## How do I differentiate this in Maple?...

Dear Experts,

Please how do I carry out the differentiation of

`y[1](t)*y[2](t)*(y[1](t)+y[2](t))^3`

with respect to y[1] using maple? I know how to use maple if the derivative is with respect to t.
Thank you in anticipation

## tridiagonal linear system ...

Dear all

I would like to solve a linear system A X=b whee A is a matrix n times n

If A is a tri-diagonal matrix, how can we write simple code to make A upper-triangular and then we solve the system using backward substitution

many thanks

## A strange bug, perhaps in limit....

Here is a strange one...

1> /Library/Frameworks/Maple.framework/Versions/2019/bin/maple ; exit;
|\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> version():
User Interface: 1435526
Kernel: 1435526
Library: 1435526
> I0:=(x - 11)^(n)*x/(x^(n + 1));
n
(x - 11)  x
I0 := -----------
(n + 1)
x

> I1:=(x - 11)^(n)/(x^(n));
n
(x - 11)
I1 := ---------
n
x

> is(I1=I0);
memory used=2.5MB, alloc=40.3MB, time=0.14
true

> Limit(I0,x=infinity)=limit(I0,x=infinity) assuming n::posint;
n
(x - 11)  x
lim       ----------- = infinity
x -> infinity    (n + 1)
x

> Limit(I1,x=infinity)=limit(I1,x=infinity) assuming n::posint;
n
(x - 11)
lim       --------- = 1
x -> infinity      n
x

This was in Maple 2019.2 ... but I had Maple 18 (from 2014) running here, and it does the same thing.

How strange is this: replace 11 by 10 (or less) and the error goes away.

## Is there a tetrahedron or not...

Recently found out about Steiner ellipsoids. This is an ellipsoid inscribed in a tetrahedron, and an ellipsoid described near a tetrahedron. One ellipsoid touches the faces of the tetrahedron in centroids, the other ellipsoid touches the planes in vertices of the tetrahedron, and these planes are parallel to the faces.
steiner_in_ellipsoid.mw
steiner_out_ellipsoid.mw

There is a desire to find out if 4 vertices determine the tetrahedron or not. And it seems Maple answer this question:

```restart: with(geom3d):
point(A, 0, 0, 0), point(B, 1, 0, 0), point(C, 0, 0, 1), point(F, 0, 1, 0):
gtetrahedron(T1, [A, B, C, F]):
i := nops(op(0, detail(T1)));
if i = 1 then print("Ok gtetrahedron") else print("No gtetrahedron") end if:
```

I want to stop further execution of the program if the tetrahedron is not determine, for example, when point
B = [0,0,0], but I don’t know how to do it.

## Groupping a nested list...

I have a nested list like this,

Spectrums:=[ [graph1,eigenvalue of the graph1] , [graph2,eigenvalue of the graph2], ... ,[graphN,eigenvalue of the graphN] ]

What is the easiest / efficient way to group the list with respect to second value (eigenvalue)?

## Why this unterminated loop error?...

```rfin := proc(m::integer)
local c, i, flg := 0;
for i from 0 to m do
local b := i;
do
c := b mod 3;
if (c <> 2) then next else flg := 1;
end if;
b := 1/3*b - 1/3*c;
until b = 0;
if evalb(flg = 0) then print(i);
end if;
end do;
end proc;```

Hello everyone. I've written a procedure that outputs all numbers <= a given user I/P whose ternary representation has no 2.

However, I get an "Error, unterminated loop" message. Can someone please out the mistake(s)?

## I can't remove rootOf...

I am trying to simplify an expression, and leave W in terms of other variables. But unfortunately I can't delete the RootOf, and I can't see the expressions. Could you please help me.

## optimization problem postive integer solution ...

Dear all

I have an optimization problem. I would like to add a condition to obtain only a positive integer as the solution to the problem

Positive_integer.mw

thanks

## New Bug of Maple 2020？...

Update:This bug ONLY occurs when the file title containing Chinese Characters.

The .mw files have already been associated with Maple 2020, but when clicking on any of them, Maple 2020 won't launch as expected and nothing actually will happen.
I have tried to reinstall Maple 2020, but the problem just keep existing.

The Windows version where the bug occurs is Windows 10 version 1909.

## Please how I can find the value of x and y ?...

Hello everyone I need your help  please, I found a problem with solving an equation to explain this in detail ,here is  the problem how it is posed :

first of all we have N(q)=(exp(q)/sqrt(q))*sqrt(3/2)*D(3*q/2) .     (1)

with: D(3*q/2)=exp(-3*q/2)*integral(t^2)*dt with t varie from 0 to sqrt(3*q/2) this integral is known as Dawson's name     (2)

then we have q=(24/(n-3))*(x*k*m)/t with : t=0.6,n=6,k=1.3, so q=18.66666667*x*m    (3)

finaly we have m = 1/2*[(exp(q)/(q*N(q)))-1-1/q]     (4)

the quetion : is we must  find the expression of m  (4)  as a function of x only .

thank you evryone .

## How to generate a random integer with customized p...

Hi everyone,

In the RandomTools package, the Generate(integer(range = A..B)) function generates a random integer in the range A..B. All integers in that range have the same probability to be generated, that is, 1/nops([seq(A..B)]). However, I would like to specify the probabilities of each integer. How to do so?

Example: range = 1..5. Instead of P(X=j)=1/5 with j =1,2,3,4,5, let's say the probabilities should be as follows:

P(X=1) = 0.2, P(X=2) = 0.5, P(X=3) = P(X=4) = P(X=5) = 0.1

How to generate a random integer between 1 and 5 with these probabilities?

Thank you in advance.

## Error, numeric exception: division by zero...

Error, numeric exception: division by zeroprpblem_maple_2.mw

 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 >
 >

## Looking for tips to solve system of two (complicat...

Hello experts,

I am trying to use solve to find a solution to a system of two equations. The two equations involved are quite complicated, and so sometimes Maple has difficulty with this. In particular, the solve command tries evaluating but never comes up with a solution (I've waited at least an hour, before giving up).

I recently learned about fsolve, which gives approximate numeric solutions (which would be fine for my purposes), but fsolve too struggles with a solution and simply returns my input to me. I tried plotting the system of equations using plots:-implictplot to see if a solution existed, and as expected it does. I was hoping to get some tips on trying to solve a difficult system like this, perhaps given the knowledge that a solution definitely exists. Unfortunately, I need a solution for many variations of the same system, so simply reading off the approximate solution isn't really an option.

In my attatched code, the system with W = 49 is the first one where Maple really begins to struggle, and I believe that solutions for W>49 are also difficult.

06042020_Predicting_w_AB_Ratio_Maple_Primes.mw

Thanks!

## How to count the number of nonlinear terms in a li...

Hello

I need to count and separate the nonlinear terms in a list.  Example:

```w:=[[z, y, x, 1], [x*z, x*y, y, 1], [x*z, z, x*y]];
```

there are 4 nonlinear terms, x*z, x*y, x*z, and x*y.

The terms can be any combination of the given variables, that is, x, y, and z.

My solution to the problem of counting the nonlinear terms is

```aux1:=[seq([seq(nops(w[j,i]),i=1..nops(w[j]))],j=1..nops(w))];

aux2:=[seq(selectremove(x->x>1,aux1[i])[1],i=1..nops(aux1))]

res:=convert([seq(convert(nops(aux2[i]),`+`),i=1..nops(aux2))],`+`);```

It works but I wonder whether there is a better solution that includes showing the nonlinear terms themselves.

Many thanks

Ed

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