# 기초수학-실습

## 2411 days 전, sky 작성

plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]]))
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
 12 12
sage: s=34 sage: s
 34 34
sage: t=7 sage: t=t+1 sage: t
 8 8
sage: t=7 sage: t=t/4.5 sage: t
 1.55555555555556 1.55555555555556
f(x)= x^2 + x + 1 f(123456789)
 15241578873647311 15241578873647311
 x |--> x^2 + x + 1 x |--> x^2 + x + 1
f(x=120)
 14521 14521
sage: [6,28,496,8128]
 [6, 28, 496, 8128] [6, 28, 496, 8128]
sage: [1,11..121]
 [1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121] [1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121]
sage: [1,4,16,25..81]
 [1, 4, 16, 25, 34, 43, 52, 61, 70, 79] [1, 4, 16, 25, 34, 43, 52, 61, 70, 79]
sage: [pi,4*pi..32]
 [pi, 4*pi, 7*pi, 10*pi] [pi, 4*pi, 7*pi, 10*pi]
A = Set([2,3,3,3,2,1,8,6,21,7,3]) A
 {1, 2, 3, 21, 6, 7, 8} {1, 2, 3, 21, 6, 7, 8}
sage: A.cardinality()
 7 7
sage: 8 in A
 True True
sage: 21 in A
 True True
sage: 124 in A
 False False
sage: 8 in A, 211 in A
 (True, False) (True, False)
sage: B = Set([8,6,17,-4,20, -2 ]) sage: B
 {17, 20, 6, 8, -4, -2} {17, 20, 6, 8, -4, -2}
sage: A.intersection(B)
 {8, 6} {8, 6}
sage: A.union(B)
 {1, 2, 3, 6, 7, 8, 17, 20, 21, -4, -2} {1, 2, 3, 6, 7, 8, 17, 20, 21, -4, -2}
sage: A.difference(B)
 {1, 2, 3, 21, 7} {1, 2, 3, 21, 7}
sage: B.difference(A)
 {17, 20, -4, -2} {17, 20, -4, -2}
sage: A.symmetric_difference(B)
 {1, 2, 3, 7, 17, 20, 21, -4, -2} {1, 2, 3, 7, 17, 20, 21, -4, -2}
sage: A = Set([1,2,3]); A
 {1, 2, 3} {1, 2, 3}
sage: powA = A.subsets(); powA
 Subsets of {1, 2, 3} Subsets of {1, 2, 3}
sage: pairsA = A.subsets(2); pairsA
 Subsets of {1, 2, 3} of size 2 Subsets of {1, 2, 3} of size 2
sage: [tan(0),tan(pi/4),tan(3*pi/4),tan(pi)]
 [0, 1, -1, 0] [0, 1, -1, 0]
A = Set([3,6,9..18]); A
 {18, 3, 6, 9, 12, 15} {18, 3, 6, 9, 12, 15}
sage: powA = A.subsets(); powA
 Subsets of {18, 3, 6, 9, 12, 15} Subsets of {18, 3, 6, 9, 12, 15}
sage: powA.cardinality()
 64 64
[tan(x)for x in [0,pi/4..pi]]
 [0, 1, Infinity, -1, 0] [0, 1, Infinity, -1, 0]
divmod(141,2)
 (70, 1) (70, 1)
14 // 4
 3 3
14 & 3
 2 2
14 % 3
 2 2
10305.divides(123)
 False False
5.divides(125)
 True True
12.divisors()
 [1, 2, 3, 4, 6, 12] [1, 2, 3, 4, 6, 12]
9000.divisors()
 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000] [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000]
(2^19-1).is_prime()
 True True
(2^19-1).divisors()
 [1, 524287] [1, 524287]
62.factor()
 2 * 31 2 * 31
factor(122)
 2 * 61 2 * 61
24.prime_divisors()
 [2, 3] [2, 3]
gcd(14,63)
 7 7
gcd(184,693)#서로소#
 1 1
lcm(14,21)
 42 42
divmod(956,98)
 (9, 74) (9, 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]
491.is_prime()
 True True
134.is_prime()
 False False
491.is_prime()
 True True
422.is_prime()
 False False
[ a.is_prime() for a in [1, 2, 3, 6, 167, 334, 501, 1002]]
 [False, True, True, False, True, False, False, False] [False, True, True, False, True, False, False, False]
gcd(2,5)
 1 1
gcd(4,10)
 2 2
gcd(18,51)
 3 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
max(1,5,8, 9999999999999999999999999)
 9999999999999999999999999 9999999999999999999999999
min(1/2,sin(pi),cos(pi/2))
 0 0
abs(-10)
 10 10
abs(4)
 4 4
plot (abs(x),(x, -3, 3))