# Basic numeric literals

Literal....................................Interpretation


```python
1234,-24,0,99999999999999999999    # Integers (unlimited size)
```




    (1234, -24, 0, 99999999999999999999)




```python
1.23,1.,3.14e-10,4E210,4.0e+210  # Floating-point numbers
```




    (1.23, 1.0, 3.14e-10, 4e+210, 4e+210)




```python
0o177,0x9ff,0b101010            # Octal,hex,and binary literasl in 2.6
```




    (127, 2559, 42)




```python
3+4j,3.0+4.0j,3J        # Complex number literals
```




    ((3+4j), (3+4j), 3j)




```python
print(3.14e-10)
```

    3.14e-10


# Hexadecimal,octal and binary literals

Hexadecimals start with a leading 0X or OX, followed by a string of hexadecimal digits (0-9 and A-F).Hex digits may be coded in lower-or upper-case. Octal literals start with a leading 0o or 0o (zero and lower- or uppercase letter "o"), followed by a string of digits (0-7).In 2.6 and earlier,octal literals can also be coded with just a leading 0, but not in 3.0 (this original octal form is too easily confused with decimal, and is replaced by the new 0o format). Binary literals, new in 2.6 and 3.0, begin with a leading 0b or 0B,followed by binary digits (0-1).


```python
oct(127),hex(2559),bin(42),int('127',10)
```




    ('0o177', '0x9ff', '0b101010', 127)




```python
0o1,0o07,0o007,0o127,0o100,7+7*8+1*8**2
```




    (1, 7, 7, 87, 64, 127)




```python
0xf,0xf0,0xf00,240/15,3840/240
```




    (15, 240, 3840, 16.0, 16.0)




```python
0x0,0x1,0x2,0x3,0x4,0x5,0x6,0x7,0x8,0x9,0xA,0xB,...,0xf
```




    (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, Ellipsis, 15)



what's Sheldon's favorite number?


```python
check = int(input("Please input a number: "))
```

    Please input a number: 23



```python
def prime(check):
    for i in range(2, check):
        if check % i == 0:
            return False
        else:
            return True
if prime(check):
    print("This is prime number.")
else:
    print("This is not prime number.")
```

    This is prime number.



```python
def prime(x):
    for i in range(2,x):
        if x%i==0:
            return False
        if i==x-1:
            return True
```


```python
output = filter(prime,range(2,100001))
```


```python
print(list(output))
```

    [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 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92377, 92381, 92383, 92387, 92399, 92401, 92413, 92419, 92431, 92459, 92461, 92467, 92479, 92489, 92503, 92507, 92551, 92557, 92567, 92569, 92581, 92593, 92623, 92627, 92639, 92641, 92647, 92657, 92669, 92671, 92681, 92683, 92693, 92699, 92707, 92717, 92723, 92737, 92753, 92761, 92767, 92779, 92789, 92791, 92801, 92809, 92821, 92831, 92849, 92857, 92861, 92863, 92867, 92893, 92899, 92921, 92927, 92941, 92951, 92957, 92959, 92987, 92993, 93001, 93047, 93053, 93059, 93077, 93083, 93089, 93097, 93103, 93113, 93131, 93133, 93139, 93151, 93169, 93179, 93187, 93199, 93229, 93239, 93241, 93251, 93253, 93257, 93263, 93281, 93283, 93287, 93307, 93319, 93323, 93329, 93337, 93371, 93377, 93383, 93407, 93419, 93427, 93463, 93479, 93481, 93487, 93491, 93493, 93497, 93503, 93523, 93529, 93553, 93557, 93559, 93563, 93581, 93601, 93607, 93629, 93637, 93683, 93701, 93703, 93719, 93739, 93761, 93763, 93787, 93809, 93811, 93827, 93851, 93871, 93887, 93889, 93893, 93901, 93911, 93913, 93923, 93937, 93941, 93949, 93967, 93971, 93979, 93983, 93997, 94007, 94009, 94033, 94049, 94057, 94063, 94079, 94099, 94109, 94111, 94117, 94121, 94151, 94153, 94169, 94201, 94207, 94219, 94229, 94253, 94261, 94273, 94291, 94307, 94309, 94321, 94327, 94331, 94343, 94349, 94351, 94379, 94397, 94399, 94421, 94427, 94433, 94439, 94441, 94447, 94463, 94477, 94483, 94513, 94529, 94531, 94541, 94543, 94547, 94559, 94561, 94573, 94583, 94597, 94603, 94613, 94621, 94649, 94651, 94687, 94693, 94709, 94723, 94727, 94747, 94771, 94777, 94781, 94789, 94793, 94811, 94819, 94823, 94837, 94841, 94847, 94849, 94873, 94889, 94903, 94907, 94933, 94949, 94951, 94961, 94993, 94999, 95003, 95009, 95021, 95027, 95063, 95071, 95083, 95087, 95089, 95093, 95101, 95107, 95111, 95131, 95143, 95153, 95177, 95189, 95191, 95203, 95213, 95219, 95231, 95233, 95239, 95257, 95261, 95267, 95273, 95279, 95287, 95311, 95317, 95327, 95339, 95369, 95383, 95393, 95401, 95413, 95419, 95429, 95441, 95443, 95461, 95467, 95471, 95479, 95483, 95507, 95527, 95531, 95539, 95549, 95561, 95569, 95581, 95597, 95603, 95617, 95621, 95629, 95633, 95651, 95701, 95707, 95713, 95717, 95723, 95731, 95737, 95747, 95773, 95783, 95789, 95791, 95801, 95803, 95813, 95819, 95857, 95869, 95873, 95881, 95891, 95911, 95917, 95923, 95929, 95947, 95957, 95959, 95971, 95987, 95989, 96001, 96013, 96017, 96043, 96053, 96059, 96079, 96097, 96137, 96149, 96157, 96167, 96179, 96181, 96199, 96211, 96221, 96223, 96233, 96259, 96263, 96269, 96281, 96289, 96293, 96323, 96329, 96331, 96337, 96353, 96377, 96401, 96419, 96431, 96443, 96451, 96457, 96461, 96469, 96479, 96487, 96493, 96497, 96517, 96527, 96553, 96557, 96581, 96587, 96589, 96601, 96643, 96661, 96667, 96671, 96697, 96703, 96731, 96737, 96739, 96749, 96757, 96763, 96769, 96779, 96787, 96797, 96799, 96821, 96823, 96827, 96847, 96851, 96857, 96893, 96907, 96911, 96931, 96953, 96959, 96973, 96979, 96989, 96997, 97001, 97003, 97007, 97021, 97039, 97073, 97081, 97103, 97117, 97127, 97151, 97157, 97159, 97169, 97171, 97177, 97187, 97213, 97231, 97241, 97259, 97283, 97301, 97303, 97327, 97367, 97369, 97373, 97379, 97381, 97387, 97397, 97423, 97429, 97441, 97453, 97459, 97463, 97499, 97501, 97511, 97523, 97547, 97549, 97553, 97561, 97571, 97577, 97579, 97583, 97607, 97609, 97613, 97649, 97651, 97673, 97687, 97711, 97729, 97771, 97777, 97787, 97789, 97813, 97829, 97841, 97843, 97847, 97849, 97859, 97861, 97871, 97879, 97883, 97919, 97927, 97931, 97943, 97961, 97967, 97973, 97987, 98009, 98011, 98017, 98041, 98047, 98057, 98081, 98101, 98123, 98129, 98143, 98179, 98207, 98213, 98221, 98227, 98251, 98257, 98269, 98297, 98299, 98317, 98321, 98323, 98327, 98347, 98369, 98377, 98387, 98389, 98407, 98411, 98419, 98429, 98443, 98453, 98459, 98467, 98473, 98479, 98491, 98507, 98519, 98533, 98543, 98561, 98563, 98573, 98597, 98621, 98627, 98639, 98641, 98663, 98669, 98689, 98711, 98713, 98717, 98729, 98731, 98737, 98773, 98779, 98801, 98807, 98809, 98837, 98849, 98867, 98869, 98873, 98887, 98893, 98897, 98899, 98909, 98911, 98927, 98929, 98939, 98947, 98953, 98963, 98981, 98993, 98999, 99013, 99017, 99023, 99041, 99053, 99079, 99083, 99089, 99103, 99109, 99119, 99131, 99133, 99137, 99139, 99149, 99173, 99181, 99191, 99223, 99233, 99241, 99251, 99257, 99259, 99277, 99289, 99317, 99347, 99349, 99367, 99371, 99377, 99391, 99397, 99401, 99409, 99431, 99439, 99469, 99487, 99497, 99523, 99527, 99529, 99551, 99559, 99563, 99571, 99577, 99581, 99607, 99611, 99623, 99643, 99661, 99667, 99679, 99689, 99707, 99709, 99713, 99719, 99721, 99733, 99761, 99767, 99787, 99793, 99809, 99817, 99823, 99829, 99833, 99839, 99859, 99871, 99877, 99881, 99901, 99907, 99923, 99929, 99961, 99971, 99989, 99991]


Python expression operators and precedence

Operators.................................Description
yield x-----------------------------------Generator function send protocol;

lambda args: expression-------------------Anonymous function generation;

x if y else z-----------------------------Ternary selection (x is evaluted only if y is true)

x or y------------------------------------Logical OR (y is evaluated only if x is false)

x and y-----------------------------------Logical AND (y is evaluated only if x is true)

not x-------------------------------------Logical negation

x in y, x not in y------------------------Membership (iterables, sets)

x is y, x is not y------------------------Object identity tests

x < y, x <= y, x > y, x > = y, x==y, x!=y---------Magnitude comparison, set subset and superset; value equality operators

x | y ------------------------------------Bitwise OR, set union

x ^ y ------------------------------------Bitwise XOR, set symmetric difference

x & y -------------------------------------Bitwise AND,set intersection

x <<y, x>>y--------------------------------Shift x left or right by y bits

x + y, x-y ---------------------------------Addition,concatenation; Subtraction,set difference

x * y, x % y, x/y, x//y---------------------Multiplication, repetition; Remainder,format; Division: true and floor

-x,+x --------------------------------------Negation,identity

-x  ----------------------------------------Bitwise NOT (inversion)

x * * y ------------------------------------Power (exponentatiation)

x[i]  --------------------------------------Indexing (sequence,mapping,others)

x[i:j:k] ------------------------------------Slicing

x(...) --------------------------------------Call(function,method,class,other callable)

x.attr ------------------------------------ Attribute reference

(...)  ------------------------------------ Tuple,expression,generator experession

[...] ------------------------------------- List, list comprehension

{...} ------------------------------------- Dictionary,set,set and dictionary comprehensions


```python
bin(73)
```




    '0b1001001'




```python
def fib(x):
    yield 1
    a,b = 1,1
    while x:
        a,b = b,a+b
        yield a
        x=x-1         
for i in fib(5):
    print(i)
```

    1
    1
    2
    3
    5
    8





```python
from sympy import *
```


```python
X = symbols('X')
Y = symbols('Y')
Z = symbols('Z')
```


```python
(X+Y)*Z, X +(Y*Z),X+Y*Z
```




    (Z*(X + Y), X + Y*Z, X + Y*Z)




```python
(X+Y)*Z == X*Z+Y*Z, X+(Y*Z)==X+Y*Z,(3+4)*5 == 3*5+4*5
```




    (False, True, True)



Double equals signs (==) are used to test equality. However, this tests expressions exactly, not symbolically. For example:


```python
x = symbols('x')
y = symbols('y')
z = symbols('z')
```


```python
(x+1)**2 == x**2 + 2*x + 1, (x+1)**2 == (x+1)**2
```




    (False, True)



If you want to test for symbolic equality, one way is to subtract one expression from the other and run it through functions like expand(), simplify(), and trigsimp() and see if the equation reduces to 0.


```python
from sympy import simplify,expand,trigsimp
```


```python
simplify((x+1)**2-(x**2 + 2*x + 1))
```




$\displaystyle 0$




```python
eq = (x+1)**2-(x**2 + 2*x + 1)
```


```python
simplify(eq),expand(eq,trig=True)
```




    (0, 0)




```python
expand((x+1)**2) == x**2 + 2*x + 1
```




    True




```python
expand((x+1)**16)
```




$\displaystyle x^{16} + 16 x^{15} + 120 x^{14} + 560 x^{13} + 1820 x^{12} + 4368 x^{11} + 8008 x^{10} + 11440 x^{9} + 12870 x^{8} + 11440 x^{7} + 8008 x^{6} + 4368 x^{5} + 1820 x^{4} + 560 x^{3} + 120 x^{2} + 16 x + 1$



# Mixed operators follow operator precedence


```python
A = symbols('A')
B = symbols('B')
C = symbols('C')
D = symbols('D')
```

When dealing with mixed operators, Python follows what are called precedence rules. The table above is ordered by operator precedence: 
* Operators lower in the table have higher precedence, and so bind more tightly in mixed expressions.
* Operators in the same row in the table above generally group from left to right when combined.


```python
(A+B)*C,A+(B*C)
```




    (C*(A + B), A + B*C)




```python
int(3.1415),float(3)
```




    (3, 3.0)



Ranking of the complexity of numeric types:
1. Integers
2. Floating point numbers
3. Complex numbers

Preview: Operator overloading and polymorphism


```python
a = 3
b = 4
```


```python
a + 1, a-1, b*3, b/2, a%2, b**2, 2 + 4.0, 2.0 **b
```




    (4, 2, 12, 2.0, 1, 16, 6.0, 16.0)




```python
b/2+a, print(b/(2.0+a))
```

    0.8





    (5.0, None)




```python
b/(2.0+a)
```




    0.8




```python
1/2.0
```




    0.5




```python
num = 1/3.0
```


```python
num
print(num)
```

    0.3333333333333333



```python
'%e ' % num
```




    '3.333333e-01 '




```python
'%4.2f' % num, '{0:4.2f}'.format(num)
```




    ('0.33', '0.33')



## Str and repr Display Formats


```python
num = 1/3
```


```python
repr(num),str(num)
```




    ('0.3333333333333333', '0.3333333333333333')




```python
repr(num)==str(num)
```




    True



# Comparsions: Normal and Chained


```python
1 < 2, 2.0 >= 1, 2.0 == 2.0, 2.0 != 2.0
```




    (True, True, True, False)



Python also allows us to chain multiple comparsions together.


```python
X = 2
Y = 4
Z = 6
```


```python
X < Y < Z, X < Y and Y < Z
```




    (True, True)




```python
X < Y > Z, X < Y and Y > 2
```




    (False, True)




```python
1 < 2 < 3.0 < 4, 1 > 2 > 3.0 > 4
```




    (True, False)




```python
1 == 2 < 3
```




    False



## Divsion: Classic, Floor, and True


```python
10/4, 10//4, 10/4.0, 10//4.0
```




    (2.5, 2, 2.5, 2.0)




```python
from __future__ import division
```


```python
10/4,10//4
```




    (2.5, 2)



# Floor versus truncation


```python
import math
print(math.floor(2.5))
print(math.floor(-2.5))
print(math.trunc(2.5))
print(math.trunc(-2.5))
```

    2
    -3
    2
    -2


# Sympy tutorials


```python
from __future__ import division
```


```python
from sympy import *
```


```python
x, y, z, t = symbols('x y z t')
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
```


```python
a = Integral(cos(x)*exp(x), x)
```


```python
pprint(a)
```

    ⌠             
    ⎮  x          
    ⎮ ℯ ⋅cos(x) dx
    ⌡             



```python
pprint(Eq(a, a.doit()))
```

    ⌠                 x           x       
    ⎮  x             ℯ ⋅sin(x)   ℯ ⋅cos(x)
    ⎮ ℯ ⋅cos(x) dx = ───────── + ─────────
    ⌡                    2           2    



```python
repr(Eq(a, a.doit()))
```




    'Eq(Integral(exp(x)*cos(x), x), exp(x)*sin(x)/2 + exp(x)*cos(x)/2)'




```python
 from sympy import init_printing
```


```python
init_printing()
```


```python
pprint(a), pprint(Eq(a, a.doit()))
```

    ⌠             
    ⎮  x          
    ⎮ ℯ ⋅cos(x) dx
    ⌡             
    ⌠                 x           x       
    ⎮  x             ℯ ⋅sin(x)   ℯ ⋅cos(x)
    ⎮ ℯ ⋅cos(x) dx = ───────── + ─────────
    ⌡                    2           2    





    (None, None)




```python
pprint(a, use_unicode=False)
```

      /            
     |             
     |  x          
     | e *cos(x) dx
     |             
    /              



```python
pprint(Eq(a, a.doit()),use_unicode=False)
```

      /                                    
     |                 x           x       
     |  x             e *sin(x)   e *cos(x)
     | e *cos(x) dx = --------- + ---------
     |                    2           2    
    /                                      



```python
pretty(a, use_unicode=False)
```




    '  /            \n |             \n |  x          \n | e *cos(x) dx\n |             \n/              '




```python
print(pretty(a, use_unicode=False))
```

      /            
     |             
     |  x          
     | e *cos(x) dx
     |             
    /              



```python
from sympy import init_session
```


```python
init_session(quiet=True)
```

    



```python
from matplotlib import *
```


```python
a
```


```python
X = symbols('X')
```


```python
X + 1
```


```python
init_session()
```

    IPython console for SymPy 1.4 (Python 3.6.7-64-bit) (ground types: gmpy)
    
    These commands were executed:
    >>> from __future__ import division
    >>> from sympy import *
    >>> x, y, z, t = symbols('x y z t')
    >>> k, m, n = symbols('k m n', integer=True)
    >>> f, g, h = symbols('f g h', cls=Function)
    >>> init_printing()
    
    Documentation can be found at https://docs.sympy.org/1.4/
    



```python
X + 1
```


```python
pprint(X+1)
```

    X + 1



```python
Eq(x + 1, 4)
```


```python
init_printing(use_unicode=True)
```


```python
simplify(sin(x)**2 + cos(x)**2)
```


```python
pprint(simplify((x**3 + x**2 - x - 1)/(x**2 + 2*x + 1)))
```

    x - 1



```python
pprint(simplify(gamma(x)/gamma(x - 2)))
```

    (x - 2)⋅(x - 1)



```python
factor(x**3 - x**2 + x - 1)
```


```python
factor(x**2*z + 4*x*y*z + 4*y**2*z)
```


```python
def list_to_frac(l):
    expr = Integer(0)
    for i in reversed(l[1:]):
        expr += i
        expr = 1/expr
    return l[0] + expr
```


```python
list_to_frac([x, y, z])
```


```python
syms = symbols('a0:5')
```


```python
syms
```


```python
frac = list_to_frac(syms)
```


```python
frac
```


```python
frac = cancel(frac)
```


```python
frac
```


```python
eval('64'),eval('0o100'),eval('0x40'),eval('0b10000000')
```


```python
'{0:o},{1:x},{2:b}'.format(64,64,64)
```




    '100,40,1000000'




```python
'%o,%x,%X' % (64,255,255)
```




    '100,ff,FF'




```python
'{0:o},{2:x},{1:b}'.format(64,64,64)
```




    '100,40,1000000'




```python
X = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
```


```python
X
```


```python
oct(X)
```




    '0o377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777'




```python
bin(X)
```




    '0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111'



# Bitwise Operations


```python
x = 1
```


```python
bin(x)
```




    '0b1'




```python
x << 2, x << 3, x << 4, x << 5, x << 6
```


```python
bin(2), x | 2, x | 16, 32 | 64, x & 1, x & 2, x & 3, x & 4, x & 5, x & 16, 32 & 64
```




    ('0b10', 3, 17, 96, 1, 0, 1, 0, 1, 0, 0)




```python
X = 0b0001
X <<2
```


```python
bin(X <<2)
```




    '0b100'




```python
bin(X | 0b010)
```




    '0b11'




```python
bin(X & 0b1)
```




    '0b1'




```python
bin(2 & 3),bin(64 & 32)
```




    ('0b10', '0b0')




```python
x = 0xFF
```


```python
bin(x)
```




    '0b11111111'




```python
0b10101010
```


```python
x
```


```python
255 ^ 170,255-170,64 ^ 32,64-32
```


```python
bin(255),bin(170),bin(64),bin(32)
```




    ('0b11111111', '0b10101010', '0b1000000', '0b100000')




```python
bin(85),bin(96),bin(32)
```




    ('0b1010101', '0b1100000', '0b100000')




```python
bin(0b11111111-0b10101010),bin(0b1000000-0b100000)
```




    ('0b1010101', '0b100000')




```python
1^1, 1^2, 1^3,1^4,1^5,bin(1),bin(2),bin(3),bin(4),bin(5)
```




    (0, 3, 2, 5, 4, '0b1', '0b10', '0b11', '0b100', '0b101')




```python
for i in range(101):
    print('%d, %s ===> %s^%s'%(100^i,bin(100^i),bin(100),bin(i)))
```

    100, 0b1100100 ===> 0b1100100^0b0
    101, 0b1100101 ===> 0b1100100^0b1
    102, 0b1100110 ===> 0b1100100^0b10
    103, 0b1100111 ===> 0b1100100^0b11
    96, 0b1100000 ===> 0b1100100^0b100
    97, 0b1100001 ===> 0b1100100^0b101
    98, 0b1100010 ===> 0b1100100^0b110
    99, 0b1100011 ===> 0b1100100^0b111
    108, 0b1101100 ===> 0b1100100^0b1000
    109, 0b1101101 ===> 0b1100100^0b1001
    110, 0b1101110 ===> 0b1100100^0b1010
    111, 0b1101111 ===> 0b1100100^0b1011
    104, 0b1101000 ===> 0b1100100^0b1100
    105, 0b1101001 ===> 0b1100100^0b1101
    106, 0b1101010 ===> 0b1100100^0b1110
    107, 0b1101011 ===> 0b1100100^0b1111
    116, 0b1110100 ===> 0b1100100^0b10000
    117, 0b1110101 ===> 0b1100100^0b10001
    118, 0b1110110 ===> 0b1100100^0b10010
    119, 0b1110111 ===> 0b1100100^0b10011
    112, 0b1110000 ===> 0b1100100^0b10100
    113, 0b1110001 ===> 0b1100100^0b10101
    114, 0b1110010 ===> 0b1100100^0b10110
    115, 0b1110011 ===> 0b1100100^0b10111
    124, 0b1111100 ===> 0b1100100^0b11000
    125, 0b1111101 ===> 0b1100100^0b11001
    126, 0b1111110 ===> 0b1100100^0b11010
    127, 0b1111111 ===> 0b1100100^0b11011
    120, 0b1111000 ===> 0b1100100^0b11100
    121, 0b1111001 ===> 0b1100100^0b11101
    122, 0b1111010 ===> 0b1100100^0b11110
    123, 0b1111011 ===> 0b1100100^0b11111
    68, 0b1000100 ===> 0b1100100^0b100000
    69, 0b1000101 ===> 0b1100100^0b100001
    70, 0b1000110 ===> 0b1100100^0b100010
    71, 0b1000111 ===> 0b1100100^0b100011
    64, 0b1000000 ===> 0b1100100^0b100100
    65, 0b1000001 ===> 0b1100100^0b100101
    66, 0b1000010 ===> 0b1100100^0b100110
    67, 0b1000011 ===> 0b1100100^0b100111
    76, 0b1001100 ===> 0b1100100^0b101000
    77, 0b1001101 ===> 0b1100100^0b101001
    78, 0b1001110 ===> 0b1100100^0b101010
    79, 0b1001111 ===> 0b1100100^0b101011
    72, 0b1001000 ===> 0b1100100^0b101100
    73, 0b1001001 ===> 0b1100100^0b101101
    74, 0b1001010 ===> 0b1100100^0b101110
    75, 0b1001011 ===> 0b1100100^0b101111
    84, 0b1010100 ===> 0b1100100^0b110000
    85, 0b1010101 ===> 0b1100100^0b110001
    86, 0b1010110 ===> 0b1100100^0b110010
    87, 0b1010111 ===> 0b1100100^0b110011
    80, 0b1010000 ===> 0b1100100^0b110100
    81, 0b1010001 ===> 0b1100100^0b110101
    82, 0b1010010 ===> 0b1100100^0b110110
    83, 0b1010011 ===> 0b1100100^0b110111
    92, 0b1011100 ===> 0b1100100^0b111000
    93, 0b1011101 ===> 0b1100100^0b111001
    94, 0b1011110 ===> 0b1100100^0b111010
    95, 0b1011111 ===> 0b1100100^0b111011
    88, 0b1011000 ===> 0b1100100^0b111100
    89, 0b1011001 ===> 0b1100100^0b111101
    90, 0b1011010 ===> 0b1100100^0b111110
    91, 0b1011011 ===> 0b1100100^0b111111
    36, 0b100100 ===> 0b1100100^0b1000000
    37, 0b100101 ===> 0b1100100^0b1000001
    38, 0b100110 ===> 0b1100100^0b1000010
    39, 0b100111 ===> 0b1100100^0b1000011
    32, 0b100000 ===> 0b1100100^0b1000100
    33, 0b100001 ===> 0b1100100^0b1000101
    34, 0b100010 ===> 0b1100100^0b1000110
    35, 0b100011 ===> 0b1100100^0b1000111
    44, 0b101100 ===> 0b1100100^0b1001000
    45, 0b101101 ===> 0b1100100^0b1001001
    46, 0b101110 ===> 0b1100100^0b1001010
    47, 0b101111 ===> 0b1100100^0b1001011
    40, 0b101000 ===> 0b1100100^0b1001100
    41, 0b101001 ===> 0b1100100^0b1001101
    42, 0b101010 ===> 0b1100100^0b1001110
    43, 0b101011 ===> 0b1100100^0b1001111
    52, 0b110100 ===> 0b1100100^0b1010000
    53, 0b110101 ===> 0b1100100^0b1010001
    54, 0b110110 ===> 0b1100100^0b1010010
    55, 0b110111 ===> 0b1100100^0b1010011
    48, 0b110000 ===> 0b1100100^0b1010100
    49, 0b110001 ===> 0b1100100^0b1010101
    50, 0b110010 ===> 0b1100100^0b1010110
    51, 0b110011 ===> 0b1100100^0b1010111
    60, 0b111100 ===> 0b1100100^0b1011000
    61, 0b111101 ===> 0b1100100^0b1011001
    62, 0b111110 ===> 0b1100100^0b1011010
    63, 0b111111 ===> 0b1100100^0b1011011
    56, 0b111000 ===> 0b1100100^0b1011100
    57, 0b111001 ===> 0b1100100^0b1011101
    58, 0b111010 ===> 0b1100100^0b1011110
    59, 0b111011 ===> 0b1100100^0b1011111
    4, 0b100 ===> 0b1100100^0b1100000
    5, 0b101 ===> 0b1100100^0b1100001
    6, 0b110 ===> 0b1100100^0b1100010
    7, 0b111 ===> 0b1100100^0b1100011
    0, 0b0 ===> 0b1100100^0b1100100



```python
X = 99
```


```python
bin(X),X.bit_length()
```




    ('0b1100011', 7)




```python
bin(100),(100).bit_length()
```




    ('0b1100100', 7)




```python
len(bin(256))-2
```

In Python 3, the integer bit_length method allows you to query the number of bits required to represent a number's value in binary.It can be also achieved by substracting 2 from the length of the bin string using the len built-in function.


```python
0.1 + 0.1 + 0.1 - 0.3, 0.1*3-0.3
```


```python
print(0.1*3-0.3)
```

    5.551115123125783e-17


Decimal Type: Printing the result to produce the user-friendly display format doesn't completely help because the hardware related to floating-point math is inherently limited in terms of accuracy.


```python
print(0.1+0.1+0.1-0.3)
```

    5.551115123125783e-17



```python
from decimal import Decimal
```


```python
Decimal('0.1') + Decimal('0.1') + Decimal('0.1')-Decimal('0.3')
```




    Decimal('0.0')




```python
Decimal('0.1')+Decimal('0.100')+Decimal('0.100')-Decimal('0.3000')
```




    Decimal('0.0000')



# Setting precision globally


```python
import decimal 
```


```python
decimal.Decimal(1)/decimal.Decimal(7)
```




    Decimal('0.1428571428571428571428571429')




```python
decimal.getcontext().prec = 4
```


```python
decimal.Decimal(1)/decimal.Decimal(7)
```




    Decimal('0.1429')




```python
1999 + 1.33
```


```python
decimal.getcontext().prec = 2
```


```python
pay = decimal.Decimal(str(1999+1.33))
```


```python
pay
```




    Decimal('2000.33')



Decimal context manager


```python
import decimal
```


```python
decimal.Decimal('1.00')/decimal.Decimal('7.00')
```




    Decimal('0.14')




```python
with decimal.localcontext() as ctx:
    ctx.prec = 1
    a = decimal.Decimal('1.00')/decimal.Decimal('3.00')
    print(a)
```

    0.3



```python
decimal.Decimal('1.00')/decimal.Decimal('3.00')
```




    Decimal('0.33')



Fraction Type


```python
from fractions import Fraction
```


```python
x = Fraction(1,3)
y = Fraction(4,9)
```


```python
x,y
```




    (Fraction(1, 3), Fraction(4, 9))




```python
print(x, y)
```

    1/3 4/9



```python
(2.5).as_integer_ratio()
```


```python
f = 2.5
```


```python
from fractions import Fraction
```


```python
z = Fraction(*f.as_integer_ratio())
```


```python
z
```




    Fraction(5, 2)




```python
x = Fraction(1,3)
```


```python
x + z,float(x),float(z),float(x+z)
```




    (Fraction(17, 6), 0.3333333333333333, 2.5, 2.8333333333333335)




```python
Fraction.from_float(1.75)
```




    Fraction(7, 4)




```python
Fraction(*(1.75).as_integer_ratio())
```




    Fraction(7, 4)




```python
x, x+2,x+2.0,x+(1./3),x+(4./3),x+Fraction(4,3)
```




    (Fraction(1, 3),
     Fraction(7, 3),
     2.3333333333333335,
     0.6666666666666666,
     1.6666666666666665,
     Fraction(5, 3))




```python
4.0/3,(4.0/3).as_integer_ratio(),x, x+Fraction(*(4.0/3).as_integer_ratio())
```




    (1.3333333333333333,
     (6004799503160661, 4503599627370496),
     Fraction(1, 3),
     Fraction(22517998136852479, 13510798882111488))




```python
a = x + Fraction(*(4.0/3).as_integer_ratio())
```


```python
a, 22517998136852479/13510798882111488
```




    (Fraction(22517998136852479, 13510798882111488), 1.6666666666666665)




```python
a.limit_denominator(10)
```




    Fraction(5, 3)




```python
a.limit_denominator(10)
```




    Fraction(5, 3)




```python
x = set('abcde')
y = set('bdxyz')
```


```python
x,y
```




    ({'a', 'b', 'c', 'd', 'e'}, {'b', 'd', 'x', 'y', 'z'})




```python
'e' in x,x-y,x|y,x&y,x^y,x>y,x<y
```




    (True,
     {'a', 'c', 'e'},
     {'a', 'b', 'c', 'd', 'e', 'x', 'y', 'z'},
     {'b', 'd'},
     {'a', 'c', 'e', 'x', 'y', 'z'},
     False,
     False)




```python
(x|y)-(x&y)
```




    {'a', 'c', 'e', 'x', 'y', 'z'}




```python
z = x.intersection(y)
```


```python
z
```




    {'b', 'd'}




```python
z.add('SPAM')
```


```python
z
```




    {'SPAM', 'b', 'd'}




```python
z.update(set(['X','Y']))
```


```python
z
```




    {'SPAM', 'X', 'Y', 'b', 'd'}




```python
z.remove('b')
```


```python
z
```




    {'SPAM', 'X', 'Y', 'd'}



sets support len,for loops,and list comprehensions. Because they are unordered,though, they don't support sequence operations like indexing and slicing.


```python
for item in set('abc'): print(item*9)
```

    aaaaaaaaa
    bbbbbbbbb
    ccccccccc



```python
S = set([1,2,3])
```


```python
S | set([3,4])
```




    {1, 2, 3, 4}




```python
S.union([3,4])
```




    {1, 2, 3, 4}




```python
S.intersection((1,3,5))
```




    {1, 3}




```python
S.issubset(range(-5,5))
```




    True



An unordered collection of unique and immutable objects that supports operations corresponding to mathematical set theory.


```python
set([1,2,3,4])=={1,2,3,4}
```




    True




```python
set([1,2,3,4]),set('spam'),{1,2,3,4}
```




    ({1, 2, 3, 4}, {'a', 'm', 'p', 's'}, {1, 2, 3, 4})




```python
S = {'s','p','a','m'}
```


```python
S.add('alot')
```


```python
S
```




    {'a', 'alot', 'm', 'p', 's'}




```python
S1 = {1,2,3,4}
```


```python
S1 & {1,3}
```




    {1, 3}




```python
{1,5,3,6} | S1
```




    {1, 2, 3, 4, 5, 6}




```python
S1-{1,3,4}
```




    {2}




```python
S1>{1,3}
```




    True




```python
S1-{1,2,3,4}
```




    set()




```python
type({})
```




    dict




```python
S = set()
```


```python
S.add(1.23)
```


```python
S
```




    {1.23}




```python
{1,2,3} | {3,4}
```




    {1, 2, 3, 4}




```python
{1,2,3}.union([3,4]),{1,2,3}.union({3,4})
```




    ({1, 2, 3, 4}, {1, 2, 3, 4})




```python
{1,2,3}.union(set([3,4])),{1,2,3}.intersection((1,3,5))
```




    ({1, 2, 3, 4}, {1, 3})




```python
S = {1.23}
```

S.add([1,2,3])   TypeError: unhashable type: 'list'

S.add({'a':1})   TypeError: unhashable type: 'dict'


```python
S.add((1,2,3))
```


```python
S
```




    {(1, 2, 3), 1.23}




```python
S | {(4,5,6),(1,2,3)}
```




    {(1, 2, 3), (4, 5, 6), 1.23}




```python
(1,2,3) in S, (1,4,3) in S
```




    (True, False)




```python
{x**2 for x in [1,2,3,4]}
```




    {1, 4, 9, 16}




```python
{x for x in 'spam'}
```




    {'a', 'm', 'p', 's'}




```python
{c*5 for c in 'spam'}
```




    {'aaaaa', 'mmmmm', 'ppppp', 'sssss'}




```python
{c*4 for c in 'spamham'}
```




    {'aaaa', 'hhhh', 'mmmm', 'pppp', 'ssss'}




```python
S = {c*4 for c in 'spam'}
```


```python
S | {'mmmm','xxxx'}
```




    {'aaaa', 'mmmm', 'pppp', 'ssss', 'xxxx'}




```python
S & {'mmmm','xxxx'}
```




    {'mmmm'}




```python
L = [1,2,3,4,1,2,3,4,5,1,2,4,2,3]
```


```python
set(L) # filter duplicates out of other collections
```




    {1, 2, 3, 4, 5}




```python
L
```




    [1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 4, 2, 3]




```python
L = list(set(L))
```


```python
L
```




    [1, 2, 3, 4, 5]




```python
engineers = {'bob','sue','ann','vic'}
```


```python
managers = {'tom','sue'}
```


```python
'bob' in engineers
```




    True




```python
engineers & managers
```




    {'sue'}




```python
engineers | managers
```




    {'ann', 'bob', 'sue', 'tom', 'vic'}




```python
engineers - managers
```




    {'ann', 'bob', 'vic'}




```python
managers - engineers
```




    {'tom'}




```python
engineers > managers
```




    False




```python
{'bob','sue'}< engineers
```




    True




```python
(managers | engineers) > managers
```




    True




```python
managers ^ engineers == (managers|engineers) - (managers & engineers)
```




    True




```python
managers ^ engineers
```




    {'ann', 'bob', 'tom', 'vic'}




```python
(managers | engineers)-(managers^ engineers)
```




    {'sue'}




```python
type(True)
```




    bool




```python
isinstance(True,int)
```




    True




```python
True == 1
```




    True




```python
True is 1
```




    False




```python
True or False
```




    True




```python
True + 4
```




    5



Numeric Extensions----Numpy

# Chapter Summary

This chapter has taken a tour of Python’s numeric object types and the operations we can apply to them. Along the way, we met the standard integer and floating-point types, as well as some more exotic and less commonly used types such as complex numbers, fractions, and sets. We also explored Python’s expression syntax, type conversions, bitwise operations, and various literal forms for coding numbers in scripts.

# Test Your knowledge: Quiz


```python
2 * (3+4)
```




    14




```python
2*3+4
```




    10




```python
2+3*4
```




    14




```python
import math
```


```python
math.sqrt(144),pow(144,2)
```




    (12.0, 20736)




```python
type(1+2.0+3)
```




    float




```python
round(math.pi,9)
```




    3.141592654




```python
float(3)
```




    3.0




```python
math.trunc(math.pi)
```




    3




```python
math.floor(math.pi)
```




    3




```python
math.floor(-2.5)
```




    -3




```python
math.trunc(-2.5)
```




    -2




```python
oct(8),hex(7),bin(2)
```




    ('0o10', '0x7', '0b10')




```python
int('10',8),int('0x7',16),int('0b10',2)
```




    (8, 7, 2)



2e30e8663952cd971850bc49f9fa4d5ef291edbd
ipynb
Jupyter Notebook
Chapter 5 Numeric.ipynb
nickcafferry/Learning-Python-4th-Edition
6684afc3a97d9719c3cdb2d451959ac15cc896cd
MIT
2019-12-08T07:56:09.000Z
2019-12-08T07:56:09.000Z
Chapter 5 Numeric.ipynb
nickcafferry/Learning-Python-4th-Edition
6684afc3a97d9719c3cdb2d451959ac15cc896cd
MIT
Chapter 5 Numeric.ipynb
nickcafferry/Learning-Python-4th-Edition
6684afc3a97d9719c3cdb2d451959ac15cc896cd
MIT
Qwen/Qwen-72B
1. YES
2. YES