Two versions of QQ(sqrt{-1}) upon startup

[Nils Bruin]

We have two copies upon startup:

sage: import gc
sage: Ks=[K for K in gc.get_objects() if
....: isinstance(K,sage.rings.number_field.number_field.NumberField_quadratic)]
sage: [latex(k.0) for k in Ks]
[i, \sqrt{-1}]

I suspect they are coming from symbolic/pynac.pyx:2046 (in init_pynac_I)

    K = QuadraticField(-1, 'I', embedding=CC.gen(), latex_name='i')

and from rings/qqbar.py:7699 (in _init_qqbar)

    QQbar_I_nf = QuadraticField(-1, 'I', embedding=CC.gen())

Should we perhaps both give them the same latex name so that these can be the same field?

[Nils Bruin]

A preliminary test shows that changing rings/qqbar.py:7699 to

QQbar_I_nf = QuadraticField(-1, 'I', embedding=CC.gen(), latex_name='i')

works fine and ensures that there's only one field created upon startup. Note that:

sage: latex(QQbar.0)
\text{\texttt{1*I}}

so it looks like the latex printing will not be affected by this change either.

[Frédéric Chapoton]

done

---

New commits:

​8aee254

trac 15298 only one field for I

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​cf4d4f8

trac 15298 only one field for I

[Ralf Stephan]

Doctest fails in qqbar.py which are logical. You can set to positive after adaptation.

[git]

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

​5aa64be

trac 15928 fixing doctests

[Frédéric Chapoton]

Thanks. This introduces a non-uniform behaviour for the latex of QQbar elements. Sometimes "i" will still be displayed as sqrt{-1}. I propose to keep that issue for another ticket. Objection ?

[Ralf Stephan]

Replying to chapoton:

Objection ?

None. Please go ahead.

[Frédéric Chapoton]

then let it be positive