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Series algorithm changed between Mathematica 11.0.0.0 and 11.1.0.0

Amir-Kian Kashani-Poor
Posted 10 years ago

The series algorithm appears to have changed in the latest Mathematica version.

Series[Exp[x]/Sqrt[x], {x, 0, 1}]

still yields a series expansion in O[x]^{1/2}

but 

Series[Exp[1 - x]/Sqrt[1 - x], {x, 1, 1}]

now yields a series O[x-1] instead of O[x-1]^{1/2}, as it previously did. Is there some logic to this, or is this bug? If the latter, how does one go about reporting such a thing?

Thanks for your input.
POSTED BY: Amir-Kian Kashani-Poor
9 Replies
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POSTED BY: Daniel Lichtblau
POSTED BY: Michael Rogers 
Normal @ Series[(x - y)^2, {x, x0, 1}, {y, y0, 1}] // Expand

2 x x0 - x0^2 - 2 x y + 2 y y0 - y0^2

((x - y)^2 /. {x -> x0, 
     y -> y0}) + ((D[(x - y)^2, {{x, y}}]) /. {x -> x0, y -> y0}).{x -
      x0, y - y0} // Expand

2 x x0 - x0^2 - 2 x0 y - 2 x y0 + 2 x0 y0 + 2 y y0 - y0^2
POSTED BY: Frank Kampas

Do you have an actual, specific proposal? I've yet to see anything concrete, not even in answer to specific questions I raised. This is the sort of thing that typically gets removed by moderators.
POSTED BY: Daniel Lichtblau

Given that Taylor series are taught in first-year calculus courses, it seems to me that having a function to do them is a no-brainer.
POSTED BY: Frank Kampas

This feature, does it have a specification beyond "implement multivariate series"? What might that spec be? For example what would be a sample input and output? What would be the restrictions on inputs? Holomorphic functions in some region? Something else? Would the result use order terms?

What I'm getting at is I don't see this as in any way a part of the current Series function. A TaylorPolynomial function might be useful. But it would be a different function. I see no way this could be construed as feature missing from Series.

Will such a function show up in a future release? I'm not sure. There is an ongoing project to extend multivariate capabilities in some areas related to this, so it would not surprise me. But I do not have definite knowledge one way or the other.
POSTED BY: Daniel Lichtblau

You're right. I'm talking about a feature that should have gone into Series when it was first introduced (or a separate function created), not the changes in the most recent version.
POSTED BY: Frank Kampas

(1) Multivariate series mean different things to different people. The iterated form supported makes perfect sense and works in a way that requires no departure from univariate.

(2) If what is wanted is a total degree series, the method to do this is fairly well known. It requires introduction of a new variable. I have to wonder how that would fit into the framework of Series? (Short answer: Quite poorly.)

(3) This would appear to be a case of hijacking a thread. It has naught to do with the Series changes that went into 11.1.
POSTED BY: Daniel Lichtblau

It would be nice if there were an option to Series so that it would give a correct Taylor series expansion when the expansion is done on more than one variable.
POSTED BY: Frank Kampas
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