The problem with the upgrade is that the installer tried to install the upgrade for the 32-bit version onto the 64-bit version.  The result was that I had to install Maple 2015 64 bit from the beginning and then allow the upgrade or upgrades to be included automatically.  Why was there no test by the installer to prevent such a problem? 

     When I sent the request to the technical support at Maple, they tried to be helpful but misdiagnosed the problem, so I had to solve it, crudely, myself.

     Why was there no indication of the size of the files for the upgrades?  That is a natural part of the information that a user requires to monitor the progress of the downloading, especially with internet connexions of only moderate speed.

     When I was eventually able to run Maple 2015.2 in both 32-bit (because I prefer to use the classic interface) and 64-bit versions, I discovered that a plot command that last worked properly in Maple 15 has not been corrected in Maple 2015.2, despite being reported to Maplesoft technical support months ago, and that a solution of a differential equation that worked properly in Maple 17 AND Maple 2015 64-bit version still does not work properly in either 32-bit version, despite also being reported to Maplesoft technical support months ago.  What is the point of an upgrade that does not repair known problems?

As soon as I read the announcement about the release of Maple 2015.2, I undertook the downloading and installation.  As I use the classic interface, I first downloaded the 32-bit platform.  The installation seemed to proceed smoothly but when I tested afterward to discover the version number the Maple Help indicated Maple 2015.1 from May 19.  Undeterred, I downloaded the 64-bit platform and tried to install it, but the installation was refused on the grounds that it had already been installed.

     It seems that the testing at Maplesoft for these installations was incomplete.

     This information might be for the benefit of other users who might be prepared for similar problems.

How does one discover one's reputation score?

The resourcefulness and ambition of Dr. Cheb-Terrab in implementing all solutions of Einstein's equations for general relativity in Maple is indeed laudable.  There is, however, more to physics than general relativity, such as quantum mechanics that includes solutions to Schroedinger's equations, Feynman path integrals, matrix mechanics and so forth.  I have no doubt that many users of Maple would welcome not only the complete inclusion of the mathematical functions from 'Abramowitz and Stegun' but further all the content of its successor, the NIST Handbook of Mathematical Functions.  Maple boasts, uniquely, the provision of Heun functions, but there is much development that can be undertaken to make these Heun functions easier to use, to plot, and to convert to other functions.  How many of the known 192 conversions of Heun functiions have been implemented?

     The use of the physics package in practical calculations would benefit from an updating of the values of the fundamental constants of physics and related content of the package Scientific Constants, which dates from 1998, and which has been superseded by data of 2002, 2006 and 2010.

A task mentioned on the indicated page has been implemented in Maple, namely conversion between roman and arabic numerals.  Explicitly,

   convert(56, roman);

generates "LVI", and

   convert("LVI", arabic);

generates 56.

Maple has many valuable operations and functions, but control of the quality of each new release is a major deficiency.  For instance, although each new release in recent years has included the provision of the 'classic' interface, many legitimate plots that worked properly in preceding releases generated with this interface now simply do not work.  As another example, a differential equatiion was solved in Maple 2015 correctly in the 64-bit interface, but not in either 32-bit interface, in contrast with Maple 17.  How can that happen?  An operation in package LinearAlgebra worked in Maple 15 but not since.  There is really no excuse for these gross flaws that result from blunders of the developers.  It seems that much more attention is devoted to esoteric new features than ensuring that standard features, such as plots, differential equations, matrix operations ... continue to work properly.  Developers are much too prone to tinker with existing code for unfathomable reasons with the result that operations specified in the Help pages not only fail to yield the defined output but also merely stall rather than to state an error.  When these matters are brought to the attention of Maplesoft support staff, they seem not to care about the failures sufficiently to take action to overcome the problem or to provide temporary 'workaround'.

Maple is exceedingly weak in its solution of integral equations, and is remiss in lacking operations in fractional calculus; these facilities are much more directly related to the teaching and practice of mathematics than some abstruse operations that have been recently implemented.  One area of admirable continuing development is the physics package, but the scientific constants that would be used with it date from the preceding millennium!

Please, Maplesoft, for your faithful users exert improved control of the quality of new releases.

The author of this list of 'short cuts' omitted to mention that of these operations most, or all, are applicable to the Java interface and inapplicable to the classic interface. 

The only suggestion is that the lines might be made thicker as the circles are rather faint, especially the

green circle.  Changing green to blue helps little, but thicker lines would definitely be an advantage.

Anyhow, it is w worthy demonstration of plotting fascinating shapes.

with Maple 2015.1 classic interface; an errror message

                        Plotting error, unknown element  in ANIMATE

appears.

                    J F. Ogilvie

even with Maple 2015.1 classic interface.  Thanks,   John Ogilvie

@acer Unlike the original procedure, this revised procedure produces in Maple 2015.1 only a warning, no plot.

An obvious extension to this example is an epicycloid, with slightly altered defining equations.

I watched this show with interest and found the presentation excellent and highly convincing.  The only suggestion that comes to mind is that the presenter might have spoken more slowly so that listeners whose first language is not English might have comprehended better the spoken component of the presentation.

@MartinUser   I strongly support the case of the needed Lame functions, as well as spheroidal wave functions and much improved functionality and conversion facility of Heun functions.  Maple is the only advance mathematical software that incorporates Heun functions, but does so in a way that severely hampers their usage.  The solution of a differential equation appears in the form of one or other Heun function, but then what?  It can be plotted, slowly, but numerical integration involving it is interminably slow.  Here is a serious case for extension and improvement.

I am particularly delighted to see the improved capability of at least HeunC functions, as they occur in important solutions of differential equations in physics, and I trust that analogous improvement in otherHeun functions, especially HeunG, will not lag far behind.

An area open for future improvement is the solution of non-trivial integral equations, especially since a mathematical and programmable basis has been available for nearly four decades.

This plot is fascinating, but what is its point?  Julia fractals are mentioned, but what is the context?