Markiyan Hirnyk

## 7163 Reputation

11 years, 162 days

## Bug in pdsolve, numeric...

Maple

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.

## Bad help and needless command in SignalP...

Maple

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

## Bug in Optimization...

Maple 2016

Let us consider the linear integer programming problem:

```A := Matrix([[1, 7, 1, 3], [1, 6, 4, 6], [17, 1, 5, 1], [1, 6, 10, 4]]):
n := 4; z := add(add(A[i, j]*x[i, j], j = 1 .. n), i = 1 .. n):
restr := {seq(add(x[i, j], i = 1 .. n) = 1, j = 1 .. n), seq(add(x[i, j], j = 1 .. n) = 1, i = 1 .. n)}:
sol := Optimization[LPSolve](z, restr, assume = binary);

Error, (in Optimization:-LPSolve) no feasible integer point found;
use feasibilitytolerance option to adjust tolerance

sol1 := Optimization[LPSolve](z, restr, assume = binary, feasibilitytolerance = 100, integertolerance = 1);

Error, (in Optimization:-LPSolve) no feasible integer point found;
use feasibilitytolerance option to adjust tolerance
```

That was OK in Maple 16, outputting

.

The bug in one of the principal Maple commands lasts since Maple 2015, where the above code causes "Kernel connection has been lost". The SCRs about it were submitted three times (see http://www.mapleprimes.com/questions/204750-Bug-In-LPSolve-In-Maple-20151).

## Bug in limit...

Maple 2016

Let us consider

```restart;
MultiSeries:-limit(sin(n)/n, n = infinity, complex);
0```

The answer is wrong: in view of the Casorati-Weierstrass theorem the limit does not exist. Let us try another limit command of Maple

```limit(sin(n)/n, n = infinity, complex);

(lim) (sin(n))/(n)
```

which fails. Therefore, Maple user does not obtain the correct answer.

## Maple usage in algebraic geometry...

Maple

I'd like to pay attention of Maple community to the recent work by Alex Degtyarev in algebraic geometry done with Maple.

Bertini.zip

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