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
|
|
s
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
|
|
f
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])
|
|
A
{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 ])
|
|
B
{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])
|
|
M
{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 |
|
|