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FullSimplify with Assumptions


In the examples below I would expect FullSimplify to give L. 
However, I get results that depend on the symbols I use.
It would appear that symbols x and y are treated differently. 

How can I force FullSimplify to use the LeafCount as the ComplexityFunction?


In[14]:= r1 = FullSimplify[(L - L*y^2)/x^2, {-1 + x^2 + y^2 == 0}]

Out[14]= (L - L*y^2)/x^2

In[15]:= r2 = FullSimplify[(L - L*x^2)/y^2, {-1 + x^2 + y^2 == 0}]

Out[15]= L

In[16]:= LeafCount[r1]

Out[16]= 12

In[17]:= LeafCount[r2]

Out[17]= 1

In[18]:= $Version

Out[18]= "5.1 for Microsoft Windows (October 25, 2004)"

Thanks for any comment

Hugh Goyder

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