def test__parallel_dict_from_expr_no_gens():
assert parallel_dict_from_expr([x*y, Integer(3)]) == \
([{(1, 1): 1}, {(0, 0): 3}], (x, y))
assert parallel_dict_from_expr([x*y, 2*z, Integer(3)]) == \
([{(1, 1, 0): 1}, {(0, 0, 1): 2}, {(0, 0, 0): 3}], (x, y, z))
assert parallel_dict_from_expr((Mul(x, x**2, evaluate=False),)) == \
([{(3,): 1}], (x,))
def test__parallel_dict_from_expr_no_gens():
assert parallel_dict_from_expr([x*y, Integer(3)]) == \
([{(1, 1): 1}, {(0, 0): 3}], (x, y))
assert parallel_dict_from_expr([x*y, 2*z, Integer(3)]) == \
([{(1, 1, 0): 1}, {(0, 0, 1): 2}, {(0, 0, 0): 3}], (x, y, z))
assert parallel_dict_from_expr((Mul(x, x**2, evaluate=False),)) == \
([{(3,): 1}], (x,))
def test__parallel_dict_from_expr_if_gens():
assert parallel_dict_from_expr([x + 2*y + 3*z, Integer(7)], gens=(x,)) == \
([{(1,): 1, (0,): 2*y + 3*z}, {(0,): 7}], (x,))
assert parallel_dict_from_expr((Mul(x, x**2, evaluate=False),), gens=(x,)) == \
([{(3,): 1}], (x,))
pytest.raises(PolynomialError, lambda: parallel_dict_from_expr((A*x,), gens=(x,)))
def test__parallel_dict_from_expr_if_gens():
assert parallel_dict_from_expr([x + 2*y + 3*z, Integer(7)], gens=(x,)) == \
([{(1,): 1, (0,): 2*y + 3*z}, {(0,): 7}], (x,))
assert parallel_dict_from_expr((Mul(x, x**2, evaluate=False),), gens=(x,)) == \
([{(3,): 1}], (x,))
pytest.raises(PolynomialError, lambda: parallel_dict_from_expr((A*x,), gens=(x,)))
def test_parallel_dict_from_expr():
assert parallel_dict_from_expr([x - 1, x**2 - 2]) == ([{
(0, ): -1,
(1, ): 1
}, {
(0, ): -2,
(2, ): 1
}], (x, ))
pytest.raises(PolynomialError,
lambda: parallel_dict_from_expr([A * B - B * A]))
def test_parallel_dict_from_expr():
assert parallel_dict_from_expr([Eq(x, 1), Eq(x**2, 2)]) == ([{
(0, ):
-Integer(1),
(1, ):
Integer(1)
}, {
(0, ):
-Integer(2),
(2, ):
Integer(1)
}], (x, ))
pytest.raises(PolynomialError,
lambda: parallel_dict_from_expr([A * B - B * A]))
def sdm_from_vector(vec, O, K, **opts):
"""
Create an sdm from an iterable of expressions.
Coefficients are created in the ground field ``K``, and terms are ordered
according to monomial order ``O``. Named arguments are passed on to the
polys conversion code and can be used to specify for example generators.
Examples
========
>>> from diofant.abc import x, y, z
>>> from diofant.polys import QQ, lex
>>> sdm_from_vector([x**2+y**2, 2*z], lex, QQ)
[((1, 0, 0, 1), 2), ((0, 2, 0, 0), 1), ((0, 0, 2, 0), 1)]
"""
dics, gens = parallel_dict_from_expr(sympify(vec), **opts)
dic = {}
for i, d in enumerate(dics):
for k, v in d.items():
dic[(i,) + k] = K.convert(v)
return sdm_from_dict(dic, O)
def test__dict_from_expr_no_gens():
pytest.raises(GeneratorsNeeded,
lambda: parallel_dict_from_expr([Integer(17)]))
assert parallel_dict_from_expr([x]) == ([{(1, ): 1}], (x, ))
assert parallel_dict_from_expr([y]) == ([{(1, ): 1}], (y, ))
assert parallel_dict_from_expr([x * y]) == ([{(1, 1): 1}], (x, y))
assert parallel_dict_from_expr([x + y]) == ([{
(1, 0): 1,
(0, 1): 1
}], (x, y))
assert parallel_dict_from_expr([sqrt(2)]) == ([{(1, ): 1}], (sqrt(2), ))
pytest.raises(GeneratorsNeeded,
lambda: parallel_dict_from_expr([sqrt(2)], greedy=False))
assert parallel_dict_from_expr([x * y], domain=ZZ.inject(x)) == ([{
(1, ): x
}], (y, ))
assert parallel_dict_from_expr([x * y], domain=ZZ.inject(y)) == ([{
(1, ): y
}], (x, ))
assert parallel_dict_from_expr([3 * sqrt(2) * pi * x * y],
extension=None) == ([{
(1, 1, 1, 1): 3
}], (x, y, pi, sqrt(2)))
assert parallel_dict_from_expr([3 * sqrt(2) * pi * x * y],
extension=True) == ([{
(1, 1, 1): 3 * sqrt(2)
}], (x, y, pi))
f = cos(x) * sin(x) + cos(x) * sin(y) + cos(y) * sin(x) + cos(y) * sin(y)
assert parallel_dict_from_expr([f]) == ([{
(0, 1, 0, 1): 1,
(0, 1, 1, 0): 1,
(1, 0, 0, 1): 1,
(1, 0, 1, 0): 1
}], (cos(x), cos(y), sin(x), sin(y)))
def test__dict_from_expr_if_gens():
assert parallel_dict_from_expr([Integer(17)], gens=(x, )) == ([{
(0, ): 17
}], (x, ))
assert parallel_dict_from_expr([Integer(17)], gens=(x, y)) == ([{
(0, 0): 17
}], (x, y))
assert parallel_dict_from_expr([Integer(17)], gens=(x, y, z)) == ([{
(0, 0, 0):
17
}], (x, y, z))
assert parallel_dict_from_expr([Integer(-17)], gens=(x, )) == ([{
(0, ): -17
}], (x, ))
assert parallel_dict_from_expr([Integer(-17)], gens=(x, y)) == ([{
(0, 0):
-17
}], (x, y))
assert parallel_dict_from_expr([Integer(-17)], gens=(x, y, z)) == ([{
(0, 0, 0):
-17
}], (x, y, z))
assert parallel_dict_from_expr([17 * x], gens=(x, )) == ([{
(1, ): 17
}], (x, ))
assert parallel_dict_from_expr([17 * x], gens=(x, y)) == ([{
(1, 0): 17
}], (x, y))
assert parallel_dict_from_expr([17 * x], gens=(x, y, z)) == ([{
(1, 0, 0): 17
}], (x, y, z))
assert parallel_dict_from_expr([17 * x**7], gens=(x, )) == ([{
(7, ): 17
}], (x, ))
assert parallel_dict_from_expr([17 * x**7 * y], gens=(x, y)) == ([{
(7, 1):
17
}], (x, y))
assert parallel_dict_from_expr([17 * x**7 * y * z**12],
gens=(x, y, z)) == ([{
(7, 1, 12): 17
}], (x, y, z))
assert parallel_dict_from_expr([x + 2 * y + 3 * z], gens=(x, )) == ([{
(1, ):
1,
(0, ):
2 * y + 3 * z
}], (x, ))
assert parallel_dict_from_expr([x + 2 * y + 3 * z], gens=(x, y)) == ([{
(1, 0):
1,
(0, 1):
2,
(0, 0):
3 * z
}], (x, y))
assert parallel_dict_from_expr([x + 2 * y + 3 * z], gens=(x, y, z)) == ([{
(1, 0, 0):
1,
(0, 1, 0):
2,
(0, 0, 1):
3
}], (x, y, z))
assert parallel_dict_from_expr([x * y + 2 * x * z + 3 * y * z],
gens=(x, )) == ([{
(1, ): y + 2 * z,
(0, ): 3 * y * z
}], (x, ))
assert parallel_dict_from_expr([x * y + 2 * x * z + 3 * y * z],
gens=(x, y)) == ([{
(1, 1): 1,
(1, 0): 2 * z,
(0, 1): 3 * z
}], (x, y))
assert parallel_dict_from_expr([x * y + 2 * x * z + 3 * y * z],
gens=(x, y, z)) == ([{
(1, 1, 0): 1,
(1, 0, 1): 2,
(0, 1, 1): 3
}], (x, y, z))
assert parallel_dict_from_expr([2**y * x], gens=(x, )) == ([{
(1, ): 2**y
}], (x, ))
assert parallel_dict_from_expr([Integral(x, (x, 1, 2)) + x]) == ([{
(0, 1): 1,
(1, 0): 1
}], (x, Integral(x, (x, 1, 2))))
pytest.raises(PolynomialError,
lambda: parallel_dict_from_expr([2**y * x], gens=(x, y)))
def test_parallel_dict_from_expr():
assert parallel_dict_from_expr([Eq(x, 1), Eq(
x**2, 2)]) == ([{(0,): -1, (1,): 1},
{(0,): -2, (2,): 1}], (x,))
pytest.raises(PolynomialError, lambda: parallel_dict_from_expr([A*B - B*A]))
def test__parallel_dict_from_expr_if_gens():
assert parallel_dict_from_expr([x + 2*y + 3*z, Integer(7)], gens=(x,)) == \
([{(1,): Integer(1), (0,): 2*y + 3*z}, {(0,): Integer(7)}], (x,))
assert parallel_dict_from_expr((Mul(x, x**2, evaluate=False),), gens=(x,)) == \
([{(3,): 1}], (x,))
