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 True
False False |
not False
True True |
True and False
False False |
True and True
True True |
True or False
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 |
1 == 0
False False |
not(True or False) == True and False
False False |
1 != 1
False False |
1 != 0
True True |
1 <> 0
True True |
1 > 2
False False |
2 > 1
True True |
4.1 < 5.7
True True |
6 < 5
False False |
1 >= .99999
True True |
1 <= 35
True True |
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=34
s
34 34 |
t=7
t=t+1
t
8 8 |
a,b=1,2
a
1 1 |
b
2 2 |
c,d,e=2,3,5
c,d,e
(2, 3, 5) (2, 3, 5) |
a = b = 1
a
1 1 |
b
1 1 |
f(x) = x^2 + x + 1
|
|
x=3
f(x)
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] |
x = pi * 2
x = x / 2
x
pi 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
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}]
|
[tan(x) for x in [0,pi/4..pi]]
[0, 1, Infinity, -1, 0] [0, 1, Infinity, -1, 0] |
M = Set([3,6..20])
M.subsets().cardinality()
64 64 |
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 |
62.factor()
2 * 31 2 * 31 |
63.factor()
3^2 * 7 3^2 * 7 |
24.prime_divisors()
[2, 3] [2, 3] |
63.prime_divisors()
[3, 7] [3, 7] |
gcd(14,63)
7 7 |
gcd(15,19)
1 1 |
lcm(4,5)
20 20 |
lcm(14,21)
42 42 |
divmod(956,98)
(9, 74) (9, 74) |
956//98
9 9 |
956%98
74 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] |
[is_prime(x) for x in divisors(134)]
[False, True, True, False] [False, True, True, False] |
[is_prime(x) for x in divisors(491)]
[False, True] [False, True] |
[is_prime(x) for x in divisors(422)]
[False, True, True, False] [False, True, True, False] |
[is_prime(x) for x in divisors(1002)]
[False, True, True, False, True, False, False, False] [False, True, True, False, True, False, False, False] |
[gcd(x) for x in [(2,5),(4,10),(18,51)]]
[1, 2, 3] [1, 2, 3] |
[lcm(x) for x in [(2,5),(4,10),(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 |
min(1/2,1/3)
1/3 1/3 |
abs(-10)
10 10 |
abs(4)
4 4 |
plot(abs(4))
|
|
|
|