def test_rewrite_single():
def t(expr, c, m):
e = _rewrite_single(meijerg([a], [b], [c], [d], expr), x)
assert e is not None
assert isinstance(e[0][0][2], meijerg)
assert e[0][0][2].argument.as_coeff_mul(x) == (c, (m,))
def tn(expr):
assert _rewrite_single(meijerg([a], [b], [c], [d], expr), x) is None
t(x, 1, x)
t(x ** 2, 1, x ** 2)
t(x ** 2 + y * x ** 2, y + 1, x ** 2)
tn(x ** 2 + x)
tn(x ** y)
def u(expr, x):
from sympy import Add, exp, exp_polar
r = _rewrite_single(expr, x)
e = Add(*[res[0] * res[2] for res in r[0]]).replace(exp_polar, exp) # XXX Hack?
assert verify_numerically(e, expr, x)
u(exp(-x) * sin(x), x)
# The following has stopped working because hyperexpand changed slightly.
# It is probably not worth fixing
# u(exp(-x)*sin(x)*cos(x), x)
# This one cannot be done numerically, since it comes out as a g-function
# of argument 4*pi
# NOTE This also tests a bug in inverse mellin transform (which used to
# turn exp(4*pi*I*t) into a factor of exp(4*pi*I)**t instead of
# exp_polar).
# u(exp(x)*sin(x), x)
assert _rewrite_single(exp(x) * sin(x), x) == (
[
(
-sqrt(2) / (2 * sqrt(pi)),
0,
meijerg(
(
(Rational(-1, 2), 0, Rational(1, 4), S.Half, Rational(3, 4)),
(1,),
),
((), (Rational(-1, 2), 0)),
64 * exp_polar(-4 * I * pi) / x ** 4,
),
)
],
True,
)
def test_rewrite_single():
def t(expr, c, m):
e = _rewrite_single(meijerg([a], [b], [c], [d], expr), x)
assert e is not None
assert isinstance(e[0][0][2], meijerg)
assert e[0][0][2].argument.as_coeff_mul(x) == (c, (m,))
def tn(expr):
assert _rewrite_single(meijerg([a], [b], [c], [d], expr), x) is None
t(x, 1, x)
t(x ** 2, 1, x ** 2)
t(x ** 2 + y * x ** 2, y + 1, x ** 2)
tn(x ** 2 + x)
tn(x ** y)
def u(expr, x):
from sympy import Add, exp, exp_polar
r = _rewrite_single(expr, x)
e = Add(*[res[0] * res[2] for res in r[0]]).replace(exp_polar, exp) # XXX Hack?
assert verify_numerically(e, expr, x)
u(exp(-x) * sin(x), x)
# The following has stopped working because hyperexpand changed slightly.
# It is probably not worth fixing
# u(exp(-x)*sin(x)*cos(x), x)
# This one cannot be done numerically, since it comes out as a g-function
# of argument 4*pi
# NOTE This also tests a bug in inverse mellin transform (which used to
# turn exp(4*pi*I*t) into a factor of exp(4*pi*I)**t instead of
# exp_polar).
# u(exp(x)*sin(x), x)
assert _rewrite_single(exp(x) * sin(x), x) == (
[
(
-sqrt(2) / (2 * sqrt(pi)),
0,
meijerg(
((-S(1) / 2, 0, S(1) / 4, S(1) / 2, S(3) / 4), (1,)),
((), (-S(1) / 2, 0)),
64 * exp_polar(-4 * I * pi) / x ** 4,
),
)
],
True,
)
def u(expr, x):
from sympy import Add, exp, exp_polar
r = _rewrite_single(expr, x)
e = Add(*[res[0] * res[2] for res in r[0]]).replace(exp_polar,
exp) # XXX Hack?
assert verify_numerically(e, expr, x)
def tn(expr):
assert _rewrite_single(meijerg([a], [b], [c], [d], expr), x) is None
def t(expr, c, m):
e = _rewrite_single(meijerg([a], [b], [c], [d], expr), x)
assert e is not None
assert isinstance(e[0][0][2], meijerg)
assert e[0][0][2].argument.as_coeff_mul(x) == (c, (m, ))
def u(expr, x):
from sympy import Add, exp, exp_polar
r = _rewrite_single(expr, x)
e = Add(*[res[0] * res[2] for res in r[0]]).replace(exp_polar, exp) # XXX Hack?
assert verify_numerically(e, expr, x)
def tn(expr):
assert _rewrite_single(meijerg([a], [b], [c], [d], expr), x) is None
def t(expr, c, m):
e = _rewrite_single(meijerg([a], [b], [c], [d], expr), x)
assert e is not None
assert isinstance(e[0][0][2], meijerg)
assert e[0][0][2].argument.as_coeff_mul(x) == (c, (m,))
