Dear Mani chandra,

something really weird seems to be going on. This is a fresh session
of Sage 3.3:

sage: complex(0,1)*spherical_bessel_J(1,1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call
last)

/home/king/.sage/temp/mpc739/24191/_home_king__sage_init_sage_0.py in
<module>()

/home/king/SAGE/devel/sage-3.2.3/local/lib/python2.5/site-packages/
sage/structure/element.so in
sage.structure.element.RingElement.__mul__ (sage/structure/element.c:
8632)()

/home/king/SAGE/devel/sage-3.2.3/local/lib/python2.5/site-packages/
sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/
coerce.c:5847)()

TypeError: unsupported operand parent(s) for '*': '<type 'complex'>'
and 'Symbolic Ring'
sage: complex(0,1)*spherical_bessel_J(1,1)
1.0*(sin(1) - cos(1))*I



In other words, calling complex(0,1)*spherical_bessel_J(1,1) for the
first time yields a bug. Calling it the second time yields a result.

Do people agree that this is a bug? Shall I open a ticket?


I guess that, as a work-around, you should consider using a different
implementation of the complex unit in Sage.
There are (at least):
 * complex(0,1), which AFAIK is a Python builtin
 * I, which belongs to the "Symbolic Ring":
    sage: I^2
    -1
    sage: I.parent()
    Symbolic Ring
 * The imaginary unit in the complex double field:
    sage: CDF(0,1)
    1.0*I
    sage: CDF(0,1)^2
    -1.0 + 1.22464679915e-16*I
As you can see, CDF is numeric with the usual errors of numerical data
types.

Since "spherical_bessel_J" lives in the Symbolic world, i guess that
using "I" would work around the error.

Cheers,
       Simon
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