Severe slow-down in elliptic_curve integral_points()

[jdemeyer]

Consider the file

E = EllipticCurve([-879984,319138704])
P1 = E.point((540,1188))
P2 = E.point((576,1836))
P3 = E.point((468,3132))
P4 = E.point((612,3132))
P5 = E.point((432,4428))
t = cputime()
pts = E.integral_points([P1,P2,P3,P4,P5])
print "Time:", cputime(t)

With sage-4.8, this takes about 35 seconds. With sage-5.0.beta10, the same test takes about 50 seconds.

This is caused by #11599.

[novoselt]

As a reviewer of #11599: it was a major clean up of the generic scheme code which made it readable and conforming to current Sage framework, please don't unmerge it...

[jdemeyer]

I can confirm that this is caused by #11599. When applying #11599 to sage-5.0.beta3, I get the same slowdown.

[jdemeyer]

Replying to novoselt:

As a reviewer of #11599: it was a major clean up of the generic scheme code which made it readable and conforming to current Sage framework, please don't unmerge it...

Well, if the slow-down cannot be fixed, I have not much choice... I don't want to release sage-5.0 with such a massive speed regression.

[novoselt]

With this patch on Sage-5.0.beta12 the example from the description drops on my machine from 37 to 12 seconds, which seems to be a severe speed-up compared to pre-#11599 state.

Given that this is achieved by a one-liner taking repeated computations out of the loop, perhaps nobody was really bothered by the speed of this code and as long as it works it is fine...

[novoselt]

For the record: profiler shows drop from 24 to 9 millions of primitive calls.

[jdemeyer]

Positive review provided:

1. You put a proper commit message in your patch
2. This actually passes doctests (which I'm checking right now)

[jdemeyer]

I added a commit message and changed some timings. If you agree with my changes, you can set positive_review.