# Commercial Computer Algebra Systems, Twenty Years After... Is there much to be proud?

Discussion in 'Recreational Math' started by Vladimir Bondarenko, Jun 24, 2007.

The simplest integrals and limits fail, solutions
are lost here are there, or are invalid...

(I bet you still do not know ALL the truth... we
have posted just a tiny bit of the defects...)

It would be great to hear any comments.

Best wishes,

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

2. ### dimitrisGuest

I am not a specialist but...I think the following
phrase

"If all were easy, we could go for vacations...",

fits best the situation!

I also found very pessimistic.
I think there are many things in Maple
and Mathematica that their developers should

And to modify a little above phrase

"If all were perfect, we would not a job!"

I am kiddin!

Keep on the amazing and invaluable job
you do!

Cheers,

Dimitris

dimitris, Jun 24, 2007

I meant that about 20 years ago (approximately) both Mathematica
and Maple appeared.

And they still cannot calculate important practical stuff, say,
elliptic integrals.

Mathematica 6

N[Integrate[Sqrt[2 z^3 + z^2 - 12 z + 9], {z, -1, 1}]]
NIntegrate[Sqrt[2 z^3 + z^2 - 12 z + 9], {z, -1, 1}]

15.4042
5.62684

I do NOT mean just this concrete integral.

I mean ***massive*** loss of cattle.

Wolfram Research claims

http://documents.wolfram.com/v5/The...ialTopicTheInternalsOfMathematica/1.12.5.html

"After all the testing that has been done on it, the probability
that you will actually discover an error in Mathematica in the
course of your work is extremely low."

At least for elliptic integrals, it's COMPLETELY FALSE.

This means waste of time for the buyers.

What about livestock mortality insurance for the customers?

Best wishes,

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

http://www.amazon.com/Elliptic-Functions-Applications-Mathematical-Sciences/dp/0387969659

Elliptic Functions and Applications by Derek F. Lawden

334 pp

This book develops the fundamental properties of elliptic
functions and illustrates them by applications in geometry,
mathematical physics and engineering.

Its purpose is to provide an introductory text for private
study by students and research workers who wish to be able
to use elliptic functions in the solution of both pure and
applied mathematical problems.

5. ### dimitrisGuest

It is nice to see you everyday well and active!
You know how the market works!
During the attempt to promote your product
you say some exaggerated things.
Talking about Mathematica (since I haven't work
with Maple enough to say things about it) I think
that more or less what WRI claims about its product
is real as regards of what Mma can do.
Specifically for Elliptic integrals, I don't know someone
that he/she promote its product talking about the things
his/her product CANNOT do or does in not so reliable
manner.
And as I say somewhere else, someone that use a CAS
must VERIFY the symbolic results he takes from it.
No blind application of Integrate or int. But examing the integrand
the antiderivative (if it exists) in the integration range, numerical
checking etc.

Dimitris

dimitris, Jun 25, 2007
6. ### dimitrisGuest

Mma 5.2

In[3]:=
Integrate[Sqrt[2*z^3 + z^2 - 12*z + 9], {z, -1, 1}]

Out[3]=
(1/15)*(10*Sqrt[5] + 219*EllipticE[8/9] - 219*EllipticE[Pi/3, 8/9] +
219*I*EllipticE[ArcSin[Sqrt[3]], 1/9] -
219*I*EllipticE[ArcSin[Sqrt[5]], 1/9] + 174*EllipticF[Pi/6, -8] +
73*EllipticF[Pi/3, 8/9] -
174*I*EllipticF[ArcCsc[Sqrt[3]], 9] + 174*I*EllipticF[ArcCsc[3/
Sqrt[5]], 9] - 146*I*EllipticF[ArcSin[Sqrt[3]], 1/9] +
146*I*EllipticF[ArcSin[Sqrt[5]], 1/9] - 73*EllipticK[8/9])

In[4]:=
{N[%], NIntegrate[Sqrt[2*z^3 + z^2 - 12*z + 9], {z, -1, 1}]}

Out[4]=
{5.626842056420379 + 0.*I, 5.626842056425546}

So, Mma 5.2 gets correct the integral.

Dimitris

dimitris, Jun 25, 2007

............................................................

Journal of Research of the National Institute of Standards
and Technology

............................................................

Three Improvements in Reduction and Computation of Elliptic
Integrals by B. C. Carlson, 2002

http://nvl.nist.gov/pub/nistpubs/jres/107/5/j75car.pdf

............................................................

Elliptic integrals have many applications, for example in
mathematics and physics:

arclengths of plane curves (ellipse, hyperbola,
Bernoulli's lemniscate)

surface area of an ellipsoid in 3-dimensional space

electric and magnetic fields associated with ellipsoids

periodicity of anharmonic oscillators

mutual inductance of coaxial circles

age of the universe in a Friedmann model

............................................................

8. ### dimitrisGuest

It is sure that both Maple and Mathematica's
developers will deal soon with articles like the above.
But if writting an article like the mentioned one
is a difficult task, requiring a great deal of mathematical
knowledge, I find also difficult the task of implementing
a relevant algorithm to a CAS.

Dimitris

dimitris, Jul 3, 2007