Allow negative shift for flint rational polynomial

[user202729]

Fixes #39710

Note that the behavior is compatible with the existing behavior of e.g. ZZ[].

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[tscrim]

I don't think this will (fully) fix #39710. If it indeed does, then please add the corresponding tests.

[user202729]

Actually thinking about it this will still fail if user says something like .truncate_neg(-10^30) or .truncate_neg(10^30) because the computed value overflows. Even though .truncate_neg(-10^30) is completely safe, just return self.

On the other hand .truncate_neg(10^30) cannot work (the __n is a long so it would overflow n, unless the element has infinite precision in the beginning)

Actually it is worse than that: n - self.__n may overflow and return the wrong result?

Do you think it's worth supporting these (rather exceptional, I think) cases?

[tscrim]

I don't think it is worth worrying about those cases. I don't think there will be a good reason for someone to do computations like that.

Does this also work for (t+t^2).truncate_neg(-2)? i think you coincidentally get a shift by 0, which hides a bug that would delete coefficients.

[user202729]

It does work. The point of >> is to delete coefficients (in order to truncate).

If n-self.__n is negative then it will shift left, no coefficient is deleted. (the two tests truncate_neg(-1) and truncate_neg(-2) have shift by -2 and -3 respectively.)

[tscrim]

Ah, you're right. I got the directions of everything with the signs all mixed up in my head. Thanks. Once tests pass, positive review.

From an optimization POV, I think it would be better to simply return self in the case n is less than the valuation, but that can be done on a followup (if you want).