I know that a computer can't generate a random number in the true sense of the word random. But I was expecting more when I went to do a rand(1..100); 5000 times and found most of the generated values to be between 1 and 10. Go ahead and give this a try:

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

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

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

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

I just noticed that usual parentheses work as square brackets for Matrices,

M:=Matrix(2,[a,b,c,d]);

                                 [a    b]
                            M := [      ]
                                 [c    d]
M(1,2)=M[1,2];
                                b = b

That leads to the following,

M(x,y);
Error, unsupported type of index, x

while that worked OK for matrices,

hi...!

  I m trying to slove one equation with maple but is giving warning.

"warning, solutions my have been lost"

this type of message is appering.. wat is the meaning of that? how to solve my equation?

My equation is interms of cosh, sinh, sin and cos..

Plz.. reply..

The following example arrived in my email inbox a few weeks ago. It spurred a short but lively thread of discussion amongst some Maple developers.

I thought that it was interesting enough to post here. I'll hold off on giving my own opinion right away, because I'm curious to read what other MaplePrimes members might write about it.

> q := (6*((1/3)*a-1/9))/(36*a-116+12*sqrt(12*a^3-3*a^2-54*a+93))^(1/3);
                                   6 (a/3 - 1/9...

Just read (and slightly edited) Wikipedia article about Maple. It has a picture of a stair-type plot of

plot(ln(x+2)/(x+2), x = .716 .. .72);

I checked it and it seems to look normal in Standard Maple (so I uploaded it there), but looks bad in Classic, independently of numpoints setting (it is not mine stair-like picture there). Is it going to be fixed, or Classic Maple is deprecated?

Alec