J F Ogilvie

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18 years, 34 days

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These are replies submitted by J F Ogilvie

One is naturally pleased to see further development of package Physics in Maple, but there is still much that can be done to enhance the practical use of Maple for teaching and practice of physics.  For instance, spheroidal functions and Lame functions arise in the solution of prototypical problems in physics, but they are absent from Maple.  Maple seems to contain eleven (11) Jacobi functions, but a quick search of internet indicates that there are twelve (12) such functions:  one is apparently missing, for no obvious reason.  The help files on Jacobi functions seem to provide no indication to the Jacobi elliptic functions cn(..,..), dn(..,..), sn(..,..); they might actually be present in Maple, but how to find them?  Asking help on Heun functions returns a sequence of "unknown" and "unable", whereas, as these somewhat obscure functions are touted as being present in Maple, such help is all the more important, but lacking.  Maple is strong in the solution of differential equations, with notable exceptions of considerable physical interest, but weak in the solution of integral equations, despite the fact that nearly forty years ago David Stoutemyer reported methods that were, even then, readily implemented in other software for computer algebra.  Such integral equations again have substantial physical interest.  We look for further developments along these lines.

Significant problems in physics involve differential equations of which the solutions are Lame functions, which are closely related to those sometimes intractable Heun functions.  I strongly recommend that these Lame functions be included in Maple, and also the spheroidal functions.  The latter are even included in
 the volume by Abramowitz and Stegun, whereas the Lame functions are treated in the DLMF from NIST. 

Clearly the development of Physics:-Library:-Assume is a significant advance, even if not perhaps a 'powerhouse'.  It would seem, as you suggest, to have general applicability, well beyond the Physics context. Can you suggest a simple alias that will enable use of this facility outside the Phyics packages, such as

     alias(Phyics:-Library:-Assume = assumeP);

or even

alias(Phyics:-Library:-Assume = Assume);

J.F: Ogilvie

This assume facility is curious, firstly because one had not expected the traditional action (unless one had read fine print somewhere) and secondly because it would seem sensible for this new form to replace the old form, not to supplement it.

The continual extension of this Physics capability in Maple is encouraging.  One area of physics that is permanently in demand is the solution of differential equations.  Although formally an equation might be considered solved if it yields a solution in Heun functions, the latter are difficult to apply and next to useless in many situations.  The utility of Whittaker functions depends greatly on their conversion to Laguerre, Hermite and other functions that are used in traditiional solutions of these physical systems.  An analogous facility with Heun functions is highly desirable.  Another valuable extension would be to include the few remaining functions in Abramowitz and Stegun that are not already embedded, and some further functions from the NIST Handbook of Mathematical Functions. These resources should be added sooner rather than later, and treated as a matter of priority.  Further systems of coordinates for laplacian operators would also be welcomed.

With each new release or update of Maple, I look, in vain, for the spheroidal functions that are sorely needed for the solution of common differential equations.  Maxima has them -- why not Maple?

Although some solutions of differential equations appear in terms of Heun functions, with their parameters numbering at least five and limited conversion to other functions, these Heun functions are essentially useless, even though one might count them as being (primitive) solutions.

One would have hoped that all functions that were treated as topics of chapters in Abramowitz and Stegun some half century ago would now have appeared in Maple, if not the additional functions found in the NIST Handbook.

The link to TorDiv does not work.  Why has not somebody tested that link before posting this announcement?

@Kitonum 

I tried to apply exactly this rule.

   Rule := (xx::anything)^(zz::anything)/(yy::anything)^(zz::anything) = (xx/yy)^zz:

to

     A(t)^(1-n)*a^(n-1);

You do not want to see the result, but here it is.

apply(Rule, %);
                          (zz::anything)(%2)
        (xx::anything)(%2)                     /xx(%1)\zz(%1)
        ------------------------------------ = |------|
                          (zz::anything)(%2)   \yy(%1)/
        (yy::anything)(%2)

                                  (1 - n)  (n - 1)
                        %1 := A(t)        a

             /              (zz::anything)               \
             |(xx::anything)                 / xx \zz    |
       %2 := |---------------------------- = |----|  , %1|[2 .. 2]
             |              (zz::anything)   \ yy /      |
             \(yy::anything)                             /
whereas I expected to obtain

     (A(t)/a)^(1-n)

Am I missing something?

The additions and enhancements to the facilities applicable to calculations in physics are indeed admirable.  Calculations in physics entail the solution of many differential equations, and again Maple has a commendable power to find solutions in algebraic form in those cases in which they exist, even in the form of special functions.  Some such equations yield solutions in terms of Heun functions, which have five or more parameters, and it is unclear to a user how to proceed to convert those functions into something more amenable to plotting or to expression of the solutions in a more conventional form in terms of less obscure functions.  The standard textbooks of physics, as far as I am aware, make little or no reference to Heun functions, but they do use or allude to other special functions, some of which are sufficiently important to have been included in the compilation by Abramowitz and Stegun decades ago, and indeed sufficiently important to warrant an entire chapter in the NIST Handbook, such as spheroidal functions that are completely lacking in Maple before release 18.  So it is highly desirable not only for these important functions to be present in Maple but also for their practical interconversion and reduction from other special functions of complicated nature.  For instance, for comparison with the Heun functions that involve five parameters, the spheroidal functions involve only three parameters, each of which might have a direct relation to a physical parameter in a problem to be solved. 

     It might be felt that, if the output from dsolve or pdsolve contains some function or other, that differential equation is deemed to be solved.  A user might be dissatisfied if that function be other than what he had legitimately expected on the basis of consultation of standard sources of the physics involved.  Then it would seem imperative for a conversion to the conventional form to be practicable, and perhaps even guided by information in various Help documents.

That works well, and the waiting period is not that great.   Thanks,  John Ogilvie

I should like to include this in my interactive electronic textbook Mathematics for Chemistry with Symbolic Computation (available gratis from www.cecm.sfu.ca) as a second example of a fractal.

When I tried to execute the third part -- Codetools ..... -- there appeared an error message:

    Error, mplotjpeg:  height option invalid

Please clarify.

@David Mazziotti 

I heartily endorse this suggestion.  I have continued to use the classic interface to develop my Maple worksheets in Mathematics for Chemistry so that this electronic interactive textbook remains accessible to all users of Maple, not just those with powerful processors and ample memory.  Whenever I can not avoid opening the 'standard' or Java interface, I cringe at the slow entry, complemented of course by the slow closing.  This problem is one that the developers of Maple should seriiously seek to solve, in time for the next release, in which one might look also for the updated content of all parts of the package ScientificConstants.  Thanks to the heroic efforts of Edgarbo Cheb-Terrab, Maple is THE mathematical software for applications in physics, and the combination of improved support of the classic interface or, preferably, its replacement and with the expansive coverage of chemical topics and their underlying mathematics in Mathematics for Chemistry Maple can become THE mathematical software of choice for chemistry and related chemical sciences.

         J. F. Ogilvie

@Alejandro Jakubi 

The definitive source of information about fundamental physical constants, which is regularly revised to reflect the most recent experimental and theoretical information, is

            http://http://physics.nist.gov/cuu/Constants/

but the definitive source of information about atomic masses is

          http://http://amdc.in2p3.fr/masstables/Ame2003/mass.mas03

It seems reasonable and proper, at least to my naive and scholarly mind, that, for commercially marketed software that pretends to include such data for the convenience of its users, and that is given at least annual releases of nominally improved, revised and extended versions, the content of these fundamental physical constants and atomic masses should be just as regularly revised.  Why should a user expect less?  The comment by Acer is absolutely pertinent:  the inclusion of merely a list of values of all these data is insufficient in relation to the relations and correlations between values of fundamental physical constants that were built into Maple at one stage of its evolution, but that evolution has been stunted by neglect in succeeding releases -- arrested development.  I repeat that, if Maplesoft would pretend to boast of "5565 changes and enhancements" that have been included in Maple 17, Maplesoft should, consistently, provide some further thousand changes and enhancements in the data in package Scientific Constants.

@Alejandro Jakubi 

For a student solving some exercise in physics or chemistry or ... that requires such data, whether the value of an atomic mass is the most recent from the Data Centre of Atomic Mass or whether the value of Planck'sconstant is that just released by CODATA is immaterial, but for scientists who use Maple as a tool for the solution of research problems such minor discrepancies are an irritation.  If Maplesoft seeks to release a new version annually, the company should ensure that not only '5565 changes and enhancements' are incorporated in the mathematical content but also the other content should be analogously and religiously maintained.

     Incidentally, I have received no response to my innocent query about the lack of the Worksheet File Association Selector in Maple 17, despite its presence and apparent utility in Maple 16, 15, ...

Not only the properties of elements, such as the atomic masses, but also the fundamental physical constants are much obsolescent.  Although Maple 17 was touted as incorporating some "5565 changes and enhancements", those physical constants, at least two versions out of date, are conspicuous by their absence -- their revision is long overdue.  These values would make Maple much more attractive for scientific applications, mostly in chemistry and physics, but also in any other field requiring accurate values of reference data.

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