131.sagews

8.1. [2,5,7,9]

permutations([2,5,7,9])

[[2, 5, 7, 9], [2, 5, 9, 7], [2, 7, 5, 9], [2, 7, 9, 5], [2, 9, 5, 7], [2, 9, 7, 5], [5, 2, 7, 9], [5, 2, 9, 7], [5, 7, 2, 9], [5, 7, 9, 2], [5, 9, 2, 7], [5, 9, 7, 2], [7, 2, 5, 9], [7, 2, 9, 5], [7, 5, 2, 9], [7, 5, 9, 2], [7, 9, 2, 5], [7, 9, 5, 2], [9, 2, 5, 7], [9, 2, 7, 5], [9, 5, 2, 7], [9, 5, 7, 2], [9, 7, 2, 5], [9, 7, 5, 2]]

number_of_permutations([2,5,7,9])

24

8.2. ['f', 'g', 's']

mset=['f','g','s']
permutations(mset)

[['f', 'g', 's'], ['f', 's', 'g'], ['g', 'f', 's'], ['g', 's', 'f'], ['s', 'f', 'g'], ['s', 'g', 'f']]

number_of_permutations(mset)

6

8.3. 2 2,5,7,9]

mset=[2,5,7,9]
arrangements(mset,2)

[[2, 5], [2, 7], [2, 9], [5, 2], [5, 7], [5, 9], [7, 2], [7, 5], [7, 9], [9, 2], [9, 5], [9, 7]]

number_of_arrangements(mset,2)

12

8.4. 3 2,5,7,9].

X=permutations_iterator(mset,3)
[x for x in X]

[[2, 5, 7], [2, 5, 9], [2, 7, 5], [2, 7, 9], [2, 9, 5], [2, 9, 7], [5, 2, 7], [5, 2, 9], [5, 7, 2], [5, 7, 9], [5, 9, 2], [5, 9, 7], [7, 2, 5], [7, 2, 9], [7, 5, 2], [7, 5, 9], [7, 9, 2], [7, 9, 5], [9, 2, 5], [9, 2, 7], [9, 5, 2], [9, 5, 7], [9, 7, 2], [9, 7, 5]]

8.5. 2 2,5,7,9]

combinations(mset,2)

[[2, 5], [2, 7], [2, 9], [5, 7], [5, 9], [7, 9]]

number_of_combinations(mset,2)

6

8.6. 3 2,5,7,9].

X=combinations_iterator(mset,3)
[x for x in X]

[[2, 5, 7], [2, 5, 9], [2, 7, 9], [5, 7, 9]]

8.7. 2 2,5,7,9]

tuples(mset,2)

[[2, 2], [5, 2], [7, 2], [9, 2], [2, 5], [5, 5], [7, 5], [9, 5], [2, 7], [5, 7], [7, 7], [9, 7], [2, 9], [5, 9], [7, 9], [9, 9]]

number_of_tuples(mset,2)

16

8.8. 27- .

fibonacci(27)

196418

8.9. .

[fibonacci(i) for i in range(28)]

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418]

8.10. 8-

euler_number(8)

1385

8.11.

[euler_number(i) for i in range(9)]

[1, 0, -1, 0, 5, 0, -61, 0, 1385]