## Sets, nested sets...

Hello. Let's say I have a set A1 in which there are nested sets {5,6},{8,9}. How can I get A2 from A1? Expand nested sets so that all elements are in the same set

## Can't remember the name of the command...

The eval command doesn't work on random variables.

For instance:

with(Statistics):
X := RandomVariable(Normal(mu, sigma)):
Y := eval(X, mu=1);
Mean(Y); # returns mu

I once found a Maple command whose syntax is the same as eval's and acts as eval
Y := COMMAND(X, mu=1)
Mean(Y); # returns 1

Could someone remind me of its name?

## how do i plot a probabilitry function in 3 variabl...

How can i plot a probability function such as cos(x-y)*cos(y-z)*cos^3(x-2z)=0.6 where

x=0..5, y=0..x, z=0..y.

## How do I values to constants when using Invariants...

Dear Maple users,

I am progressing, but one last hitch, see below. A want the invariants of the PDE below. However, the final expression is too general to be useful. I would like to insert specific values for F1(R), F2(R), F3(R), and F4(R):

F3=F4=0; and F2=1, and F3(R)=aR, where a is a constant. R is one of my independent variables (the Reynolds number).

I would like to do this at the step where the Infinitiesimals are generated by

For example, the first entry would then be, infinies:=[ _xi[y](y, R, l, u) = y, ... ]. Then Invariants should give me much simplified expressions which I need.  How can i do this?

Thanks

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## Opening and closing sections does not work properl...

Hi,

I am having trouble opening and closing sections in Maple 2018 (Mac OS version) recently. It used to work with just a single click to open, and another single click to close. Now sometimes it takes a single slick, sometimes two or more, and sometimes a richt-click and sometimes it doesn't work at all. This is becomming very frustrating, and I have no idea what caused the problem. The problem occurs with all my documents.

Thanks for help!

## Custom-Coloring a pointplot...

In short, I want to create a density plot but with points. So I do a pointplot and I want to color it according to the value of a third function.

So let's say I do:

>x1:=[seq(x,x=1..2,0.02)];

>y1:=[seq(y^3,y=1..2,0.02)];

>z1:=[seq(x1[i]/y1[i],i=1..51)];

And I want a plot like:

>pointplot([x1,y1])

but with a color corresponding to the gradient of z1.

What I can do is something like:

>pointplot([x1,y1], colorscheme=["valuesplit", z1, [0..0.5="Black",0.5..1="RoyalBlue"]])

but that's not as pretty as it could be. So is there a way to do something like colorscheme=["zgradient", z1]? This doesn't work because zgradient expects its first argument to be colors and then you can add markers, but they apply to the function you plot, not to a third function.

Any ideas?

## Visualising solutions to sums of polynomials...

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)

This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

## removing entries from list...

I wanted to remove entry from a list that contain y=y or x=x in it. Here is an example

f:= (x-1)*y^4/(x^2*(2*y^2-1));
S:=[singular(f)]


Where I wanted to remove those entries highlighted above to obtain

This is below how I ended up doing it. I'd like to ask if there is a better or more elegent way. I had to use map, since could not get remove() to work on the original list in one shot.

foo:= z->remove(has,z,{y = y,x = x});
map(foo,[singular(f)])


Which gives the output above.

Is there a better way to do this? I always learn when I find how to do something better.

Maple 2019.1

## How to explain this output from iscont( )?...

Why does the iscont( ) function declare that the square root function is continous over Riscont_error.mw

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## Define a block matrix...

Dear Users!

Hoped you will be fine. I want to define a block matrix A for any value of M like this way

A = [A[0], A[1], A[2], ..., A[M]]

A[i] = [A[i,0], A[i,1], A[i,2], ..., A[i,M]]

and

A[i,j] = Transpose([a[i,j,0], a[i,j,1], a[i,j,2], ..., a[i,j,M]]);

Kindly help me in this matter. Thanks in advance.

## difficult integral...

A research paper published in 1929 claimed that this integral was solved in 1896.

int(exp(I*m*omega + I*b*cos(omega) ),omega=0..2*Pi)           (m integer,  b positive constant)

but it defeats Maple (and other).  Can anybody suggest a way to solve this integral with Maple?

## Working with complex numbers...

Hello. There is a complex function U11[n]. Let's say I take its derivative and want to extract the real part. That is all right. Now let's say I want to get the derivative at a point and extract the real part. I can't. Are there any solutions?

HELP.mw

## what is the reason for imaginary result?...

is the reason for Image result?

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## Creating styles...

I would like to change the color and font type on the Maple-2019 inputs and outputs, so that these formatting would be applied every time I started a new document. I tried doing this through the Styles option on the Format menu, but I could not. Can anyone help? Thank you.

## Which sorting of differential equations related wi...

Which sorting related with famous sequence

for example

sorting differential equation in a list

then access the list with famous sequence as index such as using https://oeis.org/

after access with sequence as index, use choose function to get combinations then most result are isomorphism differential ideals?