# 기초수학-실습 [길한얼]

## 2027 days 전, charta 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
 False False
1 != 1
 False False
1 != 0
 True True
1 <> 0
 True True
1 > 2
 False False
2 > 1
 True True
4.1 < 5.7
 True True
6 < 5
 False False
1 >= .99999
 True True
1 <= 35
 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 s
 34 34
t=7 t=t+1 t
 8 8
a,b=1,2 a
 1 1
 2 2
c,d,e=2,3,5 c,d,e
 (2, 3, 5) (2, 3, 5)
a = b = 1 a
 1 1
 1 1
f(x) = x^2 + x + 1
x=3 f(x)
 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]
[4..9]
 [4, 5, 6, 7, 8, 9] [4, 5, 6, 7, 8, 9]
[2,4..10]
 [2, 4, 6, 8, 10] [2, 4, 6, 8, 10]
[1,4..13]
 [1, 4, 7, 10, 13] [1, 4, 7, 10, 13]
[1,11..31]
 [1, 11, 21, 31] [1, 11, 21, 31]
[1,11..35]
 [1, 11, 21, 31] [1, 11, 21, 31]
[pi,4*pi..32]
 [pi, 4*pi, 7*pi, 10*pi] [pi, 4*pi, 7*pi, 10*pi]
x = pi * 2 x = x / 2 x
 pi pi
A=Set([2,3,3,3,2,1,8,6,3]) A
 {8, 1, 2, 3, 6} {8, 1, 2, 3, 6}
A.cardinality()
 5 5
8 in A
 True True
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.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}]
[tan(x) for x in [0,pi/4..pi]]
 [0, 1, Infinity, -1, 0] [0, 1, Infinity, -1, 0]
M = Set([3,6..20]) M.subsets().cardinality()
 64 64
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]
63.prime_divisors()
 [3, 7] [3, 7]
gcd(14,63)
 7 7
gcd(15,19)
 1 1
lcm(4,5)
 20 20
lcm(14,21)
 42 42
divmod(956,98)
 (9, 74) (9, 74)
956//98
 9 9
956%98
 74 74
3.divides(234878)
 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]
[is_prime(x) for x in divisors(134)]
 [False, True, True, False] [False, True, True, False]
[is_prime(x) for x in divisors(491)]
 [False, True] [False, True]
[is_prime(x) for x in divisors(422)]
 [False, True, True, False] [False, True, True, False]
[is_prime(x) for x in divisors(1002)]
 [False, True, True, False, True, False, False, False] [False, True, True, False, True, False, False, False]
[gcd(x) for x in [(2,5),(4,10),(18,51)]]
 [1, 2, 3] [1, 2, 3]
[lcm(x) for x in [(2,5),(4,10),(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
abs(-10)
 10 10
abs(4)
 4 4
plot(abs(4))