# 기초수학실습-박석환

## 2411 days 전, dkdlel 작성

plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]]))
1 in ZZ
 True True
1/2 in ZZ
 False False
1/2 in QQ
 True True
sqrt(2) in QQ
 False False
sqrt(2) in RR
 True True
i^2
 -1 -1
i^3
 -I -I
I in RR
 False False
I in CC
 True True
QQ(.5)
 1/2 1/2
RR(sqrt(2))
 1.41421356237310 1.41421356237310
not True
 False False
not False
 True True
True and False
 False False
True and True
 True True
True or False
 True True
False or False
 False False
(True or False) and False
 False False
True or (False and False)
 True True
1 == 1
 True True
1 == 0
 False False
not(True or False) == (True and False)
 True True
1 != 1
 False False
1 != 0
 True True
1 <> 0
 True True
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)
 False False
x > 1/2
 x > (1/2) x > (1/2)
s = 12 s
 12 12
s = 34
t= 7 t += 1 t
 8 8
x=3 f = x^2 + x + 1 f
 13 13
[6,28,496,8128]
 [6, 28, 496, 8128] [6, 28, 496, 8128]
[1..7]
 [1, 2, 3, 4, 5, 6, 7] [1, 2, 3, 4, 5, 6, 7]
[1,8..23332]
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10788, 10795, 10802, 10809, 10816, 10823, 10830, 10837, 10844, 10851, 10858, 10865, 10872, 10879, 10886, 10893, 10900, 10907, 10914, 10921, 10928, 10935, 10942, 10949, 10956, 10963, 10970, 10977, 10984, 10991, 10998, 11005, 11012, 11019, 11026, 11033, 11040, 11047, 11054, 11061, 11068, 11075, 11082, 11089, 11096, 11103, 11110, 11117, 11124, 11131, 11138, 11145, 11152, 11159, 11166, 11173, 11180, 11187, 11194, 11201, 11208, 11215, 11222, 11229, 11236, 11243, 11250, 11257, 11264, 11271, 11278, 11285, 11292, 11299, 11306, 11313, 11320, 11327, 11334, 11341, 11348, 11355, 11362, 11369, 11376, 11383, 11390, 11397, 11404, 11411, 11418, 11425, 11432, 11439, 11446, 11453, 11460, 11467, 11474, 11481, 11488, 11495, 11502, 11509, 11516, 11523, 11530, 11537, 11544, 11551, 11558, 11565, 11572, 11579, 11586, 11593, 11600, 11607, 11614, 11621, 11628, 11635, 11642, 11649, 11656, 11663, 11670, 11677, 11684, 11691, 11698, 11705, 11712, 11719, 11726, 11733, 11740, 11747, 11754, 11761, 11768, 11775, 11782, 11789, 11796, 11803, 11810, 11817, 11824, 11831, 11838, 11845, 11852, 11859, 11866, 11873, 11880, 11887, 11894, 11901, 11908, 11915, 11922, 11929, 11936, 11943, 11950, 11957, 11964, 11971, 11978, 11985, 11992, 11999, 12006, 12013, 12020, 12027, 12034, 12041, 12048, 12055, 12062, 12069, 12076, 12083, 12090, 12097, 12104, 12111, 12118, 12125, 12132, 12139, 12146, 12153, 12160, 12167, 12174, 12181, 12188, 12195, 12202, 12209, 12216, 12223, 12230, 12237, 12244, 12251, 12258, 12265, 12272, 12279, 12286, 12293, 12300, 12307, 12314, 12321, 12328, 12335, 12342, 12349, 12356, 12363, 12370, 12377, 12384, 12391, 12398, 12405, 12412, 12419, 12426, 12433, 12440, 12447, 12454, 12461, 12468, 12475, 12482, 12489, 12496, 12503, 12510, 12517, 12524, 12531, 12538, 12545, 12552, 12559, 12566, 12573, 12580, 12587, 12594, 12601, 12608, 12615, 12622, 12629, 12636, 12643, 12650, 12657, 12664, 12671, 12678, 12685, 12692, 12699, 12706, 12713, 12720, 12727, 12734, 12741, 12748, 12755, 12762, 12769, 12776, 12783, 12790, 12797, 12804, 12811, 12818, 12825, 12832, 12839, 12846, 12853, 12860, 12867, 12874, 12881, 12888, 12895, 12902, 12909, 12916, 12923, 12930, 12937, 12944, 12951, 12958, 12965, 12972, 12979, 12986, 12993, 13000, 13007, 13014, 13021, 13028, 13035, 13042, 13049, 13056, 13063, 13070, 13077, 13084, 13091, 13098, 13105, 13112, 13119, 13126, 13133, 13140, 13147, 13154, 13161, 13168, 13175, 13182, 13189, 13196, 13203, 13210, 13217, 13224, 13231, 13238, 13245, 13252, 13259, 13266, 13273, 13280, 13287, 13294, 13301, 13308, 13315, 13322, 13329, 13336, 13343, 13350, 13357, 13364, 13371, 13378, 13385, 13392, 13399, 13406, 13413, 13420, 13427, 13434, 13441, 13448, 13455, 13462, 13469, 13476, 13483, 13490, 13497, 13504, 13511, 13518, 13525, 13532, 13539, 13546, 13553, 13560, 13567, 13574, 13581, 13588, 13595, 13602, 13609, 13616, 13623, 13630, 13637, 13644, 13651, 13658, 13665, 13672, 13679, 13686, 13693, 13700, 13707, 13714, 13721, 13728, 13735, 13742, 13749, 13756, 13763, 13770, 13777, 13784, 13791, 13798, 13805, 13812, 13819, 13826, 13833, 13840, 13847, 13854, 13861, 13868, 13875, 13882, 13889, 13896, 13903, 13910, 13917, 13924, 13931, 13938, 13945, 13952, 13959, 13966, 13973, 13980, 13987, 13994, 14001, 14008, 14015, 14022, 14029, 14036, 14043, 14050, 14057, 14064, 14071, 14078, 14085, 14092, 14099, 14106, 14113, 14120, 14127, 14134, 14141, 14148, 14155, 14162, 14169, 14176, 14183, 14190, 14197, 14204, 14211, 14218, 14225, 14232, 14239, 14246, 14253, 14260, 14267, 14274, 14281, 14288, 14295, 14302, 14309, 14316, 14323, 14330, 14337, 14344, 14351, 14358, 14365, 14372, 14379, 14386, 14393, 14400, 14407, 14414, 14421, 14428, 14435, 14442, 14449, 14456, 14463, 14470, 14477, 14484, 14491, 14498, 14505, 14512, 14519, 14526, 14533, 14540, 14547, 14554, 14561, 14568, 14575, 14582, 14589, 14596, 14603, 14610, 14617, 14624, 14631, 14638, 14645, 14652, 14659, 14666, 14673, 14680, 14687, 14694, 14701, 14708, 14715, 14722, 14729, 14736, 14743, 14750, 14757, 14764, 14771, 14778, 14785, 14792, 14799, 14806, 14813, 14820, 14827, 14834, 14841, 14848, 14855, 14862, 14869, 14876, 14883, 14890, 14897, 14904, 14911, 14918, 14925, 14932, 14939, 14946, 14953, 14960, 14967, 14974, 14981, 14988, 14995, 15002, 15009, 15016, 15023, 15030, 15037, 15044, 15051, 15058, 15065, 15072, 15079, 15086, 15093, 15100, 15107, 15114, 15121, 15128, 15135, 15142, 15149, 15156, 15163, 15170, 15177, 15184, 15191, 15198, 15205, 15212, 15219, 15226, 15233, 15240, 15247, 15254, 15261, 15268, 15275, 15282, 15289, 15296, 15303, 15310, 15317, 15324, 15331, 15338, 15345, 15352, 15359, 15366, 15373, 15380, 15387, 15394, 15401, 15408, 15415, 15422, 15429, 15436, 15443, 15450, 15457, 15464, 15471, 15478, 15485, 15492, 15499, 15506, 15513, 15520, 15527, 15534, 15541, 15548, 15555, 15562, 15569, 15576, 15583, 15590, 15597, 15604, 15611, 15618, 15625, 15632, 15639, 15646, 15653, 15660, 15667, 15674, 15681, 15688, 15695, 15702, 15709, 15716, 15723, 15730, 15737, 15744, 15751, 15758, 15765, 15772, 15779, 15786, 15793, 15800, 15807, 15814, 15821, 15828, 15835, 15842, 15849, 15856, 15863, 15870, 15877, 15884, 15891, 15898, 15905, 15912, 15919, 15926, 15933, 15940, 15947, 15954, 15961, 15968, 15975, 15982, 15989, 15996, 16003, 16010, 16017, 16024, 16031, 16038, 16045, 16052, 16059, 16066, 16073, 16080, 16087, 16094, 16101, 16108, 16115, 16122, 16129, 16136, 16143, 16150, 16157, 16164, 16171, 16178, 16185, 16192, 16199, 16206, 16213, 16220, 16227, 16234, 16241, 16248, 16255, 16262, 16269, 16276, 16283, 16290, 16297, 16304, 16311, 16318, 16325, 16332, 16339, 16346, 16353, 16360, 16367, 16374, 16381, 16388, 16395, 16402, 16409, 16416, 16423, 16430, 16437, 16444, 16451, 16458, 16465, 16472, 16479, 16486, 16493, 16500, 16507, 16514, 16521, 16528, 16535, 16542, 16549, 16556, 16563, 16570, 16577, 16584, 16591, 16598, 16605, 16612, 16619, 16626, 16633, 16640, 16647, 16654, 16661, 16668, 16675, 16682, 16689, 16696, 16703, 16710, 16717, 16724, 16731, 16738, 16745, 16752, 16759, 16766, 16773, 16780, 16787, 16794, 16801, 16808, 16815, 16822, 16829, 16836, 16843, 16850, 16857, 16864, 16871, 16878, 16885, 16892, 16899, 16906, 16913, 16920, 16927, 16934, 16941, 16948, 16955, 16962, 16969, 16976, 16983, 16990, 16997, 17004, 17011, 17018, 17025, 17032, 17039, 17046, 17053, 17060, 17067, 17074, 17081, 17088, 17095, 17102, 17109, 17116, 17123, 17130, 17137, 17144, 17151, 17158, 17165, 17172, 17179, 17186, 17193, 17200, 17207, 17214, 17221, 17228, 17235, 17242, 17249, 17256, 17263, 17270, 17277, 17284, 17291, 17298, 17305, 17312, 17319, 17326, 17333, 17340, 17347, 17354, 17361, 17368, 17375, 17382, 17389, 17396, 17403, 17410, 17417, 17424, 17431, 17438, 17445, 17452, 17459, 17466, 17473, 17480, 17487, 17494, 17501, 17508, 17515, 17522, 17529, 17536, 17543, 17550, 17557, 17564, 17571, 17578, 17585, 17592, 17599, 17606, 17613, 17620, 17627, 17634, 17641, 17648, 17655, 17662, 17669, 17676, 17683, 17690, 17697, 17704, 17711, 17718, 17725, 17732, 17739, 17746, 17753, 17760, 17767, 17774, 17781, 17788, 17795, 17802, 17809, 17816, 17823, 17830, 17837, 17844, 17851, 17858, 17865, 17872, 17879, 17886, 17893, 17900, 17907, 17914, 17921, 17928, 17935, 17942, 17949, 17956, 17963, 17970, 17977, 17984, 17991, 17998, 18005, 18012, 18019, 18026, 18033, 18040, 18047, 18054, 18061, 18068, 18075, 18082, 18089, 18096, 18103, 18110, 18117, 18124, 18131, 18138, 18145, 18152, 18159, 18166, 18173, 18180, 18187, 18194, 18201, 18208, 18215, 18222, 18229, 18236, 18243, 18250, 18257, 18264, 18271, 18278, 18285, 18292, 18299, 18306, 18313, 18320, 18327, 18334, 18341, 18348, 18355, 18362, 18369, 18376, 18383, 18390, 18397, 18404, 18411, 18418, 18425, 18432, 18439, 18446, 18453, 18460, 18467, 18474, 18481, 18488, 18495, 18502, 18509, 18516, 18523, 18530, 18537, 18544, 18551, 18558, 18565, 18572, 18579, 18586, 18593, 18600, 18607, 18614, 18621, 18628, 18635, 18642, 18649, 18656, 18663, 18670, 18677, 18684, 18691, 18698, 18705, 18712, 18719, 18726, 18733, 18740, 18747, 18754, 18761, 18768, 18775, 18782, 18789, 18796, 18803, 18810, 18817, 18824, 18831, 18838, 18845, 18852, 18859, 18866, 18873, 18880, 18887, 18894, 18901, 18908, 18915, 18922, 18929, 18936, 18943, 18950, 18957, 18964, 18971, 18978, 18985, 18992, 18999, 19006, 19013, 19020, 19027, 19034, 19041, 19048, 19055, 19062, 19069, 19076, 19083, 19090, 19097, 19104, 19111, 19118, 19125, 19132, 19139, 19146, 19153, 19160, 19167, 19174, 19181, 19188, 19195, 19202, 19209, 19216, 19223, 19230, 19237, 19244, 19251, 19258, 19265, 19272, 19279, 19286, 19293, 19300, 19307, 19314, 19321, 19328, 19335, 19342, 19349, 19356, 19363, 19370, 19377, 19384, 19391, 19398, 19405, 19412, 19419, 19426, 19433, 19440, 19447, 19454, 19461, 19468, 19475, 19482, 19489, 19496, 19503, 19510, 19517, 19524, 19531, 19538, 19545, 19552, 19559, 19566, 19573, 19580, 19587, 19594, 19601, 19608, 19615, 19622, 19629, 19636, 19643, 19650, 19657, 19664, 19671, 19678, 19685, 19692, 19699, 19706, 19713, 19720, 19727, 19734, 19741, 19748, 19755, 19762, 19769, 19776, 19783, 19790, 19797, 19804, 19811, 19818, 19825, 19832, 19839, 19846, 19853, 19860, 19867, 19874, 19881, 19888, 19895, 19902, 19909, 19916, 19923, 19930, 19937, 19944, 19951, 19958, 19965, 19972, 19979, 19986, 19993, 20000, 20007, 20014, 20021, 20028, 20035, 20042, 20049, 20056, 20063, 20070, 20077, 20084, 20091, 20098, 20105, 20112, 20119, 20126, 20133, 20140, 20147, 20154, 20161, 20168, 20175, 20182, 20189, 20196, 20203, 20210, 20217, 20224, 20231, 20238, 20245, 20252, 20259, 20266, 20273, 20280, 20287, 20294, 20301, 20308, 20315, 20322, 20329, 20336, 20343, 20350, 20357, 20364, 20371, 20378, 20385, 20392, 20399, 20406, 20413, 20420, 20427, 20434, 20441, 20448, 20455, 20462, 20469, 20476, 20483, 20490, 20497, 20504, 20511, 20518, 20525, 20532, 20539, 20546, 20553, 20560, 20567, 20574, 20581, 20588, 20595, 20602, 20609, 20616, 20623, 20630, 20637, 20644, 20651, 20658, 20665, 20672, 20679, 20686, 20693, 20700, 20707, 20714, 20721, 20728, 20735, 20742, 20749, 20756, 20763, 20770, 20777, 20784, 20791, 20798, 20805, 20812, 20819, 20826, 20833, 20840, 20847, 20854, 20861, 20868, 20875, 20882, 20889, 20896, 20903, 20910, 20917, 20924, 20931, 20938, 20945, 20952, 20959, 20966, 20973, 20980, 20987, 20994, 21001, 21008, 21015, 21022, 21029, 21036, 21043, 21050, 21057, 21064, 21071, 21078, 21085, 21092, 21099, 21106, 21113, 21120, 21127, 21134, 21141, 21148, 21155, 21162, 21169, 21176, 21183, 21190, 21197, 21204, 21211, 21218, 21225, 21232, 21239, 21246, 21253, 21260, 21267, 21274, 21281, 21288, 21295, 21302, 21309, 21316, 21323, 21330, 21337, 21344, 21351, 21358, 21365, 21372, 21379, 21386, 21393, 21400, 21407, 21414, 21421, 21428, 21435, 21442, 21449, 21456, 21463, 21470, 21477, 21484, 21491, 21498, 21505, 21512, 21519, 21526, 21533, 21540, 21547, 21554, 21561, 21568, 21575, 21582, 21589, 21596, 21603, 21610, 21617, 21624, 21631, 21638, 21645, 21652, 21659, 21666, 21673, 21680, 21687, 21694, 21701, 21708, 21715, 21722, 21729, 21736, 21743, 21750, 21757, 21764, 21771, 21778, 21785, 21792, 21799, 21806, 21813, 21820, 21827, 21834, 21841, 21848, 21855, 21862, 21869, 21876, 21883, 21890, 21897, 21904, 21911, 21918, 21925, 21932, 21939, 21946, 21953, 21960, 21967, 21974, 21981, 21988, 21995, 22002, 22009, 22016, 22023, 22030, 22037, 22044, 22051, 22058, 22065, 22072, 22079, 22086, 22093, 22100, 22107, 22114, 22121, 22128, 22135, 22142, 22149, 22156, 22163, 22170, 22177, 22184, 22191, 22198, 22205, 22212, 22219, 22226, 22233, 22240, 22247, 22254, 22261, 22268, 22275, 22282, 22289, 22296, 22303, 22310, 22317, 22324, 22331, 22338, 22345, 22352, 22359, 22366, 22373, 22380, 22387, 22394, 22401, 22408, 22415, 22422, 22429, 22436, 22443, 22450, 22457, 22464, 22471, 22478, 22485, 22492, 22499, 22506, 22513, 22520, 22527, 22534, 22541, 22548, 22555, 22562, 22569, 22576, 22583, 22590, 22597, 22604, 22611, 22618, 22625, 22632, 22639, 22646, 22653, 22660, 22667, 22674, 22681, 22688, 22695, 22702, 22709, 22716, 22723, 22730, 22737, 22744, 22751, 22758, 22765, 22772, 22779, 22786, 22793, 22800, 22807, 22814, 22821, 22828, 22835, 22842, 22849, 22856, 22863, 22870, 22877, 22884, 22891, 22898, 22905, 22912, 22919, 22926, 22933, 22940, 22947, 22954, 22961, 22968, 22975, 22982, 22989, 22996, 23003, 23010, 23017, 23024, 23031, 23038, 23045, 23052, 23059, 23066, 23073, 23080, 23087, 23094, 23101, 23108, 23115, 23122, 23129, 23136, 23143, 23150, 23157, 23164, 23171, 23178, 23185, 23192, 23199, 23206, 23213, 23220, 23227, 23234, 23241, 23248, 23255, 23262, 23269, 23276, 23283, 23290, 23297, 23304, 23311, 23318, 23325, 23332]
x = var('x') p1 = parametric_plot((cos(x),sin(x)),(x,0,2*pi),rgbcolor=hue(0.2)) p2 = parametric_plot((cos(x),sin(x)^2),(x,0,2*pi),rgbcolor=hue(0.4)) p3 = parametric_plot((cos(x),sin(x)^3),(x,0,2*pi),rgbcolor=hue(0.6)) show(p1+p2+p3, axes=false)
A = Set([2,3,3,3,2,1,8,6,3])
A.cardinality()
 5 5
B = Set([8,6,17,-4,20, -2 ])
A.union(B)
 {1, 2, 3, 6, 8, 17, 20, -4, -2} {1, 2, 3, 6, 8, 17, 20, -4, -2}
A.intersection(B)
 {8, 6} {8, 6}
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}]
[-19, -17 .. 29]
 [-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29] [-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
tmp = Set([3,6..18]) tmpt = tmp.subsets() tmpt.cardinality()
 64 64
[tan(x) for x in [0,pi/4..pi]]
 [0, 1, Infinity, -1, 0] [0, 1, Infinity, -1, 0]
14 // 4
 3 3
14 % 4
 2 2
divmod(14,4)
 (3, 2) (3, 2)
3.divides(15)
 True True
5.divides(17)
 False False
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
63.factor()
 3^2 * 7 3^2 * 7
24.prime_divisors()
 [2, 3] [2, 3]
gcd(14,63)
 7 7
lcm(4,5)
 20 20
divmod(956,98)
 (9, 74) (9, 74)
956//98
 9 9
956%98
 74 74
3.divides(234878)
 False False
[134.divisors(), 491.divisors(), 422.divisors(), 1002.divisors()]
 [[1, 2, 67, 134], [1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334, 501, 1002]] [[1, 2, 67, 134], [1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334, 501, 1002]]
491.is_prime()
 True True
gcd(2,5)
 1 1
lcm(4,20)
 20 20
18*51
 918 918
max(55555555555555555555555555555555555555555555,55555555555555555555555555555555555)
 55555555555555555555555555555555555555555555 55555555555555555555555555555555555555555555
abs(-15951)
 15951 15951