(aa, bb, cc, prec=None)
return ressqrt
r"""
    Calculates the Delta coefficient of the 3 angular momenta for
    Racah symbols. Also checks that the differences are of integer
    value.

    INPUT:

    -  ``aa`` - first angular momentum, integer or half integer

    -  ``bb`` - second angular momentum, integer or half integer

    -  ``cc`` - third angular momentum, integer or half integer

    -  ``prec`` - precision of the ``sqrt()`` calculation

    OUTPUT:

    double - Value of the Delta coefficient

    EXAMPLES::

        sage: from sage.functions.wigner import _big_delta_coeff
        sage: _big_delta_coeff(1,1,1)
        1/2*sqrt(1/6)
r"""
    Calculates the Delta coefficient of the 3 angular momenta for
    Racah symbols. Also checks that the differences are of integer
    value.
r Calculates the Delta coefficient of the 3 angular momenta for Racah symbols . Also checks that the differences are of integer value .
def _big_delta_coeff(aa, bb, cc, prec=None):
    r"""
    Calculates the Delta coefficient of the 3 angular momenta for
    Racah symbols. Also checks that the differences are of integer
    value.

    INPUT:

    -  ``aa`` - first angular momentum, integer or half integer

    -  ``bb`` - second angular momentum, integer or half integer

    -  ``cc`` - third angular momentum, integer or half integer

    -  ``prec`` - precision of the ``sqrt()`` calculation

    OUTPUT:

    double - Value of the Delta coefficient

    EXAMPLES::

        sage: from sage.functions.wigner import _big_delta_coeff
        sage: _big_delta_coeff(1,1,1)
        1/2*sqrt(1/6)
    """

    if int(aa + bb - cc) != (aa + bb - cc):
        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
    if int(aa + cc - bb) != (aa + cc - bb):
        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
    if int(bb + cc - aa) != (bb + cc - aa):
        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
    if (aa + bb - cc) < 0:
        return 0
    if (aa + cc - bb) < 0:
        return 0
    if (bb + cc - aa) < 0:
        return 0

    maxfact = max(aa + bb - cc, aa + cc - bb, bb + cc - aa, aa + bb + cc + 1)
    _calc_factlist(maxfact)

    argsqrt = Integer(_Factlist[int(aa + bb - cc)] *
                     _Factlist[int(aa + cc - bb)] *
                     _Factlist[int(bb + cc - aa)]) / \
        Integer(_Factlist[int(aa + bb + cc + 1)])

    ressqrt = sqrt(argsqrt)
    if prec:
        ressqrt = ressqrt.evalf(prec).as_real_imag()[0]
    return ressqrt
def _big_delta_coeff ( aa , bb , cc , prec = None ) : if int ( aa + bb - cc ) != ( aa + bb - cc ) : raise ValueError ( "j values must be integer or half integer and fulfill the triangle relation" ) if int ( aa + cc - bb ) != ( aa + cc - bb ) : raise ValueError ( "j values must be integer or half integer and fulfill the triangle relation" ) if int ( bb + cc - aa ) != ( bb + cc - aa ) : raise ValueError ( "j values must be integer or half integer and fulfill the triangle relation" ) if ( aa + bb - cc ) < 0 : return 0 if ( aa + cc - bb ) < 0 : return 0 if ( bb + cc - aa ) < 0 : return 0 maxfact = max ( aa + bb - cc , aa + cc - bb , bb + cc - aa , aa + bb + cc + 1 ) _calc_factlist ( maxfact ) argsqrt = Integer ( _Factlist [ int ( aa + bb - cc ) ] * _Factlist [ int ( aa + cc - bb ) ] * _Factlist [ int ( bb + cc - aa ) ] ) / Integer ( _Factlist [ int ( aa + bb + cc + 1 ) ] ) ressqrt = sqrt ( argsqrt ) if prec : ressqrt = ressqrt . evalf ( prec ) . as_real_imag ( ) [ 0 ] return ressqrt