16년1월12일 기초수학 실습 (신성주)

2029 days 전, godseongjoo 작성

plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]])) 
       
not True 
       
False
False
RR(sqrt(9)) 
       
3.00000000000000
3.00000000000000
RR(sqrt(2)) 
       
1.41421356237310
1.41421356237310
not false 
       
True
True
not true 
       
False
False
True and False 
       
False
False
True and True 
       
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
24.prime_divisors() 
       
[2, 3]
[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
s+s 
       
24
24
s^s 
       
8916100448256
8916100448256
t=7 
       
t+1 
       
8
8
a,b=1,2 
       
c,d,e=2,3,5 
       
a+b+c+d+e 
       
13
13
f = x^2 + x + 1 
       
       
x^2 + x + 1
x^2 + x + 1
x=3 
       
f(x=3) 
       
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]
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
10 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.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 = 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}]
[-9,-7..29] 
       
[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27,
29]
[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
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([3,6,9,12,15,18]) 
       
       
{18, 3, 6, 9, 12, 15}
{18, 3, 6, 9, 12, 15}
powM = M.subsets() 
       
powM = M.subsets(); powB 
       
Subsets of {18, 3, 6, 9, 12, 15}
Subsets of {18, 3, 6, 9, 12, 15}
powM.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}]
M.cardinality 
       
<bound method Set_object_enumerated_with_category.cardinality of {18,
3, 6, 9, 12, 15}>
<bound method Set_object_enumerated_with_category.cardinality of {18, 3, 6, 9, 12, 15}>
2^6 
       
64
64
[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]
101.divisors() 
       
[1, 101]
[1, 101]
(2^19-1).is_prime() 
       
True
True
153.is_prime() 
       
False
False
divmod(956,98) 
       
(9, 74)
(9, 74)
234878//3 
       
78292
78292
divmod(234878,3) 
       
(78292, 2)
(78292, 2)
134.divisors(),491.divisors(),422.divisors(),1002.divisors() 
       
([1, 2, 67, 134], [1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334,
501, 1002])
([1, 2, 67, 134], [1, 491], [1, 2, 211, 422], [1, 2, 3, 6, 167, 334, 501, 1002])
gcd(2,5) 
       
1
1
gcd(4,10) 
       
2
2
gcd(18,51) 
       
3
3
lcm(2,5) 
       
10
10
lcm(4,10) 
       
20
20
lcm(18,51) 
       
306
306
gcd(2,5)*lcm(2,5) 
       
10
10
gcd(4,10)*lcm(4,10) 
       
40
40
gcd(18,51)*lcm(18,51) 
       
918
918
max(1,5,8) 
       
8
8
min(1/2,1/3) 
       
1/3
1/3
abs(-10) 
       
10
10
abs(4) 
       
4
4