Binomial Coefficient of Real- or ComplexIntervalField

[skropf]

The computation of the binomial coefficient of a RIF or CIF (choosing an integer) gives an error:

sage: binomial(CIF(1),2)
Traceback (click to the left of this block for traceback)
...
TypeError: Either m or x-m must be an integer

This worked well in a previous Sage version (it was 5.13 or later).

[ppurka]

I suspect it is #9634 that introduced the change.

[cheuberg]

Yes, it works until commit 2202e18 and fails to work with commit d2c82ff, i.e. the merge of #9634.

[cheuberg]

The second argument 2 is converted into a CIF when Function_binomial._evalf_ is called. Therefore, it is no longer recognized as an integer in sage.rings.arith.binomial.

Actually, sage.rings.arith.binomial(CIF(1), 2) yields 0, as expected.

[ppurka]

One can take this opportunity to clean up the binomial function itself and make it clearer what it does. It is in a bit of a mess.

[cheuberg]

The following is probably related:

sage: R.<n> = ZZ[]
sage: binomial(n, 3).parent()
Symbolic Ring

is annoying; however,

sage: R.<n> = AsymptoticRing('n^QQ', QQ)
sage: binomial(n, 3)
Traceback (most recent call last):
...
TypeError: cannot coerce arguments: no canonical coercion from Asymptotic Ring <n^QQ> over Rational Field to Symbolic Ring

throws an error because aysmptotic rings intentionally do not coerce into the symbolic ring.

[cheuberg]

Replying to cheuberg:

The following is probably related:

It turns out that this is unrelated; in fact, the problem described in this ticket has been fixed at some stage.

I added a doctest.

sage: R.<n> = ZZ[]
sage: binomial(n, 3).parent()
Symbolic Ring

In fact, this works for polynomials over the rationals, so this is not a real issue.

---

New commits:

​aa86dd8

Trac #16726: Add doctest

[cheuberg]

I opened #22314 for the issue concerning the asymptotic ring. Sorry for the noise here.

[rws]

LGTM.