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
|
|
s
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 |
f
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))
|
|
|
|