Error in precision of Tate elliptic curves over Qp

[wuthrich]

The optional precision arguments for Tate's elliptic curves are incorrectly implemented. For many functions, increasing the precision does not increase the precision of the output.

[wuthrich]

New commits:

​ff01d1c

precision for tate curves

[wuthrich]

Here an example of what was wrong

sage: E = EllipticCurve("126a5")
sage: Eq = E.tate_curve(2)
sage: R = Qp(2,30)
sage: u = R(2019)
sage: Eq.parametrisation_onto_original_curve(u, prec=30)
(2^-2 + 2^-1 + 1 + 2 + 2^3 + 2^7 + 2^8 + 2^15 + O(2^18) : 2^-3 + 2^-2 + 2^-1 + 2 + 2^2 + 2^5 + 2^6 + 2^7 + 2^9 + 2^11 + 2^14 + 2^15 + O(2^16) : 1 + O(2^30))

The precision drops to 20. Now fixed returns:

(2^-2 + 2^-1 + 1 + 2 + 2^3 + 2^7 + 2^8 + 2^15 + 2^18 + 2^19 + 2^20 + 2^21 + 2^26 + O(2^28) : 2^-3 + 2^-2 + 2^-1 + 2 + 2^2 + 2^5 + 2^6 + 2^7 + 2^9 + 2^11 + 2^14 + 2^15 + 2^19 + 2^20 + 2^23 + 2^24 + 2^25 + O(2^26) : 1 + O(2^30))

[edgarcosta]

FYI, src/sage/schemes/elliptic_curves/ell_tate_curve.py:233: local variable 'n' is assigned to but never used

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​9c537fb

del one useless var

[wuthrich]

Deleted that line.

[edgarcosta]

I'm sorry, but can't fully test this at the moment, so I can't give you examples, but I spotted a couple of issues (not introduced by you), but propagate through the rest:

1- One is always hitting an AttributeError in the try block in def parameter, as it should be calling precision_absolute. Also, the try block is a bit sad, as it should be just triggered by __init__. Perhaps a getattr(self, '_q', None) would make more sense.

2- Shouldn't we be checking for precision_relative? Given that we are always working with relative precision.

3- Shouldn't parameter return a value with the right precision? If not, we might need to work more and get results with more precision than expected.

4- Similar to the previous item, we should consider replacing R = qE.parent() by R = Qp(self._p, prec=prec) in def curve.

[wuthrich]

You may be right that there are more things that should be improved in that file. The purpose of this ticket is to correct a bug: I can increase the precision of the output by increasing the parameter prec. That was broken.

My proposal is that this is done on this ticket. Then we can open a further ticket to improve things.

In particular, I can get rid of try blocks (this is early sage when there were try blocks everywhere). We could also think about getting provable correct precisions out. Honestly, I have little interest in doing so, but I would be willing to go through the file and make the necessary changes. But I doubt that anyone uses the output in that way. We should at least, give a warning that it is not provable relative/absolute precision.

If we want to do everything on this ticket, it is likely to drag for months and may get abandoned when this simple quick fix would have improved sage.

[edgarcosta]

I agree with you, you should not fix this now.

Regarding the original bug, is this an expected output, or should one raise an exception?

sage: E = EllipticCurve("126a5")
sage: Eq = E.tate_curve(2)
sage: R = Qp(2,30)
sage: u = R(2019)
sage: Eq.parametrisation_onto_original_curve(u, prec=60)
(2^-2 + 2^-1 + 1 + 2 + 2^3 + 2^7 + 2^8 + 2^15 + 2^18 + 2^19 + 2^20 + 2^21 + 2^26 + O(2^28) : 2^-3 + 2^-2 + 2^-1 + 2 + 2^2 + 2^5 + 2^6 + 2^7 + 2^9 + 2^11 + 2^14 + 2^15 + 2^19 + 2^20 + 2^23 + 2^24 + 2^25 + O(2^26) : 1 + O(2^60))

[edgarcosta]

Ignore my comment, I will just move that to a new ticket

[vbraun]

Reviewer name is missing...