Problem displaying a number field (fractional) ideal

[cremona]

With 8.3.rc1:

sage: K.<a> = NumberField(x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x - 1)
sage: K.ideal(1,1)

takes a long time to return -- why? Using %time it immediately shows 1ms for the second line but the prompt does not appear until *minutes* later. So it is the display of the ideal which is triggering something long. In a new session:

sage: K.<a> = NumberField(x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x - 1)
sage: %time I=K.ideal([1,1])
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 1.08 ms
sage: %time I
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 10 µs
<long wait>

[cremona]

Since the field discriminant is less than 10^6 the string function calls gens_reduced, and that is taking the time. Specifially the call to self_cache_bnfisprincipal() is. This suggests that something needs fixing; but also it might be a good idea to include special case code for the unit ideal -- this ideal has norm 1 which is trivial to compute so returning the string '(1)' could be done as a short cut.

[jdemeyer]

Replying to cremona:

but also it might be a good idea to include special case code for the unit ideal -- this ideal has norm 1 which is trivial to compute so returning the string '(1)' could be done as a short cut.

That's such a special case, I'm not convinced that it's worth it.

[jdemeyer]

Replying to cremona:

Since the field discriminant is less than 10^6 the string function calls gens_reduced, and that is taking the time.

Indeed. So I would say that this heuristic bound of the discriminant is not sufficient to predict that the class group is easy to compute.

[jdemeyer]

I asked pari-dev.

• ​http://pari.math.u-bordeaux.fr/archives/pari-dev-1807/msg00001.html

[slelievre]

From ​Karim Belabas's answer on pari-dev:

In any case, you should never compute a bnfinit when it's not absolutely necessary. [ I.e. you should do it on the fly when the extra structure is a prerequisite for a specific function call. ]

[cremona]

There is something strange here. Nothing to do with the representation if ideals really. For this field, if you construct its pari_bnf, it takes ages to return even with no output:

sage: K.<a> = NumberField(x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x - 1)                                                                                 
sage: %time pK = K.pari_bnf(proof=False, units=False)                    
CPU times: user 1min 11s, sys: 128 ms, total: 1min 11s
Wall time: 1min 11s

but in a fresh Sage session, if I interrupt the second line immediately and then rerun it:

sage: K.<a> = NumberField(x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x - 1)                                                                                 
sage: %time pK = K.pari_bnf(proof=False, units=False)                
<interrupt after <1s>
sage: %time pK = K.pari_bnf(proof=False, units=False)                                                                                                  
CPU times: user 36 ms, sys: 0 ns, total: 36 ms
Wall time: 37.2 ms

Also, after this, displaying K.ideal(1,1) is instantaneous. So I think that there *is* a bug in here, though I cannot tell what is happening.

Simplifying further:

sage: y = polygen(QQ, 'y')                                                                                                                             
sage: f = pari(y^6 - y^5 - 5*y^4 + 4*y^3 + 6*y^2 - 3*y - 1)                                                                                            
sage: %time f.bnfinit() 
CPU times: user 1min 9s, sys: 144 ms, total: 1min 9s
Wall time: 1min 9s

while again, interrupting immediately and reissuing the last line gives the output immediately.

Lastly,

sage: %gp                                                                                                                                              

  --> Switching to PARI/GP interpreter <--

pari: K = bnfinit(y^6 - y^5 - 5*y^4 + 4*y^3 + 6*y^2 - 3*y - 1);                                                                                        

pari: ##                                                                                                                                               
  ***   last result computed in 24 ms.

[vdelecroix]

What about 9.3.beta6? Sage 8.3.rc1 is not very relevant unless you precisely bisect where the problem is.

[vdelecroix]

(implicit note: I can not reproduce on 9.3.beta6)

[cremona]

The original posting was for an old version, but everything I wrote in the last 24 hours has been for 9.2, running on ubuntu, built from source.

[cremona]

Ah, and when I try on 9.3.beta6 is is fine. That's good! I'll mark this as invalid / won't-fix as something has fixed it between 9.2 and now.

[vdelecroix]

Maybe cypari2 upgrade #31029?

[slelievre]

Any way to add a doctest for this?

[cremona]

Replying to slelievre:

Any way to add a doctetcst for this?

Sure: the 2 lines of the original post should do.

[cremona]

I added a doctest as suggested. No code changes.

---

New commits:

​1e45e42

#25934: add doctest to show the problem has gone away

[cremona]

Review please? The patch just adds one tiny doctest.