remove deprecated function about Simon 2-descent in BSD

[fchapoton]

That was deprecated in #35621

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[dcoudert]

LGTM.

[JohnCremona]

Fine, though I do not like the code which extracts the exponent from an integer power of 2 using real arithmetic. Note that the numbers returned by two_descent_by_two_isogeny() must be powers of 2, otherwise that function has done something incorrect. It would be better to (1) test that these numbers actually are powers of 2 and raise an error if not (that could be done in the function itself); (2) use n.valuation(2) to extract the exponent.

[fchapoton]

I can do that. Do you mean that all 4 numbers are powers of 2 ? Then what was the use of ceil for ?

[JohnCremona]

I can do that. Do you mean that all 4 numbers are powers of 2 ? Then what was the use of ceil for ?

All the numbers are powers of 2 by definition, since they are the orders of finite abelian groups with exponent 2. But the numbers are obtained by counting which if a set of equations has solutions, and it can happen that some of the equations do have solutions but the code did not find them, in which case there will be a shortfall (sometimes 1 less than a power of 2 is again a power of 2, but not usually!). Note that the code in descent_two_isogeny.pyx looks like a fairly straight rewrite of some of mwrank's code into cython, by Robert Miller in 2009, so I am well aware of the pitfalls. On the other hand, I just looked at the corresponding mwrank code (in dource file mrank2.cc) and it looks as if I build these groups up in a better way (adding generators, so doubling the order each time).

Somewhere along the line there should be a check that the numbers are powers of 2, with at least a warning if not. And if not, then you might get the right answer by rounding up, but there is no guarantee. I suggest raising an error if any are not powers of 2 and running the tests, to see if any of the test curves have this issue.

[fchapoton]

ok, here is a proposal. Doctests seem to meet no problem. Let's see if the CI agrees.

[JohnCremona]

I approve of the power of 2 check

[fchapoton]

so is this a positive review, John ?

[fchapoton]

I allowed myself to set to the status to "positive review" on your behalf, John. Is this ok ?

[JohnCremona]

I allowed myself to set to the status to "positive review" on your behalf, John. Is this ok ?

Sorry, I forget that now we have to do two separate things to approve changes.