def __new__(cls, f, x, index=None, radicals=False, expand=True):
""" Construct an indexed complex root of a polynomial.
See ``rootof`` for the parameters.
The default value of ``radicals`` is ``False`` to satisfy
``eval(srepr(expr) == expr``.
"""
x = sympify(x)
if index is None and x.is_Integer:
x, index = None, x
else:
index = sympify(index)
if index is not None and index.is_Integer:
index = int(index)
else:
raise ValueError("expected an integer root index, got %s" % index)
poly = PurePoly(f, x, greedy=False, expand=expand)
if not poly.is_univariate:
raise PolynomialError("only univariate polynomials are allowed")
if not poly.gen.is_Symbol:
# PurePoly(sin(x) + 1) == PurePoly(x + 1) but the roots of
# x for each are not the same: issue 8617
raise PolynomialError("generator must be a Symbol")
degree = poly.degree()
if degree <= 0:
raise PolynomialError("can't construct CRootOf object for %s" % f)
if index < -degree or index >= degree:
raise IndexError("root index out of [%d, %d] range, got %d" %
(-degree, degree - 1, index))
elif index < 0:
index += degree
dom = poly.get_domain()
if not dom.is_Exact:
poly = poly.to_exact()
roots = cls._roots_trivial(poly, radicals)
if roots is not None:
return roots[index]
coeff, poly = preprocess_roots(poly)
dom = poly.get_domain()
if not dom.is_ZZ:
raise NotImplementedError("CRootOf is not supported over %s" % dom)
root = cls._indexed_root(poly, index)
return coeff * cls._postprocess_root(root, radicals)
def __new__(cls, f, x, index=None, radicals=True, expand=True):
"""Construct a new ``RootOf`` object for ``k``-th root of ``f``. """
x = sympify(x)
if index is None and x.is_Integer:
x, index = None, x
else:
index = sympify(index)
if index.is_Integer:
index = int(index)
else:
raise ValueError("expected an integer root index, got %d" % index)
poly = PurePoly(f, x, greedy=False, expand=expand)
if not poly.is_univariate:
raise PolynomialError("only univariate polynomials are allowed")
degree = poly.degree()
if degree <= 0:
raise PolynomialError("can't construct RootOf object for %s" % f)
if index < -degree or index >= degree:
raise IndexError("root index out of [%d, %d] range, got %d" %
(-degree, degree - 1, index))
elif index < 0:
index += degree
dom = poly.get_domain()
if not dom.is_Exact:
poly = poly.to_exact()
roots = cls._roots_trivial(poly, radicals)
if roots is not None:
return roots[index]
coeff, poly = preprocess_roots(poly)
dom = poly.get_domain()
if not dom.is_ZZ:
raise NotImplementedError("RootOf is not supported over %s" % dom)
root = cls._indexed_root(poly, index)
return coeff * cls._postprocess_root(root, radicals)