## 150 Reputation

10 years, 270 days

## Color density or schemes in 3D...

Maple

Hello, I have a simple question, yet I haven't find a plot command to do what I intend to:

I have a scalar field (density), as rho:=-4*x+4*y+4*z+3.

What I want to do is plot this density (using color gradients) on a cube, this is x=0..4, y=0..4 and z=0..4.
The color gradient would be something like from blue to red, including (maybe) some other colors in between.

I suppose this would provide me a cube with some colors schemes al over its faces.

Is there a plot command to do this, for 2D there is densityplot, but I have failed to find a 3D equivalent.

Thank you very much!

## Non-Linear System, fsolve fails to find ...

Maple 18

Non-Linear.mw

Hi, I have here a interesting non-linear system.

If I attempt to solve it using some specific form of the non-linear equations (form X*Y=Z) of the system, Maple (Verison 18) finds a solution.

But, if I replace some of them by some other forms (like form Y=Z/X), fsolve fails.

I usually use the non-quotient form. But is there any way to guide or configure fsolve to reach a solution?
I set up some of the regular options: placing a seed close to the solution, indicating intervals of possible solutions; but none of that works if I do not set up the non-quotient form of the equations. In some cases, fsolve does not reach a solution at all, no matter the form of the equations.

In the file, the equations that are causing the isssue are the last 3, those who start with the variable f1,f2 and f3.
I ran the system twice with both cases: non-quotient form and quotient form.

## Error during integration...

Maple 18

I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day

## Vector Definition Using Initial and Fina...

Maple

A simple question:

Can I define a Vector using:

a) Initial Value (a), Final Value (b) and the number of elements (N) (assuming linear spacing)
For example: Starts at 1, finishes at 12 with 5 elements:

[ 1 , 3.75 , 6.5 , 9.25 , 12 ]

b) Initial Value (a), Final Value (b) and step (s)
For example: Starts at 2, finishes at 6 with a step of 0.5

[ 2 , 2.5 , 3 , 3.5 , 4 , 4.5 , 5 , 5.5 , 6]

but using only a,b and N ; or a,b and s directly?

Thanks.

------
------

I know this can be done using the seq command and some basic definitions:

In the first case:
Vector([ seq(a+(b-a)/N*i,i=0..N) ]); should do the trick

And the second case is even easier:
Vector([seq(i,i=2..6,0.5)]);

PS. I know for the second case that using any arbitrary step can result in loosing the final value "b" of the sequence because you won't step on b using that arbitrary step value.

As I said above. I just want to know if there is a direct way to define these cases.

## Maple Fails during a while cycle - Why?...

Maple 18

Hello, I found this very strange behavior in Maple and I can't explain why this is not working

A little bit of context first:

1. I placed a polygon as a boundary for a section and then two polygons that correspond to inner holes to the first one.
2. Then I proceed to create a regular mesh that places N x M points spread across the region (OK here)
3. A procedure checks weather or not a Point is inside the region, on the borders or in the inner holes (OK here)
4. Then I want to select the closest (but exterior) ones so I can create a path using the mesh points.

Here is where I find the issue. I start at a vertex called V[1,1] and I want to arrive at V[1,2] (in the document they are blue solid points marked they are near-vertices near the original polygons). The procedure that I apply finds a path towards the V[1,2] as I was expecting but when the procedure hits the V[1,2] coordinates the while loop does not stop

The condition I wrote was:    while point<>V[1,2] do  where 'point' is correctly generated by another procedure.

This happens in a 40 by 50 mesh but with other configurations it works properly (there are also another kind of errors but it's inherent to lack of optimization in my procedures).

What baffles me is why doesn't it stop the cycle, if I test the condition outside the loop it DOES recognize the points are indeed equal. Is it something in Maple or is it something in my PC?

Thanks to anyone who can see the error or the problem because I don't understand the nature of the problem.

Not_Working.mw

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