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How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart uses either a version of the Padé technique or the method of undetermined coefficients.

I know what the latter is (clear of fractions, collect by powers of the variable, equate coefficients of corresponding powers, solve the resulting linear system). What's the former?

(I know what Padé approximation is.)

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Shouldn't this be asked on Math.SE? – m_goldberg Apr 21 '13 at 23:16
I was hoping at least for some starting direction from somebody knowledgeable about the Mathematica internals, so I know what to ask elsewhere. – murray Apr 22 '13 at 3:20

I believe it's the theorem 1.4.4 here that shows the relationship between the Padé Table and the partial fractions expansion.

Mathematica graphics Mathematica graphics

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