224.400000000000, 225.400000000000, 226.400000000000, 227.400000000000, 228.400000000000, 229.400000000000, 230.400000000000, 231.400000000000, 232.400000000000, 233.400000000000, 234.400000000000, 235.400000000000, 236.400000000000, 237.400000000000, 238.400000000000, 239.400000000000]
[2.4..10] 
       
[2.40000000000000, 3.40000000000000, 4.40000000000000, 5.40000000000000,
6.40000000000000, 7.40000000000000, 8.40000000000000, 9.40000000000000]
[2.40000000000000, 3.40000000000000, 4.40000000000000, 5.40000000000000, 6.40000000000000, 7.40000000000000, 8.40000000000000, 9.40000000000000]
[2,4..10] 
       
[2, 4, 6, 8, 10]
[2, 4, 6, 8, 10]
[1,11..35] 
       
[1, 11, 21, 31]
[1, 11, 21, 31]
[1,3..101] 
       
[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37,
39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73,
75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101]
[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101]
[pi,4*pi..32] 
       
[pi, 4*pi, 7*pi, 10*pi]
[pi, 4*pi, 7*pi, 10*pi]
A = Set([2,3,3,3,2,1,8,6,3]) 
       
       
{8, 1, 2, 3, 6}
{8, 1, 2, 3, 6}
A.cardinality() 
       
5
5
8 in A 10 in A 
       
False
False
10 in A 
       
False
False
B = Set([8,6,17,-4,20, -2 ]) B 
       
{17, 20, 6, 8, -4, -2}
{17, 20, 6, 8, -4, -2}
A.union(B) 
       
{1, 2, 3, 6, 8, 17, 20, -4, -2}
{1, 2, 3, 6, 8, 17, 20, -4, -2}
A,B.cardinality() 
       
({8, 1, 2, 3, 6}, 6)
({8, 1, 2, 3, 6}, 6)
sage: A.difference(B) 
       
{1, 2, 3}
{1, 2, 3}
B.difference(A) 
       
{17, 20, -4, -2}
{17, 20, -4, -2}
A.symmetric_difference(B) 
       
{17, 2, 3, 20, 1, -4, -2}
{17, 2, 3, 20, 1, -4, -2}
A = Set([1,2,3]); A 
       
{1, 2, 3}
{1, 2, 3}
powA = A.subsets(); powA 
       
Subsets of {1, 2, 3}
Subsets of {1, 2, 3}
pairsA = A.subsets(2); pairsA 
       
Subsets of {1, 2, 3} of size 2
Subsets of {1, 2, 3} of size 2
powA.list() 
       
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
pairsA.list() 
       
[{1, 2}, {1, 3}, {2, 3}]
[{1, 2}, {1, 3}, {2, 3}]
sin(0) 
       
0
0
A = Set([3,6,9,12,15,18]); A 
       
{18, 3, 6, 9, 12, 15}
{18, 3, 6, 9, 12, 15}
powA = A.subsets(); powA 
       
Subsets of {18, 3, 6, 9, 12, 15}
Subsets of {18, 3, 6, 9, 12, 15}
powA.list() 
       
[{}, {18}, {3}, {6}, {9}, {12}, {15}, {18, 3}, {18, 6}, {9, 18}, {18,
12}, {18, 15}, {3, 6}, {9, 3}, {3, 12}, {3, 15}, {9, 6}, {12, 6}, {6,
15}, {9, 12}, {9, 15}, {12, 15}, {18, 3, 6}, {9, 18, 3}, {18, 3, 12},
{18, 3, 15}, {9, 18, 6}, {18, 12, 6}, {18, 6, 15}, {9, 18, 12}, {9, 18,
15}, {18, 12, 15}, {9, 3, 6}, {3, 12, 6}, {3, 6, 15}, {9, 3, 12}, {9, 3,
15}, {3, 12, 15}, {9, 12, 6}, {9, 6, 15}, {12, 6, 15}, {9, 12, 15}, {9,
18, 3, 6}, {18, 3, 12, 6}, {18, 3, 6, 15}, {9, 18, 3, 12}, {9, 18, 3,
15}, {18, 3, 12, 15}, {9, 18, 12, 6}, {9, 18, 6, 15}, {18, 12, 6, 15},
{9, 18, 12, 15}, {9, 3, 12, 6}, {9, 3, 6, 15}, {3, 12, 6, 15}, {9, 3,
12, 15}, {9, 12, 6, 15}, {9, 18, 3, 12, 6}, {9, 18, 3, 6, 15}, {18, 3,
12, 6, 15}, {9, 18, 3, 12, 15}, {9, 18, 12, 6, 15}, {9, 3, 12, 6, 15},
{18, 3, 6, 9, 12, 15}]
[{}, {18}, {3}, {6}, {9}, {12}, {15}, {18, 3}, {18, 6}, {9, 18}, {18, 12}, {18, 15}, {3, 6}, {9, 3}, {3, 12}, {3, 15}, {9, 6}, {12, 6}, {6, 15}, {9, 12}, {9, 15}, {12, 15}, {18, 3, 6}, {9, 18, 3}, {18, 3, 12}, {18, 3, 15}, {9, 18, 6}, {18, 12, 6}, {18, 6, 15}, {9, 18, 12}, {9, 18, 15}, {18, 12, 15}, {9, 3, 6}, {3, 12, 6}, {3, 6, 15}, {9, 3, 12}, {9, 3, 15}, {3, 12, 15}, {9, 12, 6}, {9, 6, 15}, {12, 6, 15}, {9, 12, 15}, {9, 18, 3, 6}, {18, 3, 12, 6}, {18, 3, 6, 15}, {9, 18, 3, 12}, {9, 18, 3, 15}, {18, 3, 12, 15}, {9, 18, 12, 6}, {9, 18, 6, 15}, {18, 12, 6, 15}, {9, 18, 12, 15}, {9, 3, 12, 6}, {9, 3, 6, 15}, {3, 12, 6, 15}, {9, 3, 12, 15}, {9, 12, 6, 15}, {9, 18, 3, 12, 6}, {9, 18, 3, 6, 15}, {18, 3, 12, 6, 15}, {9, 18, 3, 12, 15}, {9, 18, 12, 6, 15}, {9, 3, 12, 6, 15}, {18, 3, 6, 9, 12, 15}]
[tan(x) for x in [0, pi/4..pi]] 
       
[0, 1, Infinity, -1, 0]
[0, 1, Infinity, -1, 0]
14/4 
       
7/2
7/2
124//5 
       
24
24
124 %5 
       
4
4
divmod(14,4) 
       
(3, 2)
(3, 2)
3.divides(15) 
       
True
True
12.divisors() 
       
[1, 2, 3, 4, 6, 12]
[1, 2, 3, 4, 6, 12]
101.divisors() 
       
[1, 101]
[1, 101]
(2^19-1).is_prime() 
       
True
True
153.is_prime() 
       
False
False
62.factor() 
       
2 * 31
2 * 31
24.prime_divisors() 
       
[2, 3]
[2, 3]
gcd(14,63) 
       
7
7
lcm(4,5) 
       
20
20
956 //5 
       
191
191
956 %5 
       
1
1
divmod(956,5) 
       
(191, 1)
(191, 1)
3.divides(234878) 
       
False
False
134.divisors() 
       
[1, 2, 67, 134]
[1, 2, 67, 134]
491.divisors(),422.divisors(),1002.divisors() 
       
([1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334, 501, 1002])
([1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334, 501, 1002])
1002.is_prime() 
       
False
False
501.is_prime() 
       
False
False
167.is_prime() 
       
True
True
gcd(2,5),gcd(4,10),gcd(18,51) 
       
(1, 2, 3)
(1, 2, 3)
lcm(2,5),lcm(4,10),lcm(18,51) 
       
(10, 20, 306)
(10, 20, 306)
2*5,4*10,18*51 
       
(10, 40, 918)
(10, 40, 918)
max(1,5,8) 
       
8
8
min(1/2,1/3) 
       
1/3
1/3
 
       
10
10