Re: Bug in series expansion

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Subject	Re: Bug in series expansion
From	"peter....@gmail.com" <peter.luschny@gmail.com>
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> The result series(egf1, z, 9) is of type `polynom(anything,z)`, 
> but its coefficients are not of type `polynom(anything,x)`. 
> They are rational polynomials with `x+1` as denominator.

Your explanation for Maple's behavior is interesting, but of course
you dodge the question of how to evaluate this behavior.

I think we agree that

    x = y  ->  f(x) = f(y)  for a function f.

To what extent does this not also apply to

    simplify(x - y) = 0  ->  f(x) = f(y) ?

Maybe you can't guarantee that in all cases, but in such a 
simple example as the one shown here, I think it's essential. 
I just expect that as a user. And other CAS deliver that too.

Here's what the example looks like in SageMath:

    x, z = var("x, z")
    egf  = (1 + x*exp(x*z+z))/(x + 1)
    egf1 = (1 + x*exp(x*z)*exp(z))/(x + 1)

    simplify(egf - egf1)

# If you expand the exponential gfs, it works 
# with 'egf' as well as with 'egf1'. 

    t = taylor(egf, z, 0, 9)

    for n in range(7):
        print((factorial(n)*t.coefficient(z, n)).list())

[1]
[0, 1]
[0, 1, 1]
[0, 1, 2, 1]
[0, 1, 3, 3, 1]
[0, 1, 4, 6, 4, 1]
[0, 1, 5, 10, 10, 5, 1]

This is the output in both cases; in the exact same Jupyter 
environment, Maple would only display the last line, which 
I think is another bug.

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Thread

Bug in series expansion "peter....@gmail.com" <peter.luschny@gmail.com> - 2023-04-18 03:31 -0700
  Re: Bug in series expansion acer <maple@rogers.com> - 2023-04-18 13:27 -0700
    Re: Bug in series expansion "peter....@gmail.com" <peter.luschny@gmail.com> - 2023-04-19 04:42 -0700
      Re: Bug in series expansion acer <maple@rogers.com> - 2023-04-19 07:03 -0700
        Re: Bug in series expansion "peter....@gmail.com" <peter.luschny@gmail.com> - 2023-04-19 12:03 -0700
        Re: Bug in series expansion "peter....@gmail.com" <peter.luschny@gmail.com> - 2023-05-01 00:56 -0700

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