def rs_hadamard_exp(p1, inverse=False):
"""
return ``sum f_i/i!*x**i`` from ``sum f_i*x**i``,
where ``x`` is the first variable.
If ``invers=True`` return ``sum f_i*i!*x**i``
Examples
========
>>> from diofant.polys.domains import QQ
>>> from diofant.polys.rings import ring
>>> R, x = ring('x', QQ)
>>> p = 1 + x + x**2 + x**3
>>> rs_hadamard_exp(p)
1/6*x**3 + 1/2*x**2 + x + 1
"""
R = p1.ring
if R.domain != QQ:
raise NotImplementedError
p = R.zero
if not inverse:
for exp1, v1 in p1.items():
p[exp1] = v1 / int(ifac(exp1[0]))
else:
for exp1, v1 in p1.items():
p[exp1] = v1 * int(ifac(exp1[0]))
return p
def rs_hadamard_exp(p1, inverse=False):
"""
return ``sum f_i/i!*x**i`` from ``sum f_i*x**i``,
where ``x`` is the first variable.
If ``invers=True`` return ``sum f_i*i!*x**i``
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.rings import ring
>>> from sympy.polys.ring_series import rs_hadamard_exp
>>> R, x = ring('x', QQ)
>>> p = 1 + x + x**2 + x**3
>>> rs_hadamard_exp(p)
1/6*x**3 + 1/2*x**2 + x + 1
"""
R = p1.ring
if R.domain != QQ:
raise NotImplementedError
p = R.zero
if not inverse:
for exp1, v1 in p1.items():
p[exp1] = v1/int(ifac(exp1[0]))
else:
for exp1, v1 in p1.items():
p[exp1] = v1*int(ifac(exp1[0]))
return p