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

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

  1. 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,

    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
     
    Vladimir Bondarenko, Jun 24, 2007
    #1
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  2. Vladimir Bondarenko

    dimitris Guest

    Hi syntrofe Vladimir.

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

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

    fits best the situation!

    Vladimir Bondarenko :

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

    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
    #2
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  3. 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,

    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
     
    Vladimir Bondarenko, Jun 25, 2007
    #3
  4. 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.
     
    Vladimir Bondarenko, Jun 25, 2007
    #4
  5. Vladimir Bondarenko

    dimitris Guest

    Vladimir Bondarenko :
    Hello comride Vladimir.
    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
    #5
  6. Vladimir Bondarenko

    dimitris Guest

    Vladimir Bondarenko :
    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
    #6
  7. ............................................................

    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

    ............................................................
     
    Vladimir Bondarenko, Jul 1, 2007
    #7
  8. Vladimir Bondarenko

    dimitris Guest

    Vladimir Bondarenko :
    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
    #8
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