Hashes of some Algebraic Field elements hang indefinitely

[gh-BrentBaccala]

The following code hangs on both Sage 7.5.1 and Sage 8.4:

R.<a> = QQ[]
NF.<b> = NumberField(4*a^7 + 27)
for hom in NF.embeddings(QQbar):
   print hash(hom(b))

[gh-BrentBaccala]

Here's another test case that I constructed after drilling down through the code:

from sage.rings.qqbar import AlgebraicGenerator, ANRoot

R.<y> = QQ[]
gen = y^14 - 6*y^7 + 18
NF.<a> = NumberField(gen)

root1 = ANRoot(gen, CIF(NF.embeddings(QQbar)[0](a)))
root2 = ANRoot(gen, CIF(NF.embeddings(QQbar)[1](a)))

ag1 = AlgebraicGenerator(NF, root1)
ag2 = AlgebraicGenerator(NF, root2)

ag1.union(ag2)

Changing gen around produces different answers. gen = y^2+18 produces the answer I'd expect from union: a number field defined by y² + 18. gen = y^3+18 produces a number field defined by a sixth degree polynomial; gen = y^7 + 18 produces a number field defined by a 42^nd degree polynomial.

I guess the 14^th degree polynomial leads to a calculation that takes excessively long, but I think it should be a very simple calculation if the two AlgebraicGenerator's are from the same number field - it should just return that field, right?

[gh-BrentBaccala]

Now that I've thought about it more, the number field might not be a splitting field, so it's more complicated than returning the same field.

[gh-BrentBaccala]

I found some comments in the code suggesting that when approximations to algebraic numbers are computed, an attempt is made to use 40 extra bits of precision, but it doesn't seem like that every actually got done.

I made the obvious change to actually compute 40 extra bits, and it seems to have solved my problem.

---

New commits:

​fc0e2e3

Trac #26898: actually use 40 bits of extra precision (like the comments say)

[mmezzarobba]

Should the ticket be set to needs_review?

[gh-BrentBaccala]

Replying to mmezzarobba:

Should the ticket be set to needs_review?

Yes, but I'm waiting for it to clear patchbot.

[mmezzarobba]

Replying to gh-BrentBaccala:

Replying to mmezzarobba:

Should the ticket be set to needs_review?

Yes, but I'm waiting for it to clear patchbot.

Unless you have your own patchbot with a special configuration, it (probably) won't even run the tests until the ticket needs_review.

But I've done it locally and all is well.

[embray]

This tickets were closed as fixed after the Sage 8.5 release.