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