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- from sympy.combinatorics.group_numbers import (is_nilpotent_number,
- is_abelian_number, is_cyclic_number, _holder_formula, groups_count)
- from sympy.ntheory.factor_ import factorint
- from sympy.ntheory.generate import prime
- from sympy.testing.pytest import raises
- from sympy import randprime
- def test_is_nilpotent_number():
- assert is_nilpotent_number(21) == False
- assert is_nilpotent_number(randprime(1, 30)**12) == True
- raises(ValueError, lambda: is_nilpotent_number(-5))
- A056867 = [1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19,
- 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45,
- 47, 49, 51, 53, 59, 61, 64, 65, 67, 69, 71, 73,
- 77, 79, 81, 83, 85, 87, 89, 91, 95, 97, 99]
- for n in range(1, 100):
- assert is_nilpotent_number(n) == (n in A056867)
- def test_is_abelian_number():
- assert is_abelian_number(4) == True
- assert is_abelian_number(randprime(1, 2000)**2) == True
- assert is_abelian_number(randprime(1000, 100000)) == True
- assert is_abelian_number(60) == False
- assert is_abelian_number(24) == False
- raises(ValueError, lambda: is_abelian_number(-5))
- A051532 = [1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25,
- 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53,
- 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87,
- 89, 91, 95, 97, 99]
- for n in range(1, 100):
- assert is_abelian_number(n) == (n in A051532)
- A003277 = [1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29,
- 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61,
- 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89,
- 91, 95, 97]
- def test_is_cyclic_number():
- assert is_cyclic_number(15) == True
- assert is_cyclic_number(randprime(1, 2000)**2) == False
- assert is_cyclic_number(randprime(1000, 100000)) == True
- assert is_cyclic_number(4) == False
- raises(ValueError, lambda: is_cyclic_number(-5))
- for n in range(1, 100):
- assert is_cyclic_number(n) == (n in A003277)
- def test_holder_formula():
- # semiprime
- assert _holder_formula({3, 5}) == 1
- assert _holder_formula({5, 11}) == 2
- # n in A003277 is always 1
- for n in A003277:
- assert _holder_formula(set(factorint(n).keys())) == 1
- # otherwise
- assert _holder_formula({2, 3, 5, 7}) == 12
- def test_groups_count():
- A000001 = [0, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1,
- 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2,
- 5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2,
- 14, 1, 6, 1, 4, 2, 2, 1, 52, 2, 5, 1, 5,
- 1, 15, 2, 13, 2, 2, 1, 13, 1, 2, 4, 267,
- 1, 4, 1, 5, 1, 4, 1, 50, 1, 2, 3, 4, 1,
- 6, 1, 52, 15, 2, 1, 15, 1, 2, 1, 12, 1,
- 10, 1, 4, 2]
- for n in range(1, len(A000001)):
- try:
- assert groups_count(n) == A000001[n]
- except ValueError:
- pass
- A000679 = [1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289]
- for e in range(1, len(A000679)):
- assert groups_count(2**e) == A000679[e]
- A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645]
- for e in range(1, len(A090091)):
- assert groups_count(3**e) == A090091[e]
- A090130 = [1, 1, 2, 5, 15, 77, 684, 34297]
- for e in range(1, len(A090130)):
- assert groups_count(5**e) == A090130[e]
- A090140 = [1, 1, 2, 5, 15, 83, 860, 113147]
- for e in range(1, len(A090140)):
- assert groups_count(7**e) == A090140[e]
- A232105 = [51, 67, 77, 83, 87, 97, 101, 107, 111, 125, 131,
- 145, 149, 155, 159, 173, 183, 193, 203, 207, 217]
- for i in range(len(A232105)):
- assert groups_count(prime(i+1)**5) == A232105[i]
- A232106 = [267, 504, 684, 860, 1192, 1476, 1944, 2264, 2876,
- 4068, 4540, 6012, 7064, 7664, 8852, 10908, 13136]
- for i in range(len(A232106)):
- assert groups_count(prime(i+1)**6) == A232106[i]
- A232107 = [2328, 9310, 34297, 113147, 750735, 1600573,
- 5546909, 9380741, 23316851, 71271069, 98488755]
- for i in range(len(A232107)):
- assert groups_count(prime(i+1)**7) == A232107[i]
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