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| 29 Aug 17:00

Review Request: Polynomial

Hi,
I'd like to request a review of my polynomial library which I wrote during
Google Summer of Code project this year.

The zip file is in Boost Vault (called polynomial.zip). It includes the
library, tests and documentation.
The same files (not compressed) are also available in sandbox:
http://svn.boost.org/svn/boost/sandbox/SOC/2008/polynomial/

Thanks

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Pawel Kieliszczyk
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Ronald Garcia | 30 Aug 17:49
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Re: Review Request: Polynomial

Hi Paweł,

I have added your library to the review queue.  Could you please send  
me a short description of the library?

Thanks,
ron

On Aug 29, 2008, at 11:04 AM, Paweł Kieliszczyk wrote:

> Hi,
> I'd like to request a review of my polynomial library which I wrote  
> during
> Google Summer of Code project this year.
>
> The zip file is in Boost Vault (called polynomial.zip). It includes  
> the
> library, tests and documentation.
> The same files (not compressed) are also available in sandbox:
> http://svn.boost.org/svn/boost/sandbox/SOC/2008/polynomial/
>
> Thanks
>
> -- 
> Pawel Kieliszczyk
> _______________________________________________
> Unsubscribe & other changes: http://lists.boost.org/mailman/ 
> listinfo.cgi/boost

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| 31 Aug 12:12

Re: Review Request: Polynomial

Hi,

2008/8/30 Ronald Garcia <garcia <at> cs.indiana.edu>
> Hi Paweł,
>
> I have added your library to the review queue.  Could
> you please send me a short description of the library?
>
> Thanks,
> ron

Thanks.

The library was written to enable fast and faithful polynomial manupulation.
It provides:
- main arithmetic operators (+, -, * using FFT, /, %),
- gcd,
- different methods of evaluation (Horner Scheme, Compensated Horner
Algorithm, by preconditioning),
- derivatives and integrals,
- interpolation,
- conversions between various polynomial forms (special functions for
creating Chebyshev, Hermite, Laguerre and Legendre form).

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Daryle Walker | 2 Sep 00:44
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Re: Review Request: Polynomial

On Aug 31, 2008, at 6:12 AM, Paweł Kieliszczyk wrote:

[SNIP]
> The library was written to enable fast and faithful polynomial  
> manupulation.
> It provides:
> - main arithmetic operators (+, -, * using FFT, /, %),
[TRUNCATE]

(I haven't looked at the library yet, so this may be not  
applicable.)  Isn't there something called DFT that is something like  
FFT, but uses integers with modulo arithmetic?  I think this can help  
processing polynomials and other lists that use integer coefficients  
without having to go into std::complex<double> arithmetic and risking  
rounding errors.  Maybe that could be an optimization for integer- 
based polynomial lists.

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Daryle Walker
Mac, Internet, and Video Game Junkie
darylew AT hotmail DOT com

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| 3 Sep 16:51

Re: Review Request: Polynomial

2008/9/2 Daryle Walker wrote:
>
> > (I haven't looked at the library yet, so this may be not applicable.)
> Isn't there something called DFT that is something like FFT, but
> uses integers with modulo arithmetic?  I think this can help
> processing polynomials and other lists that use integer coefficients
> without having to go into std::complex<double> arithmetic and
> risking rounding errors.  Maybe that could be an optimization for
> integer-based polynomial lists.

Hi Daryle,
I guess you're not thinking of Discrete Fourier Transform that is a form
actually and also needs roots of unity. Well, in the library I used same FFT
for every types of coefficients. Can you please expand this shortening or
tell me where I could read more about it?

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Daryle Walker | 30 Oct 17:27
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Re: Review Request: Polynomial

On Sep 3, 2008, at 10:51 AM, Paweł Kieliszczyk wrote:

> 2008/9/2 Daryle Walker wrote:
>>
>>> (I haven't looked at the library yet, so this may be not  
>>> applicable.)
>> Isn't there something called DFT that is something like FFT, but
>> uses integers with modulo arithmetic?  I think this can help
>> processing polynomials and other lists that use integer coefficients
>> without having to go into std::complex<double> arithmetic and
>> risking rounding errors.  Maybe that could be an optimization for
>> integer-based polynomial lists.
>
> Hi Daryle,
> I guess you're not thinking of Discrete Fourier Transform that is a  
> form
> actually and also needs roots of unity. Well, in the library I used  
> same FFT
> for every types of coefficients. Can you please expand this  
> shortening or
> tell me where I could read more about it?
Modulo arithmetic can also generate roots of unity.  For example, if  
the base is 31, then 2 is a fifth-root of unity (because 2**5 = 32 ->  
1 under mod-31).  The more precise term is "Number-theoretic  
transform," so look it up.

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-- 
Daryle Walker
Mac, Internet, and Video Game Junkie
darylew AT hotmail DOT com
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