An exact simplification challenge

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Vladimir Bondarenko

Posted: Mon Jun 04, 2007 9:12 pm

Guest

Hello computer algebra souls,

Is there a simplifier who can invent and display a string
of CAS commands to reduce this elliptic expression

EllipticK(sqrt(3/4)) - sqrt(4/3)*EllipticK(sqrt(4/3)) -
I*EllipticK(sqrt(1/4))

?

Just in case, its Mathematica syntax is

EllipticK[3/4] -Sqrt[4/3] EllipticK[4/3] -I EllipticK[1/4]

Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing

Thomas Richard

Posted: Tue Jun 05, 2007 7:24 am

Guest

Vladimir Bondarenko <vb@cybertester.com> wrote:

Quote:

Maple can do:

convert(%,'Int');
combine(%);
value(%);

No myths involved, just facts.

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

Vladimir Bondarenko

Posted: Tue Jun 05, 2007 7:46 am

Guest

On Jun 5, 5:24 am, t.rich...@scientific.de (Thomas Richard) writes:

TR> value(combine(convert(%,'Int')));
TR>
TR> 0

Wonderful! Thanks a lot for giving us the solution.

TR> No myths involved, just facts.

I fully agree with you. It's best to rely upon the
facts, not myth.

So, can we hear Mathematica experts? How simple is
to zero these elliptics in Mathematica?

Quote:

Vladimir Bondarenko <v...@cybertester.com> wrote:
Hello computer algebra souls,

Is there a simplifier who can invent and display a string
of CAS commands to reduce this elliptic expression

EllipticK(sqrt(3/4)) - sqrt(4/3)*EllipticK(sqrt(4/3)) -
I*EllipticK(sqrt(1/4))

Maple can do:

convert(%,'Int');
combine(%);
value(%);

No myths involved, just facts.

--
Thomas Richard
Maple Support
Scientific Computers GmbHhttp://www.scientific.de

dimitris

Posted: Tue Jun 05, 2007 2:53 pm

Guest

Hello.

I have tried to simplify the involving elliptics to zero
within Mathematica, but with no success.
It is a hard task!

Anyway in Mma 5.2 you could try

In[93]:=
Developer`ZeroQ[EllipticK[3/4] - Sqrt[4/3]*EllipticK[4/3] -
I*EllipticK[1/4]]

Out[93]=
True

But ZeroQ uses a combination of symbolic transformations and
randomized numerical evaluation.
So I guess this is not a desired solutions since may be numerical
procedures take place!

Dimitris

/ Vladimir Bondarenko :

Quote:

On Jun 5, 5:24 am, t.rich...@scientific.de (Thomas Richard) writes:

TR> value(combine(convert(%,'Int')));
TR
TR> 0

Wonderful! Thanks a lot for giving us the solution.

TR> No myths involved, just facts.

I fully agree with you. It's best to rely upon the
facts, not myth.

So, can we hear Mathematica experts? How simple is
to zero these elliptics in Mathematica?

Vladimir Bondarenko <v...@cybertester.com> wrote:
Hello computer algebra souls,

Is there a simplifier who can invent and display a string
of CAS commands to reduce this elliptic expression

EllipticK(sqrt(3/4)) - sqrt(4/3)*EllipticK(sqrt(4/3)) -
I*EllipticK(sqrt(1/4))

Maple can do:

convert(%,'Int');
combine(%);
value(%);

No myths involved, just facts.

--
Thomas Richard
Maple Support
Scientific Computers GmbHhttp://www.scientific.de

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