Markiyan Hirnyk

12 years, 3 days

## Bug in MatrixInverse...

Maple

I submit a bug through MaplePrimes because I can't do it as usually (Hope some people understand me.). Let us consider

```with(LinearAlgebra):
M := Matrix(5, 5,  (i, j) -> (10*i+j)*sin((1/180)*Pi*(10*i+j))):
MatrixInverse(M);
#One sees a long and wrong output instead of the warning "Matrix M is singular"
```

Indeed,

```Digits := 500; evalf(Determinant(M), 495);

1.3 10 ^(-488)
```

Bug_in_MatrixInverse.mw

## Bug in pdsolve...

Maple 2017

I submit a bug through MaplePrimes because I can't do it as usually (Hope some people understand me.). Let us consider

```restart; pdsolve([diff(u(t, x), t, t) = diff(u(t, x), x, x), u(t, 0) = 0, u(t, Pi) = 0]);
pdsolve([diff(u(t, x), t, t) = diff(u(t, x), x, x), u(t, 0) = 0, u(t, Pi) = 0], generalsolution);
u(t, x) = Sum(sin(n*x)*(_C5(n)*cos(n*t)+_C1(n)*sin(n*t)), n = 1 .. infinity)
u(t, x) = Sum(sin(n*x)*(_C5(n)*cos(n*t)+_C1(n)*sin(n*t)), n = 1 .. infinity)
```

The question arises: what do these outputs mean? I don't see any explanation in ?pdsolve and ?examples,pdsolve_boundaryconditions. What are _C1(n) and _C5(n)? Under which conditions does the above series converge?

Moreover,

```pdetest(%, [diff(u(t, x), t, t) = diff(u(t, x), x, x), u(t, 0) = 0, u(t, Pi) = 0]);
[0, 0, 0]
```

I think the above is simply a fake: it is possible to differentiate  a series only under certain conditions.

Bug_in_pdsolve.mw

Please, don't convert my post to a question. This is not correct and fair. Hope some people understand me.

## GeneratePDF does not work for me...

MaplePrimes

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.

## Serious and critical bugs in IntTutor...

Maple 2017

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 .

## Bugs in is and coulditbe commands...

Maple

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.

 1 2 3 4 5 6 7 Last Page 1 of 17
﻿