algebraic number package?

[Ralf Stephan]

Hello,

The qqbar source does not use a lower-level library. My question:

is there a stand-alone open-source fast version of such a package?

Reason I'm asking is linkage with Pynac.

Regards,

[John Cremona]

As far as I know the only other software offering a similar
functionality is Magma's AlgebraicallyClosedFIeld system, which was a
groundbreaking idea when first proposed and implemented there by Allan
Steele.

That's a "no" from me, but I would be very interested to be proved wrong!

John

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[Fredrik Johansson]

There are immediate plans to implement embedded number fields and qqbar in Flint/Antic (https://github.com/wbhart/antic). In fact, there will be a workshop and coding sprint in Kaiserslautern, 31 July - 4 August partially dedicated to this topic. The workshop hasn't been formally announced yet, but here is a wiki page: https://github.com/Nemocas/Nemo.jl/wiki/OSCAR-:-Antic-Workshop--and--coding-sprint

Anyone who is interested is welcome to attend.

Fredrik

[Ralf Stephan]

On Friday, May 26, 2017 at 6:04:15 PM UTC+2, Fredrik Johansson wrote:

There are immediate plans to implement embedded number fields and qqbar in Flint/Antic (https://github.com/wbhart/antic). In fact, there will be a workshop and coding sprint in Kaiserslautern, 31 July - 4 August partially dedicated to this topic. The workshop hasn't been formally announced yet, but here is a wiki page: https://github.com/Nemocas/Nemo.jl/wiki/OSCAR-:-Antic-Workshop--and--coding-sprint

Great news! 

[Jeroen Demeyer]

On 2017-05-26 15:19, Ralf Stephan wrote:
> The qqbar source does not use a lower-level library.

What do you mean with this? It actually uses quite a large fraction of
Sage (number fields, polynomials, interval arithmetic, ...)

[Ralf Stephan]

Make that "lower-language-level" i.e. C/C++. There was also

the words "one" and "fast" in my original post.

[Dima Pasechnik]

Is qqbar really so slow? Perhaps you could point out particularly slow for your purposes parts ?

 

[Ralf Stephan]

The case that started me was

sage: a=SR(1/2)
sage: b=SR(3)
sage: %timeit _=a^b
The slowest run took 9.38 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 2.14 µs per loop
sage: %timeit _=b^a
10000 loops, best of 3: 62.1 µs per loop

but I think I can shortcut Python/Cython usage here.

I also wanted to scout the software landscape before any other decisions.

[John Cremona]

On 29 May 2017 07:59, "Ralf Stephan" <gtr...@gmail.com> wrote:

The case that started me was

sage: a=SR(1/2)
sage: b=SR(3)
sage: %timeit _=a^b
The slowest run took 9.38 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 2.14 µs per loop
sage: %timeit _=b^a
10000 loops, best of 3: 62.1 µs per loop

but I think I can shortcut

Your example does not use QQbar at all!  It uses SR (Symbolic Ring) which is quite different.

Python/Cython usage here.

I also wanted to scout the software landscape before any other decisions.

On Monday, May 29, 2017 at 8:39:59 AM UTC+2, Dima Pasechnik wrote:

On Monday, May 29, 2017 at 6:09:33 AM UTC+1, Ralf Stephan wrote:

On Sunday, May 28, 2017 at 11:40:08 PM UTC+2, Jeroen Demeyer wrote:

On 2017-05-26 15:19, Ralf Stephan wrote:
> The qqbar source does not use a lower-level library.

What do you mean with this? It actually uses quite a large fraction of
Sage (number fields, polynomials, interval arithmetic, ...)

Make that "lower-language-level" i.e. C/C++. There was also

the words "one" and "fast" in my original post.

Is qqbar really so slow? Perhaps you could point out particularly slow for your purposes parts ?

 

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[Ralf Stephan]

Yes but if Pynac had such a type, and fast, the operations with any roots (as parts of expressions) would be much simplified. Relying on Python/Cython code from the C++ end is always tedious and slow.

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[Dima Pasechnik]

On Monday, May 29, 2017 at 12:03:59 PM UTC+1, Ralf Stephan wrote:

Yes but if Pynac had such a type, and fast, the operations with any roots (as parts of expressions) would be much simplified. Relying on Python/Cython code from the C++ end is always tedious and slow.

I don't know a library like this that allows you to directly manipulate non-integer powers of (real, or not) algebraic

numbers.

I am aware of GAP packages Alnuth and Radiroot (Radiroot can show you roots of polynomial equations with solvable

Galois group, expressed via radicals, so this seems to come close to what you'd like to have)

that provide some functionality to deal with roots of algebraic numbers; they interface Pari/GP for this purpose.

(they use a simple and slow interface via files, AFAIK, but that's beside the point).

Pari/GP has a C library interface, which is a part of Sage.