Add `coefficients(a::AbsPowerSeriesRingElem)`

[lgoettgens]

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##           master    #1811   +/-   ##
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  Coverage   88.03%   88.03%           
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  Files         119      119           
  Lines       30057    29995   -62     
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- Hits        26460    26406   -54     
+ Misses       3597     3589    -8     

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[thofma]

@fieker does that make sense?

[lgoettgens]

Ok, so what I wanted to add is a function that gives me all coefficients (as coeff does for a single one), but skipping the infinite sequence of zeros in the end. If there is any other clean way to get this, I am happy with using that instead as well.

[fieker]

you need to be thinking about what you want: you want the leading zeros? If the element has a valuation? @lgoettgens what do you need/ want? I think for polys we allow access past the degree - to get 0, for power series (and Laurent) even going to -infty would make sense

[lgoettgens]

I don't really care about leading zeros. I think having coefficients(a)[i] == coeff(a, i-1) work for all indices of coefficients(a) would be nice (this is as it is for polys).

[lgoettgens]

Bump

[thofma]

It is not clear to me that this right thing. length is not part of the interface and exporting pol_length was a mistake in the first place.

A faithful representation of the power series would need to include the coefficients up precision(x) - 1.

[lgoettgens]

That's true. I adapted the function an tests accordingly.

[fingolfin]

Off-topic, but: this function looks to me like another example of an extrep function as proposed in https://github.com/oscar-system/Oscar.jl/issues/4151. Which then raises the natural question: do we also have a reverse that takes such a coefficient list and turns it back into a series? E.g. a == parent(a)(coefficients(a)) ?

[thofma]

@fieker this now goes up to precision(x) -1. Are you happy with this?

[lgoettgens]

Unfortunately, due to branch names being weird, this has to get force-merged. @fingolfin @thofma could you do the favor?