On Thu, Aug 30, 2018 at 5:11 AM Jonathan Fine <jfine2358@gmail.com> wrote:

Hi Neil

We wrote

...

...

This gives the same results as Python's Fraction, except for your example [6]. There, it gives the Fraction(0) you ask for.

If the smart mathematicians and computer scientists that wrote gp/pari get the same answers, it suggests to me that improvement would be hard.

...

That's because these are just floating point numbers. These are not being processed symbolically. Wolfram Alpha gives all three roots, including the real root.

I've not used Wolfram Alpha, nor I think have many people on this list. Please copy and paste the input and output from Alpha, so we can see for ourselves (and so there's a record on this list).

It's online for everyone to use: http://www.wolframalpha.com/input/?i=(-1)+%5E+(1%2F3)

If anyone has time and ready access, it would help to know what https://www.sympy.org/en/index.html does with this.

Perhaps your innocent request conceals a request for symbolic handling of simple algebraic numbers.

Well, rational numbers. Although an algebraic number type would be interesting. And, the way I see it, Fraction is the type corresponding to the field of rational numbers.

-- best regards

Jonathan

On Thu, Aug 30, 2018 at 5:11 AM Jonathan Fine <jfine2358@gmail.com> wrote:

Hi Neil

We wrote

...

...

This gives the same results as Python's Fraction, except for your example [6]. There, it gives the Fraction(0) you ask for.

If the smart mathematicians and computer scientists that wrote gp/pari get the same answers, it suggests to me that improvement would be hard.

...

That's because these are just floating point numbers. These are not being processed symbolically. Wolfram Alpha gives all three roots, including the real root.

I've not used Wolfram Alpha, nor I think have many people on this list. Please copy and paste the input and output from Alpha, so we can see for ourselves (and so there's a record on this list).

It's online for everyone to use: http://www.wolframalpha.com/input/?i=(-1)+%5E+(1%2F3)

If anyone has time and ready access, it would help to know what https://www.sympy.org/en/index.html does with this.

Perhaps your innocent request conceals a request for symbolic handling of simple algebraic numbers.

Well, rational numbers. Although an algebraic number type would be interesting. And, the way I see it, Fraction is the type corresponding to the field of rational numbers.

-- best regards

Jonathan