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Maple Fourier series packages?

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Ray Vickson

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Nov 16, 2009, 2:49:34 PM11/16/09
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It seems that Maple (versions <= 9.5 at least) do not have Fourier
series packages; they do have Fourier transforms and discrete Fourier
capabilities for finite data sets. Has anybody developed a readily-
accessible Fourier series module for any version of Maple?

R.G. Vickson

Axel Vogt

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Nov 16, 2009, 4:11:37 PM11/16/09
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I think there is a package by Moiseev (however documented in the odd
Document mode) and one by Czech guy (forgot the name) at the Maple
application center. May be you can locate them, either there or by
searching at mapleprimes.com.

Robert Israel

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Nov 16, 2009, 4:19:44 PM11/16/09
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Ray Vickson <RGVi...@shaw.ca> writes:

Yes. Try Karel Srot's FourierTrigSeries package
<http://math.muni.cz/~xsrot/fourierseries/>
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Ray Vickson

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Nov 16, 2009, 4:36:34 PM11/16/09
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Thanks to Alex and Robert.

R.G. Vickson

Thomas Richard

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Nov 17, 2009, 3:39:50 AM11/17/09
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Please also check out Prof. Wilhelm Werner's FourierSeries package
at http://www.maplesoft.com/applications/view.aspx?SID=3606

--
Thomas Richard
Technical Support Maple/MapleSim
Scientific Computers GmbH
http://www.scientific.de

Nasser M. Abbasi

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Nov 17, 2009, 4:32:25 PM11/17/09
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"Thomas Richard" <t.ri...@scientific.de> wrote in message
news:fd964e57-c96c-49f4...@w19g2000yqk.googlegroups.com...

Hello;

How does current Maple release do in terms of its support for fourier
series? (for some reason my Maple 12 does not want to start any more on my
PC, I need to find why).

I assume Maple 13 now has complete support for this?

fyi, This below is a list of all the functions in Mathematica relating to
fourier. It will be nice to get such a list for Maple 13 just to compare.

DTFourierTransform
InverseDTFourierTransform
InverseFourierCoefficient
NDTFourierTransform
NFourierCoefficient
NFourierCosCoefficient
NFourierCosTransform
NFourierSeries
NFourierSinCoefficient
NFourierSinTransform
NFourierTransform
NFourierTrigSeries
NInverseDTFourierTransform
NInverseFourierCoefficient
NInverseFourierCosTransform
NInverseFourierSinTransform
NInverseFourierTransform
Fourier
FourierCoefficient
FourierCosCoefficient
FourierCosSeries
FourierCosTransform
FourierDCT
FourierDST
FourierSequenceTransform
FourierSeries
FourierSinCoefficient
FourierSinSeries
FourierSinTransform
FourierTransform
FourierTrigSeries
InverseFourier
InverseFourierCosTransform
InverseFourierSequenceTransform
InverseFourierSinTransform
InverseFourierTransform

thanks,
--Nasser


Grayish

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Dec 11, 2009, 7:13:10 AM12/11/09
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On 18 ноя, 00:32, "Nasser M. Abbasi" <n...@12000.org> wrote:
> "Thomas Richard" <t.rich...@scientific.de> wrote in message

>
> news:fd964e57-c96c-49f4...@w19g2000yqk.googlegroups.com...
>
> > On 16 Nov., 20:49, Ray Vickson <RGVick...@shaw.ca> wrote:
> >> It seems that Maple (versions <= 9.5 at least) do not have Fourier
> >> series packages; they do have Fourier transforms and discrete Fourier
> >> capabilities for finite data sets. Has anybody developed a readily-
> >> accessible Fourier series module for any version of Maple?
>
> > Please also check out Prof. Wilhelm Werner's FourierSeries package
> > athttp://www.maplesoft.com/applications/view.aspx?SID=3606

Maple 13 have
fourier, fouriercos, fouriersin, invfourier in inttrans package;
fourier, ifourier in MTM package;
FFT, iFFT;
fft in Matlab package;
FourierTransform, InverseFourierTransform with many options in
DiscreteTransforms package.

As for Fourier series:

Mathematica 7 have one-dimensional Fourier series:
trigonometric,
exponential,
cosine,
sine.

Moiseev package for Maple "Orthogonal series expansions"
(see http://www.maplesoft.com/applications/view.aspx?SID=33406) have
one-dimensional Fourier series:
trigonometric,
exponential,
polar,
hartley,
cosine,
sine.

Mathematica 7 have multi-dimensional exponential, cosine and sine
Fourier series in general and symbolic forms.
Multi-dimensional cosine series give wrong expansion (do not
convergence to function). General form for exponential multi-
dimensional series give wrong coefficients for majority of functions.

Moiseev package have multi-dimensional exponential, cosine and sine
Fourier series in general, symbolic and numeric forms.

Regards

Grayish

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Dec 11, 2009, 7:33:03 AM12/11/09
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>  (seehttp://www.maplesoft.com/applications/view.aspx?SID=33406) have

> one-dimensional Fourier series:
> trigonometric,
> exponential,
> polar,
> hartley,
> cosine,
> sine.
>
> Mathematica 7 have multi-dimensional exponential, cosine and sine
> Fourier series in general and symbolic forms.
> Multi-dimensional cosine series give wrong expansion (do not
> convergence to function). General form for exponential multi-
> dimensional series give wrong coefficients for majority of functions.
>
> Moiseev package have multi-dimensional exponential, cosine and sine
> Fourier series in general, symbolic and numeric forms.
>
> Regards

BTW, one command Fourier in Moiseev package has more functionality
then the following 13 commands in Mathematica 7

NFourierCoefficient
NFourierCosCoefficient
NFourierCosTransform
NFourierSeries
NFourierSinCoefficient

NFourierTrigSeries
FourierCoefficient
FourierCosCoefficient
FourierCosSeries
FourierSeries
FourierSinCoefficient
FourierSinSeries
FourierTrigSeries

Regards

Nasser M. Abbasi

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Dec 11, 2009, 9:56:03 PM12/11/09
to

"Grayish" <smoi...@kodofon.vrn.ru> wrote in message
news:a2c6948a-f812-42c9-a877-

"BTW, one command Fourier in Moiseev package has more functionality
then the following 13 commands in Mathematica 7

NFourierCoefficient
NFourierCosCoefficient
NFourierCosTransform
NFourierSeries
NFourierSinCoefficient
NFourierTrigSeries
FourierCoefficient
FourierCosCoefficient
FourierCosSeries
FourierSeries
FourierSinCoefficient
FourierSinSeries
FourierTrigSeries"

This is impressive. I downloaded this package from

http://www.maplesoft.com/view.aspx?SF=33406/0\CodeFile.ZIP

But since I have maple12, I could not read the .mw files. I did however copy
the files OrthogonalExpansions.mla and OrthogonalExpansions.hdb to my
"C:\Program Files\Maple 12\lib" folder, and then did

with(OrthogonalExpansions) ;

and it seems to have worked (no errors). But how to I now find help on those
functions?

If for example, I type

?FourierSeries

which is one of the functions listed after doing the with(), I get nothing
back. Using the help menu does not show anything about this package. So I
guess since this is done in Maple13, those who have lower versions can't use
it at all? or is there a way around this? Why can't one use this in Maple
12? Or may be I am not asking for help correctly?

--Nasser


Grayish

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Dec 14, 2009, 7:57:56 AM12/14/09
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On 12 дек, 05:56, "Nasser M. Abbasi" <n...@12000.org> wrote:
> "Grayish" <smois...@kodofon.vrn.ru> wrote in message
>
> news:a2c6948a-f812-42c9-a877-
>
> "BTW, one commandFourier in Moiseev package has more functionality

OrthogonalExpansions package work for Maple 12 and higher versions.
Access to help is conventional as ?FourierSeries, enter F2 when
cursor on command, or through Search in Help menu. You can also read
FourierSeries.mw file from folder \Source codes\help
\FourierSeries.mw. But you need standard mode, that is .mw file. Why
your Maple 12 do not read .mw files ?

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