## Is there an improvement as far as speed and memory...

Hello

I have used Groebner[UnivariatePolynomial] extensively on my procedures and I wonder whether there is an improvement in speed and memory use in Maple 2020 in relation to the version I am currently using, that is, Maple 2017.

Many thanks.

Ed

## Overflow? An abrupt in a plot suppose to be smooth...

I am doing this plot

loglogplot((.45*exp(-0.5e-1*t)+.1*exp(-.1*t))/exp(-0.5e-1*t), t = 1.4*10^4 .. 1.52*10^4);

and I got this weird abrupt change at some point: (please see the attached maple file)

1.mw

I guess it is due to how Maple implement those very large/small numbers.. Any thoughts?

## How to Plot a graph from O+ rather than fro -numbe...

Sort of revising fourier. I have a graph  however it gives result from -2pi to + 2pi. there must be a comand to modify plot to go from 0 to 2pi can someone give me a clue.

Rick

## Graph Theory graph cosmetics...

I have a graph with 267 nodes and 727 edges. I am trying to produce an eligible visualization of my graph but I'm getting a very crowded network.

Code:

with(GraphTheory);
DrawGraph(Graph(M1), style = spring, symbolsize = 10, scaling = unconstrained);

I have attatched the a JPEG file to my question to show what it looks like. I would like to space out the nodes with a more zoomed out view. How would I go about this?

## How do I compute a definite integral of a specifi...

Hello everyone .

I asked Maple to compute a definite integral of a function, numerically. Unfortunately it does not give me any values . I briefly explain what I did.

As you can see in the picture first I define a real valued function BW_dilog(x) (with complex domain), where the function dilog  already exists in maple. Then I defined another function, V, (with real domain and codomain ). Now I need the approximate value of the bi integral of V, on a triangle. The Maple file is attached.

I would be grateful if any one could help me.

## Assignment by address versus by value...

I initialized a variable name using another variable name and := . I thought that Maple would assign the value, but I soon learned by debug that the address was assigned. This led to temporary problems.

Where can I learn the rules that Maple follows for assignment by value or address ?? Do I always have to initialize with a real number, like 0, to be safe ??

Thanks.

Mike Graber

## How to preserve the order when extracting the coef...

Hello (again)

I thought I won't need help with that type of question but I came across an example that says otherwise.  Here it is

```vars:=[x,y,z];

model7 := [x*(-RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4)+y*alpha[1, 2]-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), x*z*alpha[2, 6]+y*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), x^2*(17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6])-17*x*y/alpha[2, 6]+2*z*x-z-(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6])]
```

then I issued the command

```map(w->coeffs(w,vars),model7);
```

to get

`[-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), -RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4, alpha[1, 2], RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), alpha[2, 6], -(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6]), -1, (17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6]), -17/alpha[2, 6], 2]`

clearly the order does not follow model7's.

I have also tried

`[seq(coeffs(expand(model7[i]), indets(model7[i], suffixed({vars[]}))),i=1..nops(model7))];`

Is there a solution to it?

Many thanks (again)

Ed

## Maple Graph: Command to find the average path leng...

I would like to analyse the graph I made and I cannot seem to find any command that gives me the average path length of an unweighted graph, is it perhaps referred as a different command? As I have tried searching Mean path length, distance and other derivatives with no useful result.

## How to list only real solutions when there are oth...

Hello

I have the following set of coefficients

`coef7 := [-1, 2, alpha[1, 2], alpha[2, 6], (17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6]), -17/alpha[2, 6], -33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), -(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6]), -RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4, RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)]`

Considering that alpha[1,2] and alpha[2,6] are always real, how can I extract only the real solution from coef7?

Many thanks.

Ed

## 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

## Why are eps plot files in Maple 2017 much large ...

My colleague and I are revising a paper which contains some 3dplots generated I think originally in Maple 2015 on macos as eps converted to pdf.  Originally they were around the 100 KB size.  When I generate them again in Maple 2017 they are more like 10 MB.  He is still running Maple 2015 and get the same 100 KB size.  Any idea what is going on here ?

Thanks Michael

EDIT:  An example is

with(plots);
plotsetup(postscript, plotoutput = `test.eps`, plotoptions = `color,portrait,height=350,width=350`);
plot3d(x^2+y^2+1, x = -1 .. 1, y = -1 .. 1, axes = boxed, grid = [200, 200]);

I get 7.6 MB my colleague with Maple 2015 gets 56 KB.  I tried it wtih Maple 2017 on a server I have access to also 7.6 MB.

## Maple Implementation of Euler's method...

``````my_euler := proc (func_y, x_value, y_value, n, h)
local point_list, d_x, true_f, true_f_v; point_list := [10^(-n), 0, n];
true_f := unapply(func_y, x, y);
d_x := abs(point_list[2]-point_list[3]);
while d_x < point_list[1] do
true_f_v := true_f(x_value, y_value);
y_value := y_value+h*true_f_v;
x_value := x_value+h
end do;
return y_value
end proc``````

I am using Maple to implement Euler's method, it requires 5 parameters:

• func_y (The general form of ODE)
• x_value
• y_value
• n (The accurate digits, I do not know how to control the accurate digits)
• h (The step size)

So, I do not how to control accurate digits (4 accurate digits), can you teach me how to finish this part?

## How to extract from the implicit plot when ...

Hello.

I'd like to extract numerical data from the plot of a implicit function and write it to the txt file. But, unfortunately due to a strong oscillating function and as a consequence extremely dense meshgrid I got a message that [Length of output exceeds limit of 1000000]. How to resolve this problem? Below is my code

```restart;
R0 := 1+w_c*(sum((2*(-1)^(n+1)*Pi^2/n*n)*t*sin(2*Pi*n*mu/w_c)*cos(Pi*n)*exp(-2*Pi*n*G/w_c)/(w_c*sinh(2*Pi^2*n*t/w_c)), n = 1 .. 3000))/Pi-mu;
with(plots, implicitplot);
G := 0.; t := 0.1e-2;
R1 := implicitplot(R0, w_c = 0 .. 5, mu = 0 .. 3, gridrefine = 10):
data := getdata(R1);
```