plot(Piecewise([[(0,1),x^2],[(1,2),1],[(2,3),x^2-3]]))
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|
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
|
|
s
12 12 |
s=34
|
|
s
34 34 |
t=7
|
|
t=t+1
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|
t
8 8 |
c,d,e=2,3,5
|
|
d
3 3 |
c
2 2 |
e
5 5 |
a = b = 1
(a,b)
(1, 1) (1, 1) |
f(x) = x^2 + x + 1
f(19)
381 381 |
f
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))
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