Eval help page contains the following statement:

Since eval does pointwise evaluation, eval cannot be used to evaluate an expression at a singularity. Use limit instead.

This is a serious error showing that the person writing it doesn't understand the difference between the value of a function at a point and the limit at that point.

At discontinuity, the value of a function is _not_ equal to the limit - that's why it is discontinuity. If the value of a function was equal to the limit, the function would be continuous at that point.

An example:

Hi everyone,

I am looking at the following ODE:

x'(t) + a(t)*x(t)  - t*a(t) + b*a(t)*f(x(t)) = 0

where x is the function of t to be found
with t>=0, x(t)>0
with initial condition x(0)=x0 > 0 given
with a(t) a known function of t inside the positive quadrant, a(t)>0
with f(x) a known function of x inside the positive quadrant, f(x)>0
with b a known positive real constant, b>0

If b=0, we have a first-order linear ODE, but I'm interested in b>0.

I just tried to export the following plot (from a Student forum topic) to wmf (Windows Metafile) in Standard Maple,

with(plots): 
a := plot((x^2-2)/(x-sqrt(2))): 
b := pointplot([sqrt(2), 2*sqrt(2)+0.05], 
    symbolsize = 15, symbol = circle, color = blue): 
c := pointplot([sqrt(2), 2*sqrt(2)+0.05], 
    symbolsize = 10, symbol = solidcircle, color = white): 
display(a, b, c);

It has a black background! Also, the picture is smaller size, 256x256 instead of 400x400.

Other problems - copying from Standard Maple and pasting to Notepad before copying from Notepad and pasting here, all :s were copied as ;s, and ; at the end wasn't copied at all (but it was selected.)

Also - why I had to add 0.05 in the pointplot commands - the point was located lower than it should.

Also - why I tried to export to wmf - because all other export options that I tried before that, produced low quality pictures with the point located lower than it should and with jagged lines.

Another thing - when I copied from My files and pasted here the html code for the picture, it had two </a> at the end instead of one.

Alec

My calculus book says that y = (x^2 - 2)/(x - sqrt(2)) is discontinuous at 2, but Maple finds a limit of

Does the following error message mean that the only way to remove RealDomain is to exit Maple & then start a new session?

 unwith(RealDomain):

A recent posting of Mario Lemelin showed that Maple's default numerical methods produced wrong results for a certain differential equation.  Further investigation revealed that the problem stemmed from the fact that the fourth and fifth order Runge-Kutta methods used within the rkf45 method both produce the same (exactly correct) result at any step size, causing the adaptive error analysis to go badly wrong.  This leads to the question: when do Runge-Kutta methods produce exact results for arbitrary step sizes and initial conditions?

For a partial answer, see this worksheet: View 4541_runge.mw on MapleNet or Download 4541_runge.mw

In addition to examples in that thread, here is another one,

solve({a<=a*b,b<=1});
                            {a = a, b = b}

Alec

Now that July has come and gone (along with most of the summer), it's time to announce the Maple Mentor Award winner for July.  Congratulations Acer...not only did you win, but you are our first repeat monthly winner!  You know the drill, so let us know what prize you would like.

Here's a limit where Maple stalls:

The best it can do is

I'm not sure, but it seems as if workprec in fdiff may have a bug. See an example. Or, maybe, something is wrong with the numerical ode solution there.

Alec

?subgrel page contains an interesting error example with a very short syllable c. It looks more interesting with other syllables,

subgrel({y=[a,b,averylongsyllable]}, 
    grelgroup({a,b}, {[a,a], [b,a]}));

Error, (in subgrel) generator [a, b, averylongsyllable] 
contains a syllable `averylongsyllable' that is not a generator, 
or the inverse of a generator, of the parent group

Alec

kernelopts(toolboxdir) crashes mserver both in Classic and Standard Maple 12 on Windows Vista (I didn't check the command line).

Alec

I just looked how differential forms are implemented and was quite surprized

with(DifferentialGeometry):
DGsetup([x,y,z],M):
a:=evalDG(dx &wedge dy+2*dy &wedge dz):
lprint(a);

_DG([["form", M, 2], [[[1, 2], 1], [[2, 3], 2]]])

It is an unevaluated function with nested lists as arguments.

Probably, not the worst possible choice since I can imagine few choices that would be worse - strings, for instance. But there are so many other choices that seem much better - antisymmetric Arrays, or tables, for instance. Why lists?

Alec

My calculus text says that a function cannot have an ordinary limit at an endpoint of its domain, but it can have a one-sided limit.  So, in the case of f(x) = sqrt(4 - x^2), the text says (a) that it has a left-hand limit at x = 2 and a right-hand limit at x = -2, but it does not have a left-hand limit at x = -2 or a right-hand limit at x = 2 and (b) that it does not have ordinary two-sided limits at either -2 or 2.

So there are six possibilities.  Maple gives limit = 0 for all six.  Why the discrepancy?

Alla

Multiplication by 0 gives 0 for differential forms, which is wrong. For example,

with(DifferentialGeometry):
DGsetup([x,y],M):
a:=dx &wedge dy: 
3*a;
                              3 dx ^ dy
0*a;
                                  0

It should be 0 dx^dy.

That reminds me of an old Matrix bug with M^0 being 1 instead of the identity Matrix for square Matrices.

Alec