Conversion from pari to sage

[roed314]

Conversion from pari to Sage uses the global namespace:

sage: QQ['s'].gen()._pari_().sage()
Traceback (most recent call last):
...
NameError: name 's' is not defined
sage: GF(9, 'a').gen()._pari_().sage()
Traceback (most recent call last):
...
NameError: name 'a' is not defined

We can do better.

Component: interfaces

Issue created by migration from https://trac.sagemath.org/ticket/14194

[jdemeyer]

comment:1

What's the problem? I don't really see how you want to fix this.

[kedlaya]

comment:3

I'm sure roed knows this, but the correct call syntax here is:

sage: sage: R = QQ['s']
sage: sage: t = R.gen()._pari_()
sage: sage: R(t)
s
sage: F = GF(9, 'a')
sage: t = F.gen()._pari_()
sage: F(t)
a

After all, PARI has no class hierarchy, so why should a PARI univariate polynomial be expected to know which Sage polynomial ring it should convert back to?

If I were feeling provocative, I might go further and propose that the sage method of a PARI object should be deprecated in favor of the constructor syntax shown above, even for PARI types where there isn't any ambiguity about the Sage parent (e.g., integers).