# 기초수학 실습

## 1986 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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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