provide method to access parent streams

[mantepse]

I trust that only the last element of the cache may contain the variable. I couldn't find a counterexample. It would be great if you could try to construct one.

I do not understand substitution in polynomial rings. In particular, I added a currently failing test.

The tests in lazy_series_ring.py now take about 30s on my laptop, I think that's too much.

As I mentioned elsewhere, the signature of integral should probably follow multi_power_series_ring_element.MPowerSeries.integral.

[mantepse]

Given sagemath#36575, I guess it makes sense to alert the user that define_implicitly only works if the coefficients of eqn are rational functions of the coefficients of self. Or can we do better?

[mantepse]

I'm afraid I need help with the failing test:

            sage: L.<z> = LazyPowerSeriesRing(QQ)
            sage: f = L.undefined(1)
            sage: f.define_implicity(log(1+f) - ~(1 + f) + 1, [])
            sage: f[1]
            0

This fails (ValueError: generator already executing) when trying to get the first coefficient of log(1 + f) with f "undetermined". I don't exactly see why. If I do it "by hand", I have

sage: I.<a> = InfinitePolynomialRing(QQ)
sage: L.<z> = LazyPowerSeriesRing(I)
sage: f = L(lambda n: a[n], valuation=1)
sage: F = log(1+f) - ~(1 + f) + 1
sage: F[0]
0
sage: F[1]
2*a_1

so a_1 must be zero.

I don't see what's going wrong.

[mantepse]

I think I understand now: replace does -- obviously -- not work with Stream_function.

Unfortunately, I don't see how it could.

[github-actions]

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