기초수학-실습_Hong Seok woo

2028 days 전, hsw1474@naver.com 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 False 
       
True
True
True and False 
       
False
False
sage: 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=34 
       
       
34
34
t=7 
       
t=t+1 
       
       
8
8
c,d,e=2,3,5 
       
       
3
3
       
2
2
       
5
5
a = b = 1 (a,b) 
       
(1, 1)
(1, 1)
f(x) = x^2 + x + 1 f(19) 
       
381
381
       
x |--> x^2 + x + 1
x |--> x^2 + x + 1
f(x=3) 
       
13
13
[6,28,496,8128] 
       
[6, 28, 496, 8128]
[6, 28, 496, 8128]
[2,4,6..10] 
       
[2, 4, 6, 8, 10]
[2, 4, 6, 8, 10]
[2,4..10] 
       
[2, 4, 6, 8, 10]
[2, 4, 6, 8, 10]
[1,3..9] 
       
[1, 3, 5, 7, 9]
[1, 3, 5, 7, 9]
[1,11..40] 
       
[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]
[2,3,3,3,2,1,8,6,3] 
       
[2, 3, 3, 3, 2, 1, 8, 6, 3]
[2, 3, 3, 3, 2, 1, 8, 6, 3]
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
9 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).cardinality() 
       
9
9
A.intersection(B) 
       
{8, 6}
{8, 6}
A.difference(B) 
       
{1, 2, 3}
{1, 2, 3}
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}
powA.cardinality() 
       
8
8
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(x) 
       
tan(x)
tan(x)
tan(0) 
       
0
0
tan(pi/4) 
       
1
1
tan(pi/2) 
       
Infinity
Infinity
tan(3*pi/4) 
       
-1
-1
tan(pi) 
       
0
0
[3,6..20] 
       
[3, 6, 9, 12, 15, 18]
[3, 6, 9, 12, 15, 18]
M= Set[3,6..20] M 
       
{18, 3, 6, 9, 12, 15}
{18, 3, 6, 9, 12, 15}
powM = M.subsets(); powM 
       
Subsets of {18, 3, 6, 9, 12, 15}
Subsets of {18, 3, 6, 9, 12, 15}
powM.cardinality() 
       
64
64
tan(x) 
       
tan(x)
tan(x)
[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
12.divisors() 
       
[1, 2, 3, 4, 6, 12]
[1, 2, 3, 4, 6, 12]
(2^19-1).is_prime() 
       
True
True
153.is_prime() 
       
False
False
62.factor(62) 
       
2 * 31
2 * 31
24.prime_divisors() 
       
[2, 3]
[2, 3]
gcd(14,63) 
       
7
7
lcm(4,5) 
       
20
20
divmod(956,98) 
       
(9, 74)
(9, 74)
98*9+74 
       
956
956
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]
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
g=gcd(18,51) 
       
l=lcm(18,51) 
       
g*l==18*51 
       
True
True
max(14,5,8,-3,100) 
       
100
100
plot(abs(x), (x, -3, 3))