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Re: CrossProduct[ ]

There seems to be a misunderstanding about CrossProduct[ ] in
Calculus`VectorAnalysis`.  In particular, when the default coordinate
system is Cylindrical (or anything but Cartesian) this refers to
the global coordinate system.  Grad[ ] gives results in terms of the
local, infinitesimal coordinate system which is NOT Cylindrical,
but rather Cartesian.  Thus when you use CrossProduct[ ] (or DotPrduct[ ]
or ScalarTripleProduct[ ]) with vectors from the local, infinitesimal
coordinate system, you need to specify that you are refering to a
Cartesian coordinate system:

In[1]:= <<Calculus`VectorAnalysis`

In[2]:= SetCoordinates[Cylindrical]

Out[2]= Cylindrical[r, theta, z]

In[3]:= CrossProduct[Grad[r], Grad[theta], Cartesian]

Out[3]= {0, 0, -}

It could well be argued that this is a misfeature.  Does one ever
want to take the cross product of vectors in anything other than
a Cartesian system?  If so how often?  Should the default be
Cartesian with the ability to specify something else?  I can
easily change this, but it is not the sort of mathematics that I
use and I don't know what the default should be.

Jerry B. Keiper
keiper at

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