# 기초수학실습_김재섭

## 1984 days 전, jakl7436 작성

plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]]))
plot(sin(x), (x,0,10), plot_points=20, linestyle='', marker='.')
p1=plot(x*sin(3/x), x, -0.5,0, color='blue') p2=plot(x*sin(3/x), x, 0,0.5, color='red') show(p1+p2, ymax=0.3, ymin=-0.3, aspect_ratio=1)
1 in ZZ
 True True
1/2 in ZZ
 False False
i^2
 -1 -1
i^3
 -I -I
QQ(.5)
 1/2 1/2
1 != 1
 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
s=49303
 49303 49303
t=7
t=t+1
 8 8
a,b=1,2
a,b
 (1, 2) (1, 2)
a=4 b=5
a,b
 (4, 5) (4, 5)

f = x^2 + x + 1 f
 x^2 + x + 1 x^2 + x + 1
x=3
f(x=3)
 13 13
f(x) = x^2 + x + 1 f(3)
 13 13
f(x)=x^6 + x + 356 f(3)
 1088 1088
[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..80]
 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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]
[4..9]
 [4, 5, 6, 7, 8, 9] [4, 5, 6, 7, 8, 9]
[3,7..67]
 [3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67] [3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67]
[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
 True True
6950 in A
 False False
B = Set([8,6,17,-4,20, -2 ])
 {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.union(B).cardinality()
 9 9
A.intersection(B)
 {8, 6} {8, 6}
A.intersection(B).cardinality()
 2 2
A.difference(B)
 {1, 2, 3} {1, 2, 3}
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}
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 = A.subsets(2); pairsA
 Subsets of {1, 2, 3} of size 2 Subsets of {1, 2, 3} of size 2
pairsA.list()
 [{1, 2}, {1, 3}, {2, 3}] [{1, 2}, {1, 3}, {2, 3}]
tan(0)
 0 0
tan(pi/4)
 1 1
tan(pi/2)
 Infinity Infinity
tan(3*pi/4)
 -1 -1
tan(pi)
 0 0
M = Set([3,6..20]) M
 {18, 3, 6, 9, 12, 15} {18, 3, 6, 9, 12, 15}
M.cardinality()
 6 6
[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]
(2^19-1).is_prime()
 True True
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)
234878.divides(3)
 False False
134.divisors()
 [1, 2, 67, 134] [1, 2, 67, 134]
491.divisors()
 [1, 491] [1, 491]
422.divisors()
 [1, 2, 211, 422] [1, 2, 211, 422]
1002.divisors()
 [1, 2, 3, 6, 167, 334, 501, 1002] [1, 2, 3, 6, 167, 334, 501, 1002]
134.prime_divisors()
 [2, 67] [2, 67]
491.prime_divisors()
 [491] [491]
422.prime_divisors()
 [2, 211] [2, 211]
1002.prime_divisors()
 [2, 3, 167] [2, 3, 167]
gcd(2,5)
 1 1
lcm(2,5)
 10 10
2*5
 10 10
gcd(4,10)
 2 2
lcm(4,10)
 20 20
4*10
 40 40
gcd(18,51)
 3 3
lcm(18,51)
 306 306
18*51
 918 918
max(1020383,2181981,3214322)
 3214322 3214322
min(-545,-656,-4563)
 -4563 -4563
abs(-10)
 10 10
plot(abs(x), (x, -4, 4))