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bug in raising a Series to a power

• To: mathgroup at yoda.ncsa.uiuc.edu
• Subject: bug in raising a Series to a power
• From: dabell at ruflie.umd.edu (Dan Abell)
• Date: Fri, 1 Feb 91 13:45:48 EST

In raising a polynomial Series of more than one variable to some power, 
Mathematica responds with a rational Series.  (!?)  The following 
commands (Mathematica's response not shown) illustrate the problem. 

Here is a polynomial:

poly[q_,p_] = Expand[ q+p + (q+p)^3 + (q+p)^5 ]

Now turn this into a polynomial Series, keeping terms through order 6 
in the variables q and p:

poly[eps q, eps p] + O[eps]^7

Now try squaring this Series:

ExpandAll[ (poly[eps q, eps p] + O[eps]^7)^2 ]

Mathematica responds with a Series that includes rational 
sub-expressions.  What's going on?