Markiyan Hirnyk

Markiyan Hirnyk

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Try More/GeneratePDF  in  the menu under  a post/question. See screen_26.09.17.docx as an example of a result. Also Adobe Acrobat Reader fails with it. That was submitted to MaplePrimes staff through the Contact  button at the bottom of this page. I obtained no feedback from them.

I'd like to present the following bugs in the IntTutor command.

1. Initialize

Student[Calculus1]:-IntTutor((1+cos(3*x))^(3/2), x);

then press the All Steps button. The command produces the answer (see Bug1_in_IntTutor.mw)

(4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x)

which is not correct in view of

plot(diff((4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x), x)-(1+cos(3*x))^(3/2), x = 0 .. .2);

One may compare it with the Mathematica result Step-by-step2.pdf.

2. Initialize

Student[Calculus1]:-IntTutor(cos(x)^2/(1+tan(x)), x);

In the window press the Next Step button. This crashes (The kernel connection has been lost) my comp in approximately an half of hour (see screen2.docx). One may compare it with the Mathematica result Step-by-step.pdf .

Indeed,  "We wanted the best, but it turned out like always" .

The is and coulditbe commands of Maple are known to be buggy.
Here are some math inventions done by these commands in Maple 2016.2.

restart; assume(x::real, y::real);
is(exp(x+I*y) <> 0);
                             false
coulditbe(exp(x+I*y) = 0);
                              true
coulditbe(exp(x+I*y) = infinity);
                              true
coulditbe((x+I*y)^2 = infinity);
                              true

It should be noticed that

is((-infinity)::real);
                             false

though

exp(-infinity+0*I);
                               0

The latter means

limit(exp(x),x=-infinity);
                                   0

, no more and no less.

Let us consider 

sol := pdsolve({diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) = (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t}, {u(0, t) = 0, u(x, 0) = 0, v(0, t) = 0, v(x, 0) = 0}, time = t, numeric, timestep = 0.1e-1, spacestep = 0.1e-1, range = 0 .. 1); 
sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 .. 1);

A nice plot similar to the one produced by Mma (see the  attached pdf file pdesystem.pdf) is expected. 
The exact solutions u(x,t)=x*t,v(x,t)=x*t^2 are known

pdetest({u(x, t) = x*t, v(x, t) = x*t^2}, {diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) =
(1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t});
                              {0}

But the wrong result

               module() ... end module         
Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.26000000000000006):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

is obtained. Also 

sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 ..0.1);


 

The plot 

sol:-plot3d(v(x, t), x = 0 .. .5, t = 0 .. .1);

is not better.

Let us consider the help to RectangleWindow SignalProcessing-RectangleWindow.pdf SignalProcessing-RectangleWindow.mw.
Let us execute the example, taking N:=4 (in order to display the outputs).

with(SignalProcessing):
N := 4;
a := GenerateUniform(N, -1, 1);
         Matrix(1, 4, [[.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156]])         
RectangleWindow(a);
         Vector[row](4, [.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156])      
c := Array(1 .. N, 'datatype' = 'float'[8], 'order' = 'C_order'):
RectangleWindow(Array(1 .. N, 'fill' = 1, 'datatype' = 'float'[8], 'order' = 'C_order'), 'container' = c);
              Vector[row](4, [1., 1., 1., 1.])
u := `~`[log](FFT(c)):
plots:-display(Array([plots:-listplot(Re(u)), plots:-listplot(Im(u))]));



We see an uncommented code which (intentionally or unintentionally) produces two empty plots.
The questions arise:

  • What is the aim of the RectangleWindow command which does nothing 
    but the conversion of a Matrix(1,N,...) /Array(1..N,...) to a Vector[row](N,...)? 
  • Could such help be called friendly to Maple users?

There are many questions to Maplesoft and there are no answers from them: strategic silence.
RectangleWindow.mw

 

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