can't coerce pari to rational function field

[katestange]

The following fails

sage: R.<x,y> = PolynomialRing(QQ)
sage: S = R.fraction_field()
sage: S(pari((x+y)/y))
TypeError: no canonical coercion from Fraction Field of Multivariate Polynomial Ring in x, y over Rational Field to Rational Field

However, if you replace (x+y)/y with x+y, it works (in other words, polynomials work but rational functions don't).

[katestange]

I think it is probably related that the following fails: (with R and S as above)

S('(x+y)/y')

with the same error. Again, polynomial coercion like

S('x+y')

succeeds. (If someone finds that this is a different problem, please put in a separate ticket, but I'm guessing it's related.)

[pbruin]

In newer Sage versions (for example 5.13.beta0), the example S('(x+y)/y') works correctly, but the original example (converting from PARI) still fails.

[pbruin]

The problem seems to be this:

sage: R.<x,y> = PolynomialRing(QQ)
sage: a=pari((x+y)/y); a
1/y*x + 1
sage: a.numerator()
1/y*x + 1
sage: a.denominator()
1

Note that the following does work:

sage: b=pari((x+y)/x); b
(x + y)/x
sage: b.numerator()
x + y
sage: b.denominator()
x

Note also that the PARI types are different:

sage: a.type()
't_POL'
sage: b.type()
't_RFRAC'

This difference arises because PARI treats multivariate polynomials as iterated univariate polynomials. To PARI, a lives in Q(y)[x], and b in Frac(Q[y][x]).

The solution is probably to convert PARI elements of type t_POL coefficientwise into S.

[mstreng]

I'll review this as my first git review.

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New commits:

​a9fcc83

fix conversion PARI -> rational function field in several variables