Partial sums of symbolic series?

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Alasdair McAndrew 2016-10-13

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评论： Alasdair McAndrew 2016-10-14

I am just beginning to explore the symbolic math toolbox. And I can't work out how to create a sequence of symbolic partial sums. Suppose I enter, for example:

    syms t
    T = taylor(exp(sin(t),t,'Order',12)
    c = children(T)

The answer has the constant term at the end, instead of the start, so that

cumsum(c)

is not correct. I can write a little program to list all the partial sums:

    V = []
    for n=1:12
      V = [V,taylor(exp(sin(t),t,'Order',n)];
    end

but that seems very clumsy. Is there a better, more canonic way to do this?

Finally, with the array V above, if I display V, it's done using abbreviations, so that terms aren't repeated. How can I display V simply, in full?

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Answer 1

Walter Roberson 2016-10-13

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cumsum([c(end), c(1:end-1)])

However, remember that the order of terms is not documented, so relying on children() to return them in sorted order is not robust. To get sorted order you should be looking at coeffs()

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Answer 2

Alasdair McAndrew 2016-10-13

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Thank you - yes I know that the vector I gave can be re-ordered, but in general it would be nice if "children" (at least when applied to polynomials) could give its results in lexicographic order of powers of the variables.

So I guess it's back to "coeffs", as you say:

T = taylor(exp(sin(x),x,'Order',12)
[c,p] = coeffs(T,x)
terms = fliplr(c.*p)
cumsum(terms)

Thanks again for the heads up!

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Walter Roberson 2016-10-13

Remember too that it is common for either odd or even powers in taylor to be 0, so the cumulative sum there should reflect the 0 terms. That would correspond to using the 'All' parameter of coeffs.

Alasdair McAndrew 2016-10-14