Hello everyone!

I have an expression for the resonant frequency in terms of some geometric paremeter, say "x", i.e. f(x). I want to plot it together with the resonant wavelength (lambda=c/f) in the same plot. The "dualaxisplot" produces two curves (f(x), lambda(x)) with two uniform axes to the left and to the right. I am wondering is there a reasonably simple way to make it look as one curve, but with the second (e.g. lambda) axes nonuniformely scaled to fit the curve f(x)?

Many thanks in advance for your suggestions!

Hello everyone!

I am struggling to figure out the cause of the problem with Explore command. To put it as simple as possible:

 a := <3, 4, 5>

Explore(a[i], i = 1 .. 3);
Error, (in Explore) bad index into Vector

I am pretty sure that this has to do with an attempt to evaluate A[i] with i not yet defined, but why does Explore behave this way? seq has no such problem:

seq(a[i], i = 1 .. 3);
3, 4, 5

But as soon as I put it into Explore, seq seems to forget all its "special evaluation rules":

Explore(seq(a[i], i = 1 .. 3), b = 1 .. 2);
Error, (in Explore) bad index into Vector

It is probably for the same reason that I can't solve the problem with unevaluation quotes such as: 

Explore('a[i]', i = 1 .. 3);
Error, (in Explore) bad index into Vector
 

What am I doing wrong??

Hello everyone!

In previous versions of Maple (e.g. Maple 2016) it used to be possible to use scaletorange and colorscheme options together as in:

densityplot(sin(x+y), x = -1 .. 1, y = -1 .. 1, colorscheme = [black, red, yellow, white], scaletorange = -.5 .. .5);

But Maple 2018 returns an error:

Error, (in plots/densityplot) the scaletorange option cannot be used with the colorscheme option

Why is that and can one work around this error in any simple way?

How come I got this:

as an output of plot(sqrt(Pi/(2*x))*BesselJ(3+1/2, x), x = 0 .. 0.5e-1),

and got this:

for plot(sqrt(Pi/(2*x))*BesselJ(3+.5, x), x = 0 .. 0.5e-1).

Is 1/2 so much different from 0.5 to make Bessel function misbehave at small arguments?? Or is it just a bug?

Hello everyone!

I am confronted with a problem that seems to result from different definition of spherical coordinates in Maple and in Student[VectorCalculus] package.

I want to visualize a vector field defined in spherical coordinates (r,theta,phi).

A simple exampe is < 0, theta, 0 >. If I want to see just one slice of the field in OXY plane, I type:

fieldplot3d(<0, theta, 0>, r = 0 .. 1, theta = 0 .. 2*Pi, phi = 0 .. Pi, coords = spherical, grid = [10, 20, 3], color = black, fieldstrength = fixed(1), arrows = THICK)

And get:

which looks OK more or less but I don't like the nonuniform distribution of arrows. But since the field is defined in spherical coordinates there seems to be no way to produce a uniform distribution with fieldplot3d command.

However VectorField command in Student[VectorCalculus] package seems to do just what I want. But a similar call to it:

SetCoordinates('spherical'[r, theta, phi])

VectorField(<0, theta, 0>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])  produces quite a different result:

which means that the second argument 'theta' is not the azimuthal angle but the angle from the Z axis, and amounts to Pi/2 since we look at the OXY plane.

The result of: VectorField(<0, 0, theta>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])  looks better:

but is not correct since the magnitude of the field does not change with the azimutal angle. Finally, 

VectorField(<0, 0, phi>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]]) produces almost what I want:

but it's quite different from what you get with fieldplot3d command. Apparently, not only azimuthal angle is now the third argument but it varies from -Pi to Pi, not from 0 to 2Pi as it does in fieldplot3d. I hoped to use both fieldplot3d and VectorField  with my vector fields but I cannot since they are not consistent in the definition of spherical coordinates.

My questions therefore are:

1) Is there a way to redifine spherical coordinates in VectorField command to make them consistent with the rest of Maple?

2) Can I produce a uniform 3D distribution of arrows for a field in spherical coordinates without VectorField command?

Many thanks for your help in advance!