def test_reduced_totient(): assert [reduced_totient(k) for k in range(1, 16)] == [ 1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4, ] assert reduced_totient(5005) == 60 assert reduced_totient(5006) == 2502 assert reduced_totient(5009) == 5008 assert reduced_totient(2**100) == 2**98 m = Symbol("m", integer=True) assert reduced_totient(m) assert reduced_totient(m).subs(m, 2**3 * 3**10) == 3**10 - 3**9 assert summation(reduced_totient(m), (m, 1, 16)) == 68 n = Symbol("n", integer=True, positive=True) assert reduced_totient(n).is_integer
def test_generate(): from sympy.ntheory.generate import sieve sieve._reset() assert nextprime(-4) == 2 assert nextprime(2) == 3 assert nextprime(5) == 7 assert nextprime(12) == 13 assert prevprime(3) == 2 assert prevprime(7) == 5 assert prevprime(13) == 11 assert prevprime(19) == 17 assert prevprime(20) == 19 sieve.extend_to_no(9) assert sieve._list[-1] == 23 assert sieve._list[-1] < 31 assert 31 in sieve assert nextprime(90) == 97 assert nextprime(10**40) == (10**40 + 121) assert prevprime(97) == 89 assert prevprime(10**40) == (10**40 - 17) assert list(sieve.primerange(10, 1)) == [] assert list(primerange(10, 1)) == [] assert list(primerange(2, 7)) == [2, 3, 5] assert list(primerange(2, 10)) == [2, 3, 5, 7] assert list(primerange(1050, 1100)) == [1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097] s = Sieve() for i in range(30, 2350, 376): for j in range(2, 5096, 1139): A = list(s.primerange(i, i + j)) B = list(primerange(i, i + j)) assert A == B s = Sieve() assert s[10] == 29 assert nextprime(2, 2) == 5 raises(ValueError, lambda: totient(0)) raises(ValueError, lambda: reduced_totient(0)) raises(ValueError, lambda: primorial(0)) assert mr(1, [2]) is False func = lambda i: (i**2 + 1) % 51 assert next(cycle_length(func, 4)) == (6, 2) assert list(cycle_length(func, 4, values=True)) == \ [17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14] assert next(cycle_length(func, 4, nmax=5)) == (5, None) assert list(cycle_length(func, 4, nmax=5, values=True)) == \ [17, 35, 2, 5, 26] sieve.extend(3000) assert nextprime(2968) == 2969 assert prevprime(2930) == 2927 raises(ValueError, lambda: prevprime(1))
def test_reduced_totient(): assert [reduced_totient(k) for k in range(1, 16)] == \ [1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4] assert reduced_totient(5005) == 60 assert reduced_totient(5006) == 2502 assert reduced_totient(5009) == 5008 assert reduced_totient(2**100) == 2**98 m = Symbol("m", integer=True) assert reduced_totient(m) assert reduced_totient(m).subs(m, 2**3*3**10) == 3**10 - 3**9 assert summation(reduced_totient(m), (m, 1, 16)) == 68 n = Symbol("n", integer=True, positive=True) assert reduced_totient(n).is_integer
def test_generate(): assert nextprime(-4) == 2 assert nextprime(2) == 3 assert nextprime(5) == 7 assert nextprime(12) == 13 assert nextprime(90) == 97 assert nextprime(10**40) == (10**40 + 121) assert prevprime(3) == 2 assert prevprime(7) == 5 assert prevprime(13) == 11 assert prevprime(97) == 89 assert prevprime(10**40) == (10**40 - 17) assert list(primerange(2, 7)) == [2, 3, 5] assert list(primerange(2, 10)) == [2, 3, 5, 7] assert list(primerange(1050, 1100)) == [1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097] s = Sieve() for i in range(30, 2350, 376): for j in range(2, 5096, 1139): A = list(s.primerange(i, i + j)) B = list(primerange(i, i + j)) assert A == B s = Sieve() assert s[10] == 29 assert nextprime(2, 2) == 5 raises(ValueError, lambda: totient(0)) raises(ValueError, lambda: reduced_totient(0)) raises(ValueError, lambda: primorial(0)) assert mr(1, [2]) is False func = lambda i: (i**2 + 1) % 51 assert next(cycle_length(func, 4)) == (6, 2) assert list(cycle_length(func, 4, values=True)) == \ [17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14] assert next(cycle_length(func, 4, nmax=5)) == (5, None) assert list(cycle_length(func, 4, nmax=5, values=True)) == \ [17, 35, 2, 5, 26]
def test_generate(): from sympy.ntheory.generate import sieve sieve._reset() assert nextprime(-4) == 2 assert nextprime(2) == 3 assert nextprime(5) == 7 assert nextprime(12) == 13 assert prevprime(3) == 2 assert prevprime(7) == 5 assert prevprime(13) == 11 assert prevprime(19) == 17 assert prevprime(20) == 19 sieve.extend_to_no(9) assert sieve._list[-1] == 23 assert sieve._list[-1] < 31 assert 31 in sieve assert nextprime(90) == 97 assert nextprime(10**40) == (10**40 + 121) assert prevprime(97) == 89 assert prevprime(10**40) == (10**40 - 17) assert list(sieve.primerange(10, 1)) == [] assert list(sieve.primerange(5, 9)) == [5, 7] sieve._reset(prime=True) assert list(sieve.primerange(2, 12)) == [2, 3, 5, 7, 11] assert list(sieve.totientrange(5, 15)) == [4, 2, 6, 4, 6, 4, 10, 4, 12, 6] sieve._reset(totient=True) assert list(sieve.totientrange(3, 13)) == [2, 2, 4, 2, 6, 4, 6, 4, 10, 4] assert list(sieve.totientrange(900, 1000)) == [totient(x) for x in range(900, 1000)] assert list(sieve.totientrange(0, 1)) == [] assert list(sieve.totientrange(1, 2)) == [1] assert list(sieve.mobiusrange(5, 15)) == [-1, 1, -1, 0, 0, 1, -1, 0, -1, 1] sieve._reset(mobius=True) assert list(sieve.mobiusrange(3, 13)) == [-1, 0, -1, 1, -1, 0, 0, 1, -1, 0] assert list(sieve.mobiusrange(1050, 1100)) == [mobius(x) for x in range(1050, 1100)] assert list(sieve.mobiusrange(0, 1)) == [] assert list(sieve.mobiusrange(1, 2)) == [1] assert list(primerange(10, 1)) == [] assert list(primerange(2, 7)) == [2, 3, 5] assert list(primerange(2, 10)) == [2, 3, 5, 7] assert list(primerange(1050, 1100)) == [1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097] s = Sieve() for i in range(30, 2350, 376): for j in range(2, 5096, 1139): A = list(s.primerange(i, i + j)) B = list(primerange(i, i + j)) assert A == B s = Sieve() assert s[10] == 29 assert nextprime(2, 2) == 5 raises(ValueError, lambda: totient(0)) raises(ValueError, lambda: reduced_totient(0)) raises(ValueError, lambda: primorial(0)) assert mr(1, [2]) is False func = lambda i: (i**2 + 1) % 51 assert next(cycle_length(func, 4)) == (6, 2) assert list(cycle_length(func, 4, values=True)) == \ [17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14] assert next(cycle_length(func, 4, nmax=5)) == (5, None) assert list(cycle_length(func, 4, nmax=5, values=True)) == \ [17, 35, 2, 5, 26] sieve.extend(3000) assert nextprime(2968) == 2969 assert prevprime(2930) == 2927 raises(ValueError, lambda: prevprime(1))