## How to find a smallest vertex cut of the graph g?...

The vertex connectivity of a graph  is the minimum number of vertices whose removal disconnects the
graph. With Maple, it's easy to get the connectivity of a graph, but  I can not  find a smallest vertex cut of
the graph g by maple.

If a graph has some cut vertices, I see that the function ArticulationPoints seems to be able to solve.
But for general smallest vertex cut, I don’t see a suitable function.  For example

with(GraphTheory):
G:=CompleteGraph(2,2,2,2);
DrawGraph(G);
VertexConnectivity(G)

6

This seems easy to do in Mathematica. See https://reference.wolfram.com/language/ref/FindVertexCut.html.

## Plotting of a nonlinear differential equation?...

Plotting of a nonlinear differential equation?

## why Maple asks "save large calculations" on this c...

I have not used Array much before. I made an array that has 3 elements, starting index is 0 and last index is 2.

I want each element in the array to be an empty list, so I can later add to it.  (since I do not know in advanced what size of list I need in each slot of the Array).

`Array(0..2,[seq([],i=0..2)])`

And this works in the code I am using. But the strange thing, each time I try to save the worksheet, I get Warning about saving Large calculation.

What large caclulation? The array is empty?

Even though the code is working, and I can add to each entry in the array lists OK and been using it OK, I think may be I am not doing something right.

How to correctly creat an Array from 0..N  and initialized each entry to empty list?

Maple 2021.2

## Signing in to Maple...

Every time I open Maple it has the invitation to Login in the top right-hand corner.  I would like to sign in but have had quite a bit of trouble doing that.  I have a user name and password with Maplesoft web store and the same for MaplePrimes.  Should either of these work to log in?

## why remove works different on diff(y(x),x) vs. one...

When doing

```item:=x;
res:=remove(has,item,x);
```

Maple returns, as expected

But when item is not a single symbol, say sin(x) or diff(y(x),x), then it no longer returns ()

```item:=diff(y(x),x);
res:=remove(has,item,diff(y(x),x));
```

It does not return () but it now returns the input itself, as if it was not removed.

Why is that, and how to make it return () also on composite expression?  I tried flatten and inplace option. Otherwise, I will have to do a special test before.

The strange thing is that it works on

```item:=2*diff(y(x),x);
res:=remove(has,item,diff(y(x),x));
```

Now it returns as expected. So now it did remove diff(y(x),x). But it does not remove it when it is on its own. I assume this is by design. But it is not intuitive to the user. One would expect it to work same way on removing `x` or `sin(x)` or `diff(y(x),x)`

## Draining a shaped container from the top, and the ...

Hello everybody. Ive got some questions.

As the title states: Draining a shaped container from the top, and the amount of Joule it takes to do it. That is what the questions are about.

I did make the first one, and some attempts at the sphere questions b, and c. I left them out because i want to see what you guys come up with. I think ive got the right answers, but we will see if our answers compare. :)

The Dutch text translated: Calculate in questions a, b, and c the amount of work (joule, J) it takes to drain a tank filled with water from the top with a pump. Each question has a discription of the shape of the tank. Take for gravity g=9.81m/s^2. For water take rho=1000kg/m^3.

a.
A coneshaped tank, the topangle is down, with a height of 2.0meters and a radius of 0.5meters.

b.
A sphere with a radius of 1.0meters.

c.
The lower half of a sphere with a radius 2.0meters.

Greetings,

The Function.

 >
 (1)
 >
 (2)
 >

## How can I substitute an alias by a given expressio...

In the code above expression #1 contains the term D(Phi)(X): how can I replace the "abstract" function Phi by a "specific" one  phi = k*X(t) ?

```restart:
alias(X = X(t)):
alias(Phi=Phi(X(t))):
kin := 1/2*M*diff(X, t)^2 + 1/2*m*diff(Phi, t)^2;  #1

# attempt to replace Phi by phi=k*X(t))
alias(phi=k*X(t)):
eval(kin, Phi=phi);                                #2 ... I expected phi would replace Phi
```

The attached file  How_to_eval.mw contains a more detailed explanation and a more general situation.

## nth derivative of f evaluated at zero...

Dear all

I would like to compute the monomial polynomial in taylor series, I tried
f:=cos(t);

fn:=n->subs(diff(f(x),x\$n),x=0)/factorial(n);
but it is does not work

## Is it possible to export routines from a personal ...

Is there a way to export routines from a package. The reason I ask, I was answering a question here and I needed two routines I have, that I put together a couple of years ago in a package. I used showstat copied, pasted and edited. Worked, but not great and would utterly fail with anything complicated. e.g. In the two routines pasted  below SignedArea on line 3 c[1]  is c   [1] that caused a minor problem.

## Printing math expressions...

Hi,

Does anyone know how can I write this thing in a Maple script?
I have a problem with printing math expressions when there is an increment in the matrix power.

## Need help Homework ...

 >
 >
 >

 Homothety
 Rotation on x axis

Rotation of angle k

 (3.1)

Neige

Hi, i need some help for a homework.

Here is the statement

You must first animate a series of linear transformations on the polygon formed by the following couples: [5, 0], [6., 0], [6, 3], [10, 3], [7, 5], [9, 5], [7, 7], [8, 7], [5.5, 9], [3, 7], [4, 7], [2, 5], [4, 5], [1, 3], [5, 3] It will be necessary to make, at the same time, a rotation around a line making an angle k with the axis of x, a rotation of an angle k and a scaling of variable ratio (but equal to 3 at the end animation). The k animation parameter should range from 0 to 180. I suggest you use the color green for your polygon. Then you will need to create a second animation by entering these command lines: SnowPoints: = seq ([- 30 + i, 30 - j / 2 * sin (i + j)], i = 0 .. 60): snow: = animate (pointplot, [[PointsNeige], color = black], j = 0 .. 60, view = [-30 .. 30, 0 .. 30]) : Finally, you will have to roll both animations at the same time.

The GIF shows the results that I should get according to my teacher

Thanks for the help !

## problem using dsolve first oder ode...

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

## Can maple solve an ode using asymptotic expansions...

Can Maple solve an ode by asymptotic expansions methods? series methods (power series or Frobenius series) work only on ordinary expansion point or removable singularity point. For non removable singularity (essential), Maple's dsolve with series method can't solve these. Also, if the RHS of the ode is not analytic at the expansion point, series method do not work.

The asympt command only applies to algebraic expressions.

Does Maple have something similar to Mathematica's AsymptoticDSolveValue  ?

Here is an example. This is an ode with RHS not analytic (has no Taylor series) at x=0

```ode:=diff(y(x),x)+y(x)=1/x;
dsolve(ode,y(x),'series',x=0)```

No solution.  While in Mathematica

```ode = y'[x] + y[x] == 1/x
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]```

Here is another example of ode where the coefficient of y(x) is not analytic at x=0

```ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
dsolve(ode,y(x),'series',x=0)```

No solution. In Mathematica

```ode = y'[x] + Sqrt[x] y[x] == 0
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]```

Does there exist a package in Maple that can do this? Will this functionality be added in Maple in the future if currently there is no support? ( I searched and could not find anything so far).

One possible workaround I found is to solve the ODE using normal methods (non-series), then apply the asympt command on the solution. But one needs to remove the constant of integration first, Here is the above example done this way

```ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
sol:=dsolve(ode);
Order:=8;
sol:=eval(sol,_C1=1);
asympt(eval(rhs(sol),x=1/y),y);
eval(%,y=1/x)

```

Mutliplying the above back by the constant _C1 gives same answer as Mathematica's.

Is the above how one is supposed to do it in Maple? It worked on the above simple example, but need to see if it will work for other examples. it will be better if this was more directly supported. i.e. if asympt will work directly on ode's (or a new command or a new option to dsolve similar to 'series' but call 'asympt').

## Is it possible to disable the automatic conversion...

Greetings!

For factorization and computing times purposes, I'd like Maple to not perform this automatic conversion.

gives

while gives

Alternatively, a way to factorize into could do the trick.

Here's a list of the functions I've already tried:

• factor
• collect (so coeff too)
• combine/expand

Any ideas?

Thank you!