Weaker wording for infinite continued fraction?

[Georgi Guninski]

I believe real constant $C$ is irrational iff its continued fraction
is infinite.
There are many famous constants which irrationality is unknown.
For a lot of constants sage gives exception:
```
sage: cf=list(continued_fraction(catalan))
ValueError: the length is infinite!
```

Should the error use weaker wording?

Another test is coercing to QQ and there the wording is better:
```
sage: QQ(catalan)
TypeError: unable to convert catalan to a rational

[Georgi Guninski]

```
sage: cf=list(continued_fraction(catalan))
ValueError: the length is infinite!
```

To clarify: it is an open problem if catalan is irrational and the
error gives definite answer.

[Nils Bruin]

Locally, the routine performs consistently with its documentation:

Init signature: sage.rings.continued_fraction.ContinuedFraction_real(x)

Docstring:    
Continued fraction of a real (exact) number.

This class simply wraps a real number into an attribute (that can be
accessed through the method "value()"). The number is assumed to be
irrational.

A fully rigorous verson would require a proof of irrationality of x as part of the input; probably.

The value error from `list` is specific to the type, so its terminology could be toned down, but worse things happen if the constructor gets called with a rational argument:

sage: sage.rings.continued_fraction.ContinuedFraction_real(355/113)
[3; 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]

compare with:

sage: continued_fraction(355/113)
[3; 7, 16]

Concerning:

sage: QQ(catalan)
TypeError: unable to convert catalan to a rational

that's entirely reasonable, since sage doesn't know catalan to be rational and hence cannot do the conversion. No claim about the rationality of catalan is made.

[Georgi Guninski]

>Init signature: sage.rings.continued_fraction.ContinuedFraction_real(x)
>Docstring:
> Continued fraction of a real (exact) number.

I am not using this constructor, using the constructor of
`continued_fraction` whose documentation doesn't assume irrational
number. Check the testcases and the differences for trivially
rational values.