def test_float_int():
assert int(float(sqrt(10))) == int(sqrt(10))
assert int(pi**1000) % 10 == 2
assert int(Float('1.123456789012345678901234567890e20', '')) == \
long(112345678901234567890)
assert int(Float('1.123456789012345678901234567890e25', '')) == \
long(11234567890123456789012345)
# decimal forces float so it's not an exact integer ending in 000000
assert int(Float('1.123456789012345678901234567890e35', '')) == \
112345678901234567890123456789000192
assert int(Float('123456789012345678901234567890e5', '')) == \
12345678901234567890123456789000000
assert Integer(Float('1.123456789012345678901234567890e20', '')) == \
112345678901234567890
assert Integer(Float('1.123456789012345678901234567890e25', '')) == \
11234567890123456789012345
# decimal forces float so it's not an exact integer ending in 000000
assert Integer(Float('1.123456789012345678901234567890e35', '')) == \
112345678901234567890123456789000192
assert Integer(Float('123456789012345678901234567890e5', '')) == \
12345678901234567890123456789000000
assert Float('123000e-2','') == Float('1230.00', '')
assert Float('123000e2','') == Float('12300000', '')
assert int(1 + Rational('.9999999999999999999999999')) == 1
assert int(pi/1e20) == 0
assert int(1 + pi/1e20) == 1
assert int(Add(1.2, -2, evaluate=False)) == int(1.2 - 2)
assert int(Add(1.2, +2, evaluate=False)) == int(1.2 + 2)
assert int(Add(1 + Float('.99999999999999999', ''), evaluate=False)) == 1
raises(TypeError, lambda: float(x))
raises(TypeError, lambda: float(sqrt(-1)))
assert int(12345678901234567890 + cos(1)**2 + sin(1)**2) == \
12345678901234567891
def test_evalf_integer_parts():
a = floor(log(8) / log(2) - exp(-1000), evaluate=False)
b = floor(log(8) / log(2), evaluate=False)
assert a.evalf() == 3
assert b.evalf() == 3
# equals, as a fallback, can still fail but it might succeed as here
assert ceiling(10 * (sin(1)**2 + cos(1)**2)) == 10
assert int(floor(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336800)
assert int(ceiling(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336801)
assert int(
floor((GoldenRatio**999 / sqrt(5) +
Rational(1, 2))).evalf(1000)) == fibonacci(999)
assert int(
floor((GoldenRatio**1000 / sqrt(5) +
Rational(1, 2))).evalf(1000)) == fibonacci(1000)
assert ceiling(x).evalf(subs={x: 3}) == 3
assert ceiling(x).evalf(subs={x: 3 * I}) == 3 * I
assert ceiling(x).evalf(subs={x: 2 + 3 * I}) == 2 + 3 * I
assert ceiling(x).evalf(subs={x: 3.}) == 3
assert ceiling(x).evalf(subs={x: 3. * I}) == 3 * I
assert ceiling(x).evalf(subs={x: 2. + 3 * I}) == 2 + 3 * I
assert float((floor(1.5, evaluate=False) + 1 / 9).evalf()) == 1 + 1 / 9
assert float((floor(0.5, evaluate=False) + 20).evalf()) == 20
def test_evalf_integer_parts():
a = floor(log(8)/log(2) - exp(-1000), evaluate=False)
b = floor(log(8)/log(2), evaluate=False)
assert a.evalf() == 3
assert b.evalf() == 3
# equals, as a fallback, can still fail but it might succeed as here
assert ceiling(10*(sin(1)**2 + cos(1)**2)) == 10
assert int(floor(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336800)
assert int(ceiling(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336801)
assert int(floor((GoldenRatio**999 / sqrt(5) + Rational(1, 2)))
.evalf(1000)) == fibonacci(999)
assert int(floor((GoldenRatio**1000 / sqrt(5) + Rational(1, 2)))
.evalf(1000)) == fibonacci(1000)
assert ceiling(x).evalf(subs={x: 3}) == 3
assert ceiling(x).evalf(subs={x: 3*I}) == 3*I
assert ceiling(x).evalf(subs={x: 2 + 3*I}) == 2 + 3*I
assert ceiling(x).evalf(subs={x: 3.}) == 3
assert ceiling(x).evalf(subs={x: 3.*I}) == 3*I
assert ceiling(x).evalf(subs={x: 2. + 3*I}) == 2 + 3*I
assert float((floor(1.5, evaluate=False)+1/9).evalf()) == 1 + 1/9
assert float((floor(0.5, evaluate=False)+20).evalf()) == 20
def test_float_int():
assert int(float(sqrt(10))) == int(sqrt(10))
assert int(pi**1000) % 10 == 2
assert int(Float('1.123456789012345678901234567890e20', '')) == \
long(112345678901234567890)
assert int(Float('1.123456789012345678901234567890e25', '')) == \
long(11234567890123456789012345)
# decimal forces float so it's not an exact integer ending in 000000
assert int(Float('1.123456789012345678901234567890e35', '')) == \
112345678901234567890123456789000192
assert int(Float('123456789012345678901234567890e5', '')) == \
12345678901234567890123456789000000
assert Integer(Float('1.123456789012345678901234567890e20', '')) == \
112345678901234567890
assert Integer(Float('1.123456789012345678901234567890e25', '')) == \
11234567890123456789012345
# decimal forces float so it's not an exact integer ending in 000000
assert Integer(Float('1.123456789012345678901234567890e35', '')) == \
112345678901234567890123456789000192
assert Integer(Float('123456789012345678901234567890e5', '')) == \
12345678901234567890123456789000000
assert Float('123000e-2','') == Float('1230.00', '')
assert Float('123000e2','') == Float('12300000', '')
assert int(1 + Rational('.9999999999999999999999999')) == 1
assert int(pi/1e20) == 0
assert int(1 + pi/1e20) == 1
assert int(Add(1.2, -2, evaluate=False)) == int(1.2 - 2)
assert int(Add(1.2, +2, evaluate=False)) == int(1.2 + 2)
assert int(Add(1 + Float('.99999999999999999', ''), evaluate=False)) == 1
raises(TypeError, lambda: float(x))
raises(TypeError, lambda: float(sqrt(-1)))
assert int(12345678901234567890 + cos(1)**2 + sin(1)**2) == \
12345678901234567891
def test_Catalan_EulerGamma_prec():
n = GoldenRatio
f = Float(n.n(), 5)
assert f._mpf_ == (0, long(212079), -17, 18)
assert f._prec == 20
assert n._as_mpf_val(20) == f._mpf_
n = EulerGamma
f = Float(n.n(), 5)
assert f._mpf_ == (0, long(302627), -19, 19)
assert f._prec == 20
assert n._as_mpf_val(20) == f._mpf_
def test_dmp_eval_in():
assert dmp_eval_in(
f_6, -2, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), -2, 3, ZZ)
assert dmp_eval_in(
f_6, 7, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), 7, 3, ZZ)
assert dmp_eval_in(f_6, -2, 2, 3, ZZ) == dmp_swap(
dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), -2, 3, ZZ), 0, 1, 2, ZZ)
assert dmp_eval_in(f_6, 7, 2, 3, ZZ) == dmp_swap(
dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), 7, 3, ZZ), 0, 1, 2, ZZ)
f = [[[long(45)]], [[]], [[]], [[long(-9)], [-1], [], [long(3), long(0), long(10), long(0)]]]
assert dmp_eval_in(f, -2, 2, 2, ZZ) == \
[[45], [], [], [-9, -1, 0, -44]]
def test_dmp_eval_in():
assert dmp_eval_in(
f_6, -2, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), -2, 3, ZZ)
assert dmp_eval_in(
f_6, 7, 1, 3, ZZ) == dmp_eval(dmp_swap(f_6, 0, 1, 3, ZZ), 7, 3, ZZ)
assert dmp_eval_in(f_6, -2, 2, 3, ZZ) == dmp_swap(
dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), -2, 3, ZZ), 0, 1, 2, ZZ)
assert dmp_eval_in(f_6, 7, 2, 3, ZZ) == dmp_swap(
dmp_eval(dmp_swap(f_6, 0, 2, 3, ZZ), 7, 3, ZZ), 0, 1, 2, ZZ)
f = [[[long(45)]], [[]], [[]], [[long(-9)], [-1], [], [long(3), long(0), long(10), long(0)]]]
assert dmp_eval_in(f, -2, 2, 2, ZZ) == \
[[45], [], [], [-9, -1, 0, -44]]
def test_measure_partial():
#Basic test of collapse of entangled two qubits (Bell States)
state = Qubit('01') + Qubit('10')
assert measure_partial(state, (0,)) == \
[(Qubit('10'), Rational(1, 2)), (Qubit('01'), Rational(1, 2))]
assert measure_partial(state, long(0)) == \
[(Qubit('10'), Rational(1, 2)), (Qubit('01'), Rational(1, 2))]
assert measure_partial(state, (0,)) == \
measure_partial(state, (1,))[::-1]
#Test of more complex collapse and probability calculation
state1 = sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111')
assert measure_partial(state1, (0,)) == \
[(sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111'), 1)]
assert measure_partial(state1, (1, 2)) == measure_partial(state1, (3, 4))
assert measure_partial(state1, (1, 2, 3)) == \
[(Qubit('00001'), Rational(2, 3)), (Qubit('11111'), Rational(1, 3))]
#test of measuring multiple bits at once
state2 = Qubit('1111') + Qubit('1101') + Qubit('1011') + Qubit('1000')
assert measure_partial(state2, (0, 1, 3)) == \
[(Qubit('1000'), Rational(1, 4)), (Qubit('1101'), Rational(1, 4)),
(Qubit('1011')/sqrt(2) + Qubit('1111')/sqrt(2), Rational(1, 2))]
assert measure_partial(state2, (0,)) == \
[(Qubit('1000'), Rational(1, 4)),
(Qubit('1111')/sqrt(3) + Qubit('1101')/sqrt(3) +
Qubit('1011')/sqrt(3), Rational(3, 4))]
def test_trigsimp_groebner():
from sympy.simplify.trigsimp import trigsimp_groebner
c = cos(x)
s = sin(x)
ex = (4*s*c + 12*s + 5*c**3 + 21*c**2 + 23*c + 15)/(
-s*c**2 + 2*s*c + 15*s + 7*c**3 + 31*c**2 + 37*c + 21)
resnum = (5*s - 5*c + 1)
resdenom = (8*s - 6*c)
results = [resnum/resdenom, (-resnum)/(-resdenom)]
assert trigsimp_groebner(ex) in results
assert trigsimp_groebner(s/c, hints=[tan]) == tan(x)
assert trigsimp_groebner(c*s) == c*s
assert trigsimp((-s + 1)/c + c/(-s + 1),
method='groebner') == 2/c
assert trigsimp((-s + 1)/c + c/(-s + 1),
method='groebner', polynomial=True) == 2/c
# Test quick=False works
assert trigsimp_groebner(ex, hints=[2]) in results
assert trigsimp_groebner(ex, hints=[long(2)]) in results
# test "I"
assert trigsimp_groebner(sin(I*x)/cos(I*x), hints=[tanh]) == I*tanh(x)
# test hyperbolic / sums
assert trigsimp_groebner((tanh(x)+tanh(y))/(1+tanh(x)*tanh(y)),
hints=[(tanh, x, y)]) == tanh(x + y)
def test_trigsimp_groebner():
from sympy.simplify.trigsimp import trigsimp_groebner
c = cos(x)
s = sin(x)
ex = (4 * s * c + 12 * s + 5 * c**3 + 21 * c**2 + 23 * c + 15) / (
-s * c**2 + 2 * s * c + 15 * s + 7 * c**3 + 31 * c**2 + 37 * c + 21)
resnum = 5 * s - 5 * c + 1
resdenom = 8 * s - 6 * c
results = [resnum / resdenom, (-resnum) / (-resdenom)]
assert trigsimp_groebner(ex) in results
assert trigsimp_groebner(s / c, hints=[tan]) == tan(x)
assert trigsimp_groebner(c * s) == c * s
assert trigsimp((-s + 1) / c + c / (-s + 1), method="groebner") == 2 / c
assert (trigsimp((-s + 1) / c + c / (-s + 1),
method="groebner",
polynomial=True) == 2 / c)
# Test quick=False works
assert trigsimp_groebner(ex, hints=[2]) in results
assert trigsimp_groebner(ex, hints=[long(2)]) in results
# test "I"
assert trigsimp_groebner(sin(I * x) / cos(I * x),
hints=[tanh]) == I * tanh(x)
# test hyperbolic / sums
assert trigsimp_groebner((tanh(x) + tanh(y)) / (1 + tanh(x) * tanh(y)),
hints=[(tanh, x, y)]) == tanh(x + y)
def test_measure_partial():
#Basic test of collapse of entangled two qubits (Bell States)
state = Qubit('01') + Qubit('10')
assert measure_partial(state, (0,)) == \
[(Qubit('10'), S.Half), (Qubit('01'), S.Half)]
assert measure_partial(state, long(0)) == \
[(Qubit('10'), S.Half), (Qubit('01'), S.Half)]
assert measure_partial(state, (0,)) == \
measure_partial(state, (1,))[::-1]
#Test of more complex collapse and probability calculation
state1 = sqrt(2) / sqrt(3) * Qubit('00001') + 1 / sqrt(3) * Qubit('11111')
assert measure_partial(state1, (0,)) == \
[(sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111'), 1)]
assert measure_partial(state1, (1, 2)) == measure_partial(state1, (3, 4))
assert measure_partial(state1, (1, 2, 3)) == \
[(Qubit('00001'), Rational(2, 3)), (Qubit('11111'), Rational(1, 3))]
#test of measuring multiple bits at once
state2 = Qubit('1111') + Qubit('1101') + Qubit('1011') + Qubit('1000')
assert measure_partial(state2, (0, 1, 3)) == \
[(Qubit('1000'), Rational(1, 4)), (Qubit('1101'), Rational(1, 4)),
(Qubit('1011')/sqrt(2) + Qubit('1111')/sqrt(2), S.Half)]
assert measure_partial(state2, (0,)) == \
[(Qubit('1000'), Rational(1, 4)),
(Qubit('1111')/sqrt(3) + Qubit('1101')/sqrt(3) +
Qubit('1011')/sqrt(3), Rational(3, 4))]
def test_evalf_integer_parts():
a = floor(log(8)/log(2) - exp(-1000), evaluate=False)
b = floor(log(8)/log(2), evaluate=False)
raises(PrecisionExhausted, lambda: a.evalf())
assert a.evalf(chop=True) == 3
assert a.evalf(maxn=500) == 2
assert b.evalf() == 3
# equals, as a fallback, can still fail but it might succeed as here
assert ceiling(10*(sin(1)**2 + cos(1)**2)) == 10
assert int(floor(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336800)
assert int(ceiling(factorial(50)/E, evaluate=False).evalf(70)) == \
long(11188719610782480504630258070757734324011354208865721592720336801)
assert int(floor((GoldenRatio**999 / sqrt(5) + Rational(1, 2)))
.evalf(1000)) == fibonacci(999)
assert int(floor((GoldenRatio**1000 / sqrt(5) + Rational(1, 2)))
.evalf(1000)) == fibonacci(1000)
def test_levicivita():
assert Eijk(1, 2, 3) == LeviCivita(1, 2, 3)
assert LeviCivita(1, 2, 3) == 1
assert LeviCivita(long(1), long(2), long(3)) == 1
assert LeviCivita(1, 3, 2) == -1
assert LeviCivita(1, 2, 2) == 0
i, j, k = symbols('i j k')
assert LeviCivita(i, j, k) == LeviCivita(i, j, k, evaluate=False)
assert LeviCivita(i, j, i) == 0
assert LeviCivita(1, i, i) == 0
assert LeviCivita(i, j, k).doit() == (j - i)*(k - i)*(k - j)/2
assert LeviCivita(1, 2, 3, 1) == 0
assert LeviCivita(4, 5, 1, 2, 3) == 1
assert LeviCivita(4, 5, 2, 1, 3) == -1
assert LeviCivita(i, j, k).is_integer is True
assert adjoint(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
assert conjugate(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
assert transpose(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
def test_levicivita():
assert Eijk(1, 2, 3) == LeviCivita(1, 2, 3)
assert LeviCivita(1, 2, 3) == 1
assert LeviCivita(long(1), long(2), long(3)) == 1
assert LeviCivita(1, 3, 2) == -1
assert LeviCivita(1, 2, 2) == 0
i, j, k = symbols('i j k')
assert LeviCivita(i, j, k) == LeviCivita(i, j, k, evaluate=False)
assert LeviCivita(i, j, i) == 0
assert LeviCivita(1, i, i) == 0
assert LeviCivita(i, j, k).doit() == (j - i)*(k - i)*(k - j)/2
assert LeviCivita(1, 2, 3, 1) == 0
assert LeviCivita(4, 5, 1, 2, 3) == 1
assert LeviCivita(4, 5, 2, 1, 3) == -1
assert LeviCivita(i, j, k).is_integer is True
assert adjoint(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
assert conjugate(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
assert transpose(LeviCivita(i, j, k)) == LeviCivita(i, j, k)
def test_single_indexing():
A = MatrixSymbol('A', 2, 3)
assert A[1] == A[0, 1]
assert A[long(1)] == A[0, 1]
assert A[3] == A[1, 0]
assert list(A[:2, :2]) == [A[0, 0], A[0, 1], A[1, 0], A[1, 1]]
raises(IndexError, lambda: A[6])
raises(IndexError, lambda: A[n])
B = MatrixSymbol('B', n, m)
raises(IndexError, lambda: B[1])
B = MatrixSymbol('B', n, 3)
assert B[3] == B[1, 0]
def test_long():
a = Rational(5)
assert long(a) == 5
a = Rational(9, 10)
assert long(a) == long(-a) == 0
a = Integer(2**100)
assert long(a) == a
assert long(pi) == 3
assert long(E) == 2
assert long(GoldenRatio) == 1
def test_single_indexing():
A = MatrixSymbol('A', 2, 3)
assert A[1] == A[0, 1]
assert A[long(1)] == A[0, 1]
assert A[3] == A[1, 0]
assert list(A[:2, :2]) == [A[0, 0], A[0, 1], A[1, 0], A[1, 1]]
raises(IndexError, lambda: A[6])
raises(IndexError, lambda: A[n])
B = MatrixSymbol('B', n, m)
raises(IndexError, lambda: B[1])
B = MatrixSymbol('B', n, 3)
assert B[3] == B[1, 0]
def _test_rational_new(cls):
"""
Tests that are common between Integer and Rational.
"""
assert cls(0) is S.Zero
assert cls(1) is S.One
assert cls(-1) is S.NegativeOne
# These look odd, but are similar to int():
assert cls('1') is S.One
assert cls(u('-1')) is S.NegativeOne
i = Integer(10)
assert _strictly_equal(i, cls('10'))
assert _strictly_equal(i, cls(u('10')))
assert _strictly_equal(i, cls(long(10)))
assert _strictly_equal(i, cls(i))
raises(TypeError, lambda: cls(Symbol('x')))
def test_mpmath_issues():
from sympy.mpmath.libmp.libmpf import _normalize
import sympy.mpmath.libmp as mlib
rnd = mlib.round_nearest
mpf = (0, long(0), -123, -1, 53, rnd) # nan
assert _normalize(mpf, 53) != (0, long(0), 0, 0)
mpf = (0, long(0), -456, -2, 53, rnd) # +inf
assert _normalize(mpf, 53) != (0, long(0), 0, 0)
mpf = (1, long(0), -789, -3, 53, rnd) # -inf
assert _normalize(mpf, 53) != (0, long(0), 0, 0)
from sympy.mpmath.libmp.libmpf import fnan
assert mlib.mpf_eq(fnan, fnan)
def test___hash__():
# issue 5571
# Make sure int vs. long doesn't affect hashing with Python ground types
assert DMP([[1, 2], [3]], ZZ) == DMP([[long(1), long(2)], [long(3)]], ZZ)
assert hash(DMP([[1, 2], [3]],
ZZ)) == hash(DMP([[long(1), long(2)], [long(3)]], ZZ))
assert DMF(([[1, 2], [3]], [[1]]), ZZ) == DMF(
([[long(1), long(2)], [long(3)]], [[long(1)]]), ZZ)
assert hash(DMF(
([[1, 2], [3]], [[1]]),
ZZ)) == hash(DMF(([[long(1), long(2)], [long(3)]], [[long(1)]]), ZZ))
assert ANP([1, 1], [1, 0, 1],
ZZ) == ANP([long(1), long(1)],
[long(1), long(0), long(1)], ZZ)
assert hash(ANP([1, 1], [1, 0, 1], ZZ)) == hash(
ANP([long(1), long(1)], [long(1), long(0), long(1)], ZZ))
def test_factorint():
assert primefactors(123456) == [2, 3, 643]
assert factorint(0) == {0: 1}
assert factorint(1) == {}
assert factorint(-1) == {-1: 1}
assert factorint(-2) == {-1: 1, 2: 1}
assert factorint(-16) == {-1: 1, 2: 4}
assert factorint(2) == {2: 1}
assert factorint(126) == {2: 1, 3: 2, 7: 1}
assert factorint(123456) == {2: 6, 3: 1, 643: 1}
assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
assert factorint(64015937) == {7993: 1, 8009: 1}
assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
assert multiproduct(factorint(fac(200))) == fac(200)
for b, e in factorint(fac(150)).items():
assert e == fac_multiplicity(150, b)
assert factorint(103005006059**7) == {103005006059: 7}
assert factorint(31337**191) == {31337: 191}
assert factorint(2**1000 * 3**500 * 257**127 * 383**60) == \
{2: 1000, 3: 500, 257: 127, 383: 60}
assert len(factorint(fac(10000))) == 1229
assert factorint(12932983746293756928584532764589230) == \
{2: 1, 5: 1, 73: 1, 727719592270351: 1, 63564265087747: 1, 383: 1}
assert factorint(727719592270351) == {727719592270351: 1}
assert factorint(2**64 + 1, use_trial=False) == factorint(2**64 + 1)
for n in range(60000):
assert multiproduct(factorint(n)) == n
assert pollard_rho(2**64 + 1, seed=1) == 274177
assert pollard_rho(19, seed=1) is None
assert factorint(3, limit=2) == {3: 1}
assert factorint(12345) == {3: 1, 5: 1, 823: 1}
assert factorint(12345, limit=3) == {
4115: 1,
3: 1
} # the 5 is greater than the limit
assert factorint(1, limit=1) == {}
assert factorint(0, 3) == {0: 1}
assert factorint(12, limit=1) == {12: 1}
assert factorint(30, limit=2) == {2: 1, 15: 1}
assert factorint(16, limit=2) == {2: 4}
assert factorint(124, limit=3) == {2: 2, 31: 1}
assert factorint(4 * 31**2, limit=3) == {2: 2, 31: 2}
p1 = nextprime(2**32)
p2 = nextprime(2**16)
p3 = nextprime(p2)
assert factorint(p1 * p2 * p3) == {p1: 1, p2: 1, p3: 1}
assert factorint(13 * 17 * 19, limit=15) == {13: 1, 17 * 19: 1}
assert factorint(1951 * 15013 * 15053, limit=2000) == {
225990689: 1,
1951: 1
}
assert factorint(primorial(17) + 1, use_pm1=0) == \
{long(19026377261): 1, 3467: 1, 277: 1, 105229: 1}
# when prime b is closer than approx sqrt(8*p) to prime p then they are
# "close" and have a trivial factorization
a = nextprime(2**2**8) # 78 digits
b = nextprime(a + 2**2**4)
assert 'Fermat' in capture(lambda: factorint(a * b, verbose=1))
raises(ValueError, lambda: pollard_rho(4))
raises(ValueError, lambda: pollard_pm1(3))
raises(ValueError, lambda: pollard_pm1(10, B=2))
# verbose coverage
n = nextprime(2**16) * nextprime(2**17) * nextprime(1901)
assert 'with primes' in capture(lambda: factorint(n, verbose=1))
capture(lambda: factorint(nextprime(2**16) * 1012, verbose=1))
n = nextprime(2**17)
capture(lambda: factorint(n**3, verbose=1)) # perfect power termination
capture(lambda: factorint(2 * n, verbose=1)) # factoring complete msg
# exceed 1st
n = nextprime(2**17)
n *= nextprime(n)
assert '1000' in capture(lambda: factorint(n, limit=1000, verbose=1))
n *= nextprime(n)
assert len(factorint(n)) == 3
assert len(factorint(n, limit=p1)) == 3
n *= nextprime(2 * n)
# exceed 2nd
assert '2001' in capture(lambda: factorint(n, limit=2000, verbose=1))
assert capture(lambda: factorint(n, limit=4000, verbose=1)).count(
'Pollard') == 2
# non-prime pm1 result
n = nextprime(8069)
n *= nextprime(2 * n) * nextprime(2 * n, 2)
capture(lambda: factorint(n, verbose=1)) # non-prime pm1 result
# factor fermat composite
p1 = nextprime(2**17)
p2 = nextprime(2 * p1)
assert factorint((p1 * p2**2)**3) == {p1: 3, p2: 6}
# Test for non integer input
raises(ValueError, lambda: factorint(4.5))
def test_to_mpmath():
assert sqrt(3)._to_mpmath(20)._mpf_ == (0, long(908093), -19, 20)
assert S(3.2)._to_mpmath(20)._mpf_ == (0, long(838861), -18, 20)
def test_ndim_array_initiation():
arr_with_one_element = MutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element.rank() == 1
raises(ValueError, lambda: arr_with_one_element[1])
arr_with_symbol_element = MutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = MutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector.rank() == 1
raises(ValueError, lambda: arr_with_one_element[5])
vector = MutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector._sparse_array == {}
assert vector.rank() == 1
n_dim_array = MutableDenseNDimArray(range(3**4), (3, 3, 3, 3,))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
raises(ValueError, lambda: n_dim_array[0, 0, 0, 3])
raises(ValueError, lambda: n_dim_array[3, 0, 0, 0])
raises(ValueError, lambda: n_dim_array[3**4])
array_shape = (3, 3, 3, 3)
sparse_array = MutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = MutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3,)
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = MutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = MutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = MutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5),)
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])
def test_ndim_array_initiation():
arr_with_no_elements = ImmutableDenseNDimArray([], shape=(0, ))
assert len(arr_with_no_elements) == 0
assert arr_with_no_elements.rank() == 1
raises(ValueError, lambda: ImmutableDenseNDimArray([0], shape=(0, )))
raises(ValueError, lambda: ImmutableDenseNDimArray([1, 2, 3], shape=(0, )))
raises(ValueError, lambda: ImmutableDenseNDimArray([], shape=()))
raises(ValueError, lambda: ImmutableSparseNDimArray([0], shape=(0, )))
raises(ValueError,
lambda: ImmutableSparseNDimArray([1, 2, 3], shape=(0, )))
raises(ValueError, lambda: ImmutableSparseNDimArray([], shape=()))
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == ImmutableDenseNDimArray([23])
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == ImmutableDenseNDimArray([Symbol('x')])
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (
3,
3,
3,
3,
))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3, )
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = ImmutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5), )
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])
from sympy.abc import x
for ArrayType in [ImmutableDenseNDimArray, ImmutableSparseNDimArray]:
rank_zero_array = ArrayType(x)
assert len(rank_zero_array) == 1
assert rank_zero_array.shape == ()
assert rank_zero_array.rank() == 0
assert rank_zero_array[()] == x
raises(ValueError, lambda: rank_zero_array[0])
def test_factorint():
assert primefactors(123456) == [2, 3, 643]
assert factorint(0) == {0: 1}
assert factorint(1) == {}
assert factorint(-1) == {-1: 1}
assert factorint(-2) == {-1: 1, 2: 1}
assert factorint(-16) == {-1: 1, 2: 4}
assert factorint(2) == {2: 1}
assert factorint(126) == {2: 1, 3: 2, 7: 1}
assert factorint(123456) == {2: 6, 3: 1, 643: 1}
assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
assert factorint(64015937) == {7993: 1, 8009: 1}
assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
# issue 17676
assert factorint(28300421052393658575) == {
3: 1,
5: 2,
11: 2,
43: 1,
2063: 2,
4127: 1,
4129: 1,
}
assert factorint(2063**2 * 4127**1 * 4129**1) == {
2063: 2,
4127: 1,
4129: 1
}
assert factorint(2347**2 * 7039**1 * 7043**1) == {
2347: 2,
7039: 1,
7043: 1
}
assert factorint(0, multiple=True) == [0]
assert factorint(1, multiple=True) == []
assert factorint(-1, multiple=True) == [-1]
assert factorint(-2, multiple=True) == [-1, 2]
assert factorint(-16, multiple=True) == [-1, 2, 2, 2, 2]
assert factorint(2, multiple=True) == [2]
assert factorint(24, multiple=True) == [2, 2, 2, 3]
assert factorint(126, multiple=True) == [2, 3, 3, 7]
assert factorint(123456, multiple=True) == [2, 2, 2, 2, 2, 2, 3, 643]
assert factorint(5951757, multiple=True) == [3, 7, 29, 29, 337]
assert factorint(64015937, multiple=True) == [7993, 8009]
assert factorint(2**(2**6) + 1, multiple=True) == [274177, 67280421310721]
assert factorint(fac(1, evaluate=False)) == {}
assert factorint(fac(7, evaluate=False)) == {2: 4, 3: 2, 5: 1, 7: 1}
assert factorint(fac(15, evaluate=False)) == {
2: 11,
3: 6,
5: 3,
7: 2,
11: 1,
13: 1
}
assert factorint(fac(20, evaluate=False)) == {
2: 18,
3: 8,
5: 4,
7: 2,
11: 1,
13: 1,
17: 1,
19: 1,
}
assert factorint(fac(23, evaluate=False)) == {
2: 19,
3: 9,
5: 4,
7: 3,
11: 2,
13: 1,
17: 1,
19: 1,
23: 1,
}
assert multiproduct(factorint(fac(200))) == fac(200)
assert multiproduct(factorint(fac(200, evaluate=False))) == fac(200)
for b, e in factorint(fac(150)).items():
assert e == fac_multiplicity(150, b)
for b, e in factorint(fac(150, evaluate=False)).items():
assert e == fac_multiplicity(150, b)
assert factorint(103005006059**7) == {103005006059: 7}
assert factorint(31337**191) == {31337: 191}
assert factorint(2**1000 * 3**500 * 257**127 * 383**60) == {
2: 1000,
3: 500,
257: 127,
383: 60,
}
assert len(factorint(fac(10000))) == 1229
assert len(factorint(fac(10000, evaluate=False))) == 1229
assert factorint(12932983746293756928584532764589230) == {
2: 1,
5: 1,
73: 1,
727719592270351: 1,
63564265087747: 1,
383: 1,
}
assert factorint(727719592270351) == {727719592270351: 1}
assert factorint(2**64 + 1, use_trial=False) == factorint(2**64 + 1)
for n in range(60000):
assert multiproduct(factorint(n)) == n
assert pollard_rho(2**64 + 1, seed=1) == 274177
assert pollard_rho(19, seed=1) is None
assert factorint(3, limit=2) == {3: 1}
assert factorint(12345) == {3: 1, 5: 1, 823: 1}
assert factorint(12345, limit=3) == {
4115: 1,
3: 1,
} # the 5 is greater than the limit
assert factorint(1, limit=1) == {}
assert factorint(0, 3) == {0: 1}
assert factorint(12, limit=1) == {12: 1}
assert factorint(30, limit=2) == {2: 1, 15: 1}
assert factorint(16, limit=2) == {2: 4}
assert factorint(124, limit=3) == {2: 2, 31: 1}
assert factorint(4 * 31**2, limit=3) == {2: 2, 31: 2}
p1 = nextprime(2**32)
p2 = nextprime(2**16)
p3 = nextprime(p2)
assert factorint(p1 * p2 * p3) == {p1: 1, p2: 1, p3: 1}
assert factorint(13 * 17 * 19, limit=15) == {13: 1, 17 * 19: 1}
assert factorint(1951 * 15013 * 15053, limit=2000) == {
225990689: 1,
1951: 1
}
assert factorint(primorial(17) + 1, use_pm1=0) == {
long(19026377261): 1,
3467: 1,
277: 1,
105229: 1,
}
# when prime b is closer than approx sqrt(8*p) to prime p then they are
# "close" and have a trivial factorization
a = nextprime(2**2**8) # 78 digits
b = nextprime(a + 2**2**4)
assert "Fermat" in capture(lambda: factorint(a * b, verbose=1))
raises(ValueError, lambda: pollard_rho(4))
raises(ValueError, lambda: pollard_pm1(3))
raises(ValueError, lambda: pollard_pm1(10, B=2))
# verbose coverage
n = nextprime(2**16) * nextprime(2**17) * nextprime(1901)
assert "with primes" in capture(lambda: factorint(n, verbose=1))
capture(lambda: factorint(nextprime(2**16) * 1012, verbose=1))
n = nextprime(2**17)
capture(lambda: factorint(n**3, verbose=1)) # perfect power termination
capture(lambda: factorint(2 * n, verbose=1)) # factoring complete msg
# exceed 1st
n = nextprime(2**17)
n *= nextprime(n)
assert "1000" in capture(lambda: factorint(n, limit=1000, verbose=1))
n *= nextprime(n)
assert len(factorint(n)) == 3
assert len(factorint(n, limit=p1)) == 3
n *= nextprime(2 * n)
# exceed 2nd
assert "2001" in capture(lambda: factorint(n, limit=2000, verbose=1))
assert capture(lambda: factorint(n, limit=4000, verbose=1)).count(
"Pollard") == 2
# non-prime pm1 result
n = nextprime(8069)
n *= nextprime(2 * n) * nextprime(2 * n, 2)
capture(lambda: factorint(n, verbose=1)) # non-prime pm1 result
# factor fermat composite
p1 = nextprime(2**17)
p2 = nextprime(2 * p1)
assert factorint((p1 * p2**2)**3) == {p1: 3, p2: 6}
# Test for non integer input
raises(ValueError, lambda: factorint(4.5))
# test dict/Dict input
sans = "2**10*3**3"
n = {4: 2, 12: 3}
assert str(factorint(n)) == sans
assert str(factorint(Dict(n))) == sans
def test_Float():
def eq(a, b):
t = Float("1.0E-15")
return -t < a - b < t
a = Float(2) ** Float(3)
assert eq(a.evalf(), Float(8))
assert eq((pi ** -1).evalf(), Float("0.31830988618379067"))
a = Float(2) ** Float(4)
assert eq(a.evalf(), Float(16))
assert (S(0.3) == S(0.5)) is False
x_str = Float((0, "13333333333333", -52, 53))
x2_str = Float((0, "26666666666666", -53, 53))
x_hex = Float((0, long(0x13333333333333), -52, 53))
x_dec = Float((0, 5404319552844595, -52, 53))
x2_hex = Float((0, long(0x13333333333333) * 2, -53, 53))
assert x_str == x_hex == x_dec == x2_hex == Float(1.2)
# x2_str and 1.2 are superficially the same
assert str(x2_str) == str(Float(1.2))
# but are different at the mpf level
assert Float(1.2)._mpf_ == (0, long(5404319552844595), -52, 53)
assert x2_str._mpf_ == (0, long(10808639105689190), -53, 53)
assert Float((0, long(0), -123, -1)) == Float("nan")
assert Float((0, long(0), -456, -2)) == Float("inf") == Float("+inf")
assert Float((1, long(0), -789, -3)) == Float("-inf")
raises(ValueError, lambda: Float((0, 7, 1, 3), ""))
assert Float("+inf").is_finite is False
assert Float("+inf").is_negative is False
assert Float("+inf").is_positive is True
assert Float("+inf").is_infinite is True
assert Float("+inf").is_zero is False
assert Float("-inf").is_finite is False
assert Float("-inf").is_negative is True
assert Float("-inf").is_positive is False
assert Float("-inf").is_infinite is True
assert Float("-inf").is_zero is False
assert Float("0.0").is_finite is True
assert Float("0.0").is_negative is False
assert Float("0.0").is_positive is False
assert Float("0.0").is_infinite is False
assert Float("0.0").is_zero is True
# rationality properties
assert Float(1).is_rational is None
assert Float(1).is_irrational is None
assert sqrt(2).n(15).is_rational is None
assert sqrt(2).n(15).is_irrational is None
# do not automatically evalf
def teq(a):
assert (a.evalf() == a) is False
assert (a.evalf() != a) is True
assert (a == a.evalf()) is False
assert (a != a.evalf()) is True
teq(pi)
teq(2 * pi)
teq(cos(0.1, evaluate=False))
# long integer
i = 12345678901234567890
assert same_and_same_prec(Float(12, ""), Float("12", ""))
assert same_and_same_prec(Float(Integer(i), ""), Float(i, ""))
assert same_and_same_prec(Float(i, ""), Float(str(i), 20))
assert same_and_same_prec(Float(str(i)), Float(i, ""))
assert same_and_same_prec(Float(i), Float(i, ""))
# inexact floats (repeating binary = denom not multiple of 2)
# cannot have precision greater than 15
assert Float(0.125, 22) == 0.125
assert Float(2.0, 22) == 2
assert float(Float(".12500000000000001", "")) == 0.125
raises(ValueError, lambda: Float(0.12500000000000001, ""))
# allow spaces
Float("123 456.123 456") == Float("123456.123456")
Integer("123 456") == Integer("123456")
Rational("123 456.123 456") == Rational("123456.123456")
assert Float(" .3e2") == Float("0.3e2")
# allow auto precision detection
assert Float(".1", "") == Float(0.1, 1)
assert Float(".125", "") == Float(0.125, 3)
assert Float(".100", "") == Float(0.1, 3)
assert Float("2.0", "") == Float("2", 2)
raises(ValueError, lambda: Float("12.3d-4", ""))
raises(ValueError, lambda: Float(12.3, ""))
raises(ValueError, lambda: Float("."))
raises(ValueError, lambda: Float("-."))
zero = Float("0.0")
assert Float("-0") == zero
assert Float(".0") == zero
assert Float("-.0") == zero
assert Float("-0.0") == zero
assert Float(0.0) == zero
assert Float(0) == zero
assert Float(0, "") == Float("0", "")
assert Float(1) == Float(1.0)
assert Float(S.Zero) == zero
assert Float(S.One) == Float(1.0)
assert Float(decimal.Decimal("0.1"), 3) == Float(".1", 3)
assert "{0:.3f}".format(Float(4.236622)) == "4.237"
assert "{0:.35f}".format(Float(pi.n(40), 40)) == "3.14159265358979323846264338327950288"
def test_ndim_array_initiation():
arr_with_no_elements = ImmutableDenseNDimArray([], shape=(0,))
assert len(arr_with_no_elements) == 0
assert arr_with_no_elements.rank() == 1
raises(ValueError, lambda: ImmutableDenseNDimArray([0], shape=(0,)))
raises(ValueError, lambda: ImmutableDenseNDimArray([1, 2, 3], shape=(0,)))
raises(ValueError, lambda: ImmutableDenseNDimArray([], shape=()))
raises(ValueError, lambda: ImmutableSparseNDimArray([0], shape=(0,)))
raises(ValueError, lambda: ImmutableSparseNDimArray([1, 2, 3], shape=(0,)))
raises(ValueError, lambda: ImmutableSparseNDimArray([], shape=()))
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == [23]
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == [Symbol('x')]
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (3, 3, 3, 3,))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3,)
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = ImmutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5),)
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])
from sympy.abc import x
rank_zero_array = ImmutableDenseNDimArray(x)
assert len(rank_zero_array) == 1
assert rank_zero_array.shape == ()
assert rank_zero_array.rank() == 0
assert rank_zero_array[()] == x
assert rank_zero_array[0] == x
def test___hash__():
# issue 5571
# Make sure int vs. long doesn't affect hashing with Python ground types
assert DMP([[1, 2], [3]], ZZ) == DMP([[long(1), long(2)], [long(3)]], ZZ)
assert hash(DMP([[1, 2], [3]], ZZ)) == hash(DMP([[long(1), long(2)], [long(3)]], ZZ))
assert DMF(
([[1, 2], [3]], [[1]]), ZZ) == DMF(([[long(1), long(2)], [long(3)]], [[long(1)]]), ZZ)
assert hash(DMF(([[1, 2], [3]], [[1]]), ZZ)) == hash(DMF(([[long(1),
long(2)], [long(3)]], [[long(1)]]), ZZ))
assert ANP([1, 1], [1, 0, 1], ZZ) == ANP([long(1), long(1)], [long(1), long(0), long(1)], ZZ)
assert hash(
ANP([1, 1], [1, 0, 1], ZZ)) == hash(ANP([long(1), long(1)], [long(1), long(0), long(1)], ZZ))
def test_factorint():
assert primefactors(123456) == [2, 3, 643]
assert factorint(0) == {0: 1}
assert factorint(1) == {}
assert factorint(-1) == {-1: 1}
assert factorint(-2) == {-1: 1, 2: 1}
assert factorint(-16) == {-1: 1, 2: 4}
assert factorint(2) == {2: 1}
assert factorint(126) == {2: 1, 3: 2, 7: 1}
assert factorint(123456) == {2: 6, 3: 1, 643: 1}
assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
assert factorint(64015937) == {7993: 1, 8009: 1}
assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
assert multiproduct(factorint(fac(200))) == fac(200)
for b, e in factorint(fac(150)).items():
assert e == fac_multiplicity(150, b)
assert factorint(103005006059**7) == {103005006059: 7}
assert factorint(31337**191) == {31337: 191}
assert factorint(2**1000 * 3**500 * 257**127 * 383**60) == \
{2: 1000, 3: 500, 257: 127, 383: 60}
assert len(factorint(fac(10000))) == 1229
assert factorint(12932983746293756928584532764589230) == \
{2: 1, 5: 1, 73: 1, 727719592270351: 1, 63564265087747: 1, 383: 1}
assert factorint(727719592270351) == {727719592270351: 1}
assert factorint(2**64 + 1, use_trial=False) == factorint(2**64 + 1)
for n in range(60000):
assert multiproduct(factorint(n)) == n
assert pollard_rho(2**64 + 1, seed=1) == 274177
assert pollard_rho(19, seed=1) is None
assert factorint(3, limit=2) == {3: 1}
assert factorint(12345) == {3: 1, 5: 1, 823: 1}
assert factorint(
12345, limit=3) == {4115: 1, 3: 1} # the 5 is greater than the limit
assert factorint(1, limit=1) == {}
assert factorint(0, 3) == {0: 1}
assert factorint(12, limit=1) == {12: 1}
assert factorint(30, limit=2) == {2: 1, 15: 1}
assert factorint(16, limit=2) == {2: 4}
assert factorint(124, limit=3) == {2: 2, 31: 1}
assert factorint(4*31**2, limit=3) == {2: 2, 31: 2}
p1 = nextprime(2**32)
p2 = nextprime(2**16)
p3 = nextprime(p2)
assert factorint(p1*p2*p3) == {p1: 1, p2: 1, p3: 1}
assert factorint(13*17*19, limit=15) == {13: 1, 17*19: 1}
assert factorint(1951*15013*15053, limit=2000) == {225990689: 1, 1951: 1}
assert factorint(primorial(17) + 1, use_pm1=0) == \
{long(19026377261): 1, 3467: 1, 277: 1, 105229: 1}
# when prime b is closer than approx sqrt(8*p) to prime p then they are
# "close" and have a trivial factorization
a = nextprime(2**2**8) # 78 digits
b = nextprime(a + 2**2**4)
assert 'Fermat' in capture(lambda: factorint(a*b, verbose=1))
raises(ValueError, lambda: pollard_rho(4))
raises(ValueError, lambda: pollard_pm1(3))
raises(ValueError, lambda: pollard_pm1(10, B=2))
# verbose coverage
n = nextprime(2**16)*nextprime(2**17)*nextprime(1901)
assert 'with primes' in capture(lambda: factorint(n, verbose=1))
capture(lambda: factorint(nextprime(2**16)*1012, verbose=1))
n = nextprime(2**17)
capture(lambda: factorint(n**3, verbose=1)) # perfect power termination
capture(lambda: factorint(2*n, verbose=1)) # factoring complete msg
# exceed 1st
n = nextprime(2**17)
n *= nextprime(n)
assert '1000' in capture(lambda: factorint(n, limit=1000, verbose=1))
n *= nextprime(n)
assert len(factorint(n)) == 3
assert len(factorint(n, limit=p1)) == 3
n *= nextprime(2*n)
# exceed 2nd
assert '2001' in capture(lambda: factorint(n, limit=2000, verbose=1))
assert capture(
lambda: factorint(n, limit=4000, verbose=1)).count('Pollard') == 2
# non-prime pm1 result
n = nextprime(8069)
n *= nextprime(2*n)*nextprime(2*n, 2)
capture(lambda: factorint(n, verbose=1)) # non-prime pm1 result
# factor fermat composite
p1 = nextprime(2**17)
p2 = nextprime(2*p1)
assert factorint((p1*p2**2)**3) == {p1: 3, p2: 6}
# Test for non integer input
raises(ValueError, lambda: factorint(4.5))
def test_Float():
def eq(a, b):
t = Float("1.0E-15")
return (-t < a - b < t)
a = Float(2) ** Float(3)
assert eq(a.evalf(), Float(8))
assert eq((pi ** -1).evalf(), Float("0.31830988618379067"))
a = Float(2) ** Float(4)
assert eq(a.evalf(), Float(16))
assert (S(.3) == S(.5)) is False
x_str = Float((0, '13333333333333', -52, 53))
x2_str = Float((0, '26666666666666', -53, 53))
x_hex = Float((0, long(0x13333333333333), -52, 53))
x_dec = Float((0, 5404319552844595, -52, 53))
x2_hex = Float((0, long(0x13333333333333)*2, -53, 53))
assert x_str == x_hex == x_dec == x2_hex == Float(1.2)
# x2_str and 1.2 are superficially the same
assert str(x2_str) == str(Float(1.2))
# but are different at the mpf level
assert Float(1.2)._mpf_ == (0, long(5404319552844595), -52, 53)
assert x2_str._mpf_ == (0, long(10808639105689190), -53, 53)
assert Float((0, long(0), -123, -1)) == Float('nan')
assert Float((0, long(0), -456, -2)) == Float('inf') == Float('+inf')
assert Float((1, long(0), -789, -3)) == Float('-inf')
raises(ValueError, lambda: Float((0, 7, 1, 3), ''))
assert Float('+inf').is_bounded is False
assert Float('+inf').is_negative is False
assert Float('+inf').is_positive is True
assert Float('+inf').is_unbounded is True
assert Float('+inf').is_zero is False
assert Float('-inf').is_bounded is False
assert Float('-inf').is_negative is True
assert Float('-inf').is_positive is False
assert Float('-inf').is_unbounded is True
assert Float('-inf').is_zero is False
assert Float('0.0').is_bounded is True
assert Float('0.0').is_negative is False
assert Float('0.0').is_positive is False
assert Float('0.0').is_unbounded is False
assert Float('0.0').is_zero is True
# rationality properties
assert Float(1).is_rational is None
assert Float(1).is_irrational is None
assert sqrt(2).n(15).is_rational is None
assert sqrt(2).n(15).is_irrational is None
# do not automatically evalf
def teq(a):
assert (a.evalf() == a) is False
assert (a.evalf() != a) is True
assert (a == a.evalf()) is False
assert (a != a.evalf()) is True
teq(pi)
teq(2*pi)
teq(cos(0.1, evaluate=False))
i = 12345678901234567890
assert _aresame(Float(12, ''), Float('12', ''))
assert _aresame(Float(Integer(i), ''), Float(i, ''))
assert _aresame(Float(i, ''), Float(str(i), 20))
assert not _aresame(Float(str(i)), Float(i, ''))
# inexact floats (repeating binary = denom not multiple of 2)
# cannot have precision greater than 15
assert Float(.125, 22) == .125
assert Float(2.0, 22) == 2
assert float(Float('.12500000000000001', '')) == .125
raises(ValueError, lambda: Float(.12500000000000001, ''))
# allow spaces
Float('123 456.123 456') == Float('123456.123456')
Integer('123 456') == Integer('123456')
Rational('123 456.123 456') == Rational('123456.123456')
assert Float(' .3e2') == Float('0.3e2')
# allow auto precision detection
assert Float('.1', '') == Float(.1, 1)
assert Float('.125', '') == Float(.125, 3)
assert Float('.100', '') == Float(.1, 3)
assert Float('2.0', '') == Float('2', 2)
raises(ValueError, lambda: Float("12.3d-4", ""))
raises(ValueError, lambda: Float(12.3, ""))
raises(ValueError, lambda: Float('.'))
raises(ValueError, lambda: Float('-.'))
zero = Float('0.0')
assert Float('-0') == zero
assert Float('.0') == zero
assert Float('-.0') == zero
assert Float('-0.0') == zero
assert Float(0.0) == zero
assert Float(0) == zero
assert Float(0, '') == Float('0', '')
assert Float(1) == Float(1.0)
assert Float(S.Zero) == zero
assert Float(S.One) == Float(1.0)
assert Float(decimal.Decimal('0.1'), 3) == Float('.1', 3)
assert '{0:.3f}'.format(Float(4.236622)) == '4.237'
assert '{0:.35f}'.format(Float(pi.n(40), 40)) == '3.14159265358979323846264338327950288'
def test_ndim_array_initiation():
arr_with_one_element = MutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element.rank() == 1
raises(ValueError, lambda: arr_with_one_element[1])
arr_with_symbol_element = MutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = MutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector.rank() == 1
raises(ValueError, lambda: arr_with_one_element[5])
vector = MutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector._sparse_array == {}
assert vector.rank() == 1
n_dim_array = MutableDenseNDimArray(range(3**4), (
3,
3,
3,
3,
))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
raises(ValueError, lambda: n_dim_array[0, 0, 0, 3])
raises(ValueError, lambda: n_dim_array[3, 0, 0, 0])
raises(ValueError, lambda: n_dim_array[3**4])
array_shape = (3, 3, 3, 3)
sparse_array = MutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = MutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3, )
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = MutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = MutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = MutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5), )
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])