Hope you do not mind ... the needed formula through the above posts is:

  Y := (x/2)^(2/3):
  VectorCalculus:-ArcLength(<x,Y>, x=u..v);
  len:=subs( u=0,v=2, %);

Now Maple has a peculiarity: it often does not use assumptions on
integration variables, which are obvious - and seems not to try
substitutions, which seem 'natural' for us (and are allowed here):

  simplify(len) assuming (0 < x, x <2); # of course 
  Change(%, x=xi^3,xi);                 # staring at the result: we have positives, so transform
  simplify(%) assuming 0 < xi;          # sure, give it a try ...
  value(%);                             # do it!
  simplify(%);                          # done

                                1/2
                           20 10
                           -------- - 2/27
                              27

Anyway: Robert Israel's answer is a fine and more general idea, I like it :-)

So it is a nice and warm place it is rarely the ground to pick up money.
But good to grow loyality to a product. However a nicish GUI producing
pretty documents will not result in users finding their advantage later
on in using that, but never stepped deeper into the abilities - because
the Standard interface sets a high barrier for straight forward use.

Even if I understand needs to decline costs by standardizing across all
the operating systems and platt forms there ought to be no reason for the
peculiar design of a user interface. I bet, that already most would be
happy to use indexed variables as variables, to have an intelligent and
complete help system without caring to much for exact writings and better
graphics and a reasonable coding environment. A user who wants to avoid
the input of multiplication signs will never survive as later user ...

The rest of the prediction - using Maple as base for developments and then
deploy a specific solution - more or less is what I have seen in industry
for other products both in Finance and Automotives. One immediately would
be shot if delivering open solutions to operative departments. Besides the
natural problems of speed and direct costs etc.

But for that there is no deeper need to waste chances for funny functionality
in GUIs, which beyond that are useless.

However there is one thing that might be seen as a side effect: to provide
applications through Maplets and MapleNet. Have not looked into it (lack
of personal interest vs available time), but it sounds like an interesting
idea - not sure, whether it might complement serious web applications (as
they have their own demands for user dialogs and mostly have to be done
based on the companys style guides and CI).

There where question about "what is new in Maple 12 ?", which simply
says: come on, your infos are to rare, feed your users. Almost nothing
happened, http://www.mapleprimes.com/forum/maple12changesandnewfeatures
has 1 reply and I got another through mail.

Though both where quite friendly the message is: we ignore you, just
eat what you give you.

Certainly this is not the thinking of the developpers, who have good
reasons to be proud of their work done - even if it never can be free
of errors, perfect etc.

However it is a simple fact: even such an easy task "show substantials"
is not fullfilled by the company. While it would be easy by using material
certainly available from testing.

This is not only ignorance, in the longer run it may become a deadly sin.


I can not imagine another (SW) company having its own www active presence,
who  is not able to exhibit their progresses there.

It is - midly said - a bit astonishing that not even 1 attempt was made
to present progress (beyond advertsing material) to technical interested
users. And I am absolutely sure that far more of such are reading here
than those who contribute.

May be that I am just a Bavarian backwoodsman that I do not understand
why those disseminators are not used? Why this forum seems almost only
to exist to give 2/3rd level support without cost? That funny presentation
videos will not retain users.

Also I am not aware of many companies (besides MS) who ignore fundamental
demands like continuing the classical interface (for good reasons): no,
also the new version ignores to operate that on 64 bit, nothings seems to
have been done.

You say: it is a mature company and a mature product. Yes. It was said
by Tarr (the Mariner) they wnt to expand sales. Guess so, yes.

However I learned at least 2 things in Marketing and sales (beyond not
to ignore clients at which level ever and certainly not in public):

Almost nothing is more expensive than to substitute existing business.
And that a ripe market has no longer to be feed, it has to be 'milked'.
And looking for new segments means to find 'magic triangles'.


May be it is my current mood. But it is waisting time to discuss that,
here it is a kind of monologue.


NB: I ordered version 12, but it was based on a private mail - showing
me simple and good reasons through ~ 8 examples. Thx!

soweit ich das verstehe braucht man keine lokale Installation, sondern nur einen Browser (mit aktiviertem Java), da die Anwendung auf einem Server läuft.

Folgenden Hinweis findet man dazu unter der Menü-Hilfe 'Take a Tour of Maple', nachdem man den letzten Link 'Maplets and MapleNet' im dann aufgerufenen Sheet aktiviert:

Maplets can be used from within Maple (as we saw above). Maplets can also be saved to a file and then launched via double-clicking from the desktop. Finally, a Maplet can be deployed to a MapleNet server and used online, through a Web browser, without needing a local copy of Maple: The Maplet is run from the server, via MapleNet.

soweit ich das verstehe braucht man keine lokale Installation, sondern nur einen Browser (mit aktiviertem Java), da die Anwendung auf einem Server läuft.

Folgenden Hinweis findet man dazu unter der Menü-Hilfe 'Take a Tour of Maple', nachdem man den letzten Link 'Maplets and MapleNet' im dann aufgerufenen Sheet aktiviert:

Maplets can be used from within Maple (as we saw above). Maplets can also be saved to a file and then launched via double-clicking from the desktop. Finally, a Maplet can be deployed to a MapleNet server and used online, through a Web browser, without needing a local copy of Maple: The Maplet is run from the server, via MapleNet.

It is the integrator which makes an error, Int(BesselK(a,r)*r,r=r1..r2)
seems to be wrong for a=0, but correct for using limit(-, a=0) used later:

try both with r2 = 1 and numerical evaluation.

If you change to G:=(r1,r2)->Int(BesselK(0,r)*r,r=r1..r2) (plotting will
be very slow) and use limit(G(0,t),t=0) it is correct (do not use the r
for the limit, it is the integration variable, Maple does not like that).

Better do it step by step, it helps to find out possible problems:

  f:= x -> (a*b)/sqrt((a*cos(x))^2 + (b*sin(x))^2);

  eval( f(x), [a=14, b=20]);

                                 280
                    ------------------------------
                               2             2 1/2
                    (196 cos(x)  + 400 sin(x) )

  plot(%, x=0..2*Pi, coords = polar); # use UpperCase Pi, not lOWERcAse pi

If you are used to handle several variables the following is a reasonable way:

  g:= (x,a,b) -> (a*b)/sqrt((a*cos(x))^2 + (b*sin(x))^2);
  plot( g(x,14,20), x=0..2*Pi, coords = polar);

Better do it step by step, it helps to find out possible problems:

  f:= x -> (a*b)/sqrt((a*cos(x))^2 + (b*sin(x))^2);

  eval( f(x), [a=14, b=20]);

                                 280
                    ------------------------------
                               2             2 1/2
                    (196 cos(x)  + 400 sin(x) )

  plot(%, x=0..2*Pi, coords = polar); # use UpperCase Pi, not lOWERcAse pi

If you are used to handle several variables the following is a reasonable way:

  g:= (x,a,b) -> (a*b)/sqrt((a*cos(x))^2 + (b*sin(x))^2);
  plot( g(x,14,20), x=0..2*Pi, coords = polar);

For the language dependency in Excel & Windows one either can
preprocess. Or temporarily changes settings. Or uses Maple:

  fd := fopen(dataFile,READ,TEXT):
    theData:=readdata(fd,string, 3): # 3 columns
  fclose(fd):

  A:=convert(theData,Array);

  map( t -> StringTools[SubstituteAll](t,",","."), A); 
  map(parse,%);

Which gives it for your given *.txt

For the language dependency in Excel & Windows one either can
preprocess. Or temporarily changes settings. Or uses Maple:

  fd := fopen(dataFile,READ,TEXT):
    theData:=readdata(fd,string, 3): # 3 columns
  fclose(fd):

  A:=convert(theData,Array);

  map( t -> StringTools[SubstituteAll](t,",","."), A); 
  map(parse,%);

Which gives it for your given *.txt

Nice suggestion, I like the idea do see a periodic sample of interesting things (so I am not sure what the criteria should be).

However I would expect that Maple itself has to contribute (beyond pure advertising) and there is some 'overlapping' with the Application Center and other things (and certainly they would not intend to hit somebody on his nose).

Beyond that my gut feeling is not to suggest persons in public without having cleared that. It is - mildly spoken -  like assigning tasks to innocents :-)

The challenge in the long run might be to mine for those not actively posting here, certainly there are lots of them and they would be quite valuable for others (and Maplesoft) through their knowledge and their solutions and ideas ...

But I like your idea.

Even if it may sound lame at a first glance: it depends where to read
this expressions and manipulations,it makes a difference to read that
for numbers or for other objects and use numbers later (like polynomials
and polynomial functions for me are not the same).

1.
Let us start with the expression f = 1/x - 1/x, for which Alec suggests
"being undefined at 0 and equal 0 otherwise".

However I want to read f as being in a field (or better: representing
an equivalence class in R(x), the rational functions over R) and thus
for me f represents 0. With no doubt.

The other question would be: "How to evaluate in X, for X in R?" which
is the mathematical 'evaluation' ev: R(x) @ R ---> R [it is not defined
everywhere, it is meromorphic]. For this it must be a single term (or
choose some other way of norming).

So for me it is more than ok, that Maple treats 1/x - 1/x symbolical
as Zero, while numerical it would protest.

2.
The next steps more towards Analysis: "Is 1/x a continuous function?"
and the immediate reaction is "NO". However nothing is said about the
domain ... And if specifying it as D:= R\{0} then still many would say
"No". It may depend on their 'school', but what those have in mind is
to extend it to the whole Reals.

For me that function *is* continuous. But I find it convenient that
Maple's discont(1/x,x) gives {0}. And if I read 1/x as an expression
for the obvious function to be evaluated this makes sense.

3. 
Related is the problem that sqrt or ln is a function on C or C* using
Maple. My teacher would have hitten me on my nose and his teacher would
have fired him - this older generation in Analysis had the attitude,
that a holomorphic function finds its own maximal domain of existence.
So they naturally live on their Riemannian surfaces. The 'rest' is the
painful story of branching cuts to pass to C (another way is to work
with the old notion of 'correspondences' = multivalued functions).

4.
Now for the example, f=x*y*(x^2-y^2)/(x^2+y^2). If reading that as an
element of R(x,y), the field of rational functions in 2 variables it
is correct, that Dx and Dy commute (as one learns in (higher) Algebra).
The problem comes in through evaluating and extending the domain to R^2.

However that extension is purely by Analysis - but Maple does Symbolics
which for me is 'Algebra' ... a kind of frontier.

And that extension is 'unnatural' in some sense: it is not analytic
(in dim=1 a continuous extension would be, by Morera's theorem) and
that usually is needed to let the algebraic machinerie work.

So for short for me it is ok to view at f as a meromorphic function
with commuting partial derivatives.


But that are only my 2 Cents, being not a Computer Scientist.

Alec,

My guessing is that Maple is somewhat short on developpers and if they leap around here their work is not be done. One simply can not compare due to size and money. For me it is not unreasonable that only a few participate, it is expensive (for example at our company the 'coders' are strictly forbidden to comment on errors within projects).

I made brute interface to Pari some time ago and posted it at this board, here is the result for the 'updated list' as pdf: Maple is off by 1 against Pari (which may be the underlying used in SAGE). My DLL is not very fast (it is on Windows and does not use GMP), but for the timing shown ~ 0.37 sec is for Pari, the rest is overhead + Maple's time (~ half a minute).

PS: calling SAGE is not illegal, GPL does mean something different (~making money by selling using otherones code without publishing)

www.mapleprimes.com/files/102_check_numbpart_Maple11_vs_Pari.pdf (22 Kb)

Edited to fix the link ...

Your illness has to be regretted. The way to handle its consequences
for your studies is to resolve issues through the administration of
your faculty or your teachers, may be the students council may assist
you. Quite certainly this board is not the very place for that.

Whatever your personal reasons are, there is no excuse for your manners.

You bump in grawling in capital letters, do not even give your name in
the profile, sling some exercises onto the desk and order a solution
ASAP in your prefered format, without caring for any of the rules for
the Student's section - especially without doing a single jota of own
work.

Reading your reply I can not find "sorry for ..." and the spirit does
merely indicate anything towards that. At least a consistent attitude.

Get well soon, in any sense.