Maple Questions and Posts

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Hi, 

I represent 3 thin parallel slices of colors red, green and blue; all have the same transparency equal to 0.5
For the default orientation of the display, the blue slice is on the forefront, the red one in the background and the green one in beween. Then the blue slice is "bluer" than green and  the green one "greener" than red (FIG 1)
If you rotate manually the figure in order to place the red slice in the forefront and the blue one in the background, you expect to have the red slice "redder" than the green one and the green one "greener" than the blue one (FIG 2)
This is not the case.

The order in which the slices appear in the PLOT3D command defines the foreground and the background, but these latter are not dynamically recalculated when the figure is rotated.
To recover the correct colors one must revert the order of the slices in PLOT3D (FIG 3)

Are we comdamned to change to change manually the order of the slices in PLOT3D or does it exist an option whixh avoids doing so?

Don't pay too much attention to the plots above for the foreground is strangely correct on figure 2 ???

restart

with(plottools):

alpha := Pi/18.:
a := 2*cos(alpha):
b := 2*sin(alpha):
e := 0.02:
p := [[0,0,0],[a,b,0],[a,b,1],[0,0,1]],
     [[0,e,0],[a,b+e,0],[a,b+e,1],[0,e,1]],
     [[0,0,0],[0,e,0],[0,e,1],[0,0,1]],
     [[a,b,0],[a,b+e,0],[a,b+e,1],[a,b,1]],
     [[0,0,0],[a,b,0],[a,b+e,0],[0,e,0]],
     [[0,0,1],[a,b,1],[a,b+e,1],[0,e,1]]

[[0, 0, 0], [1.969615506, .3472963554, 0], [1.969615506, .3472963554, 1], [0, 0, 1]], [[0, 0.2e-1, 0], [1.969615506, .3672963554, 0], [1.969615506, .3672963554, 1], [0, 0.2e-1, 1]], [[0, 0, 0], [0, 0.2e-1, 0], [0, 0.2e-1, 1], [0, 0, 1]], [[1.969615506, .3472963554, 0], [1.969615506, .3672963554, 0], [1.969615506, .3672963554, 1], [1.969615506, .3472963554, 1]], [[0, 0, 0], [1.969615506, .3472963554, 0], [1.969615506, .3672963554, 0], [0, 0.2e-1, 0]], [[0, 0, 1], [1.969615506, .3472963554, 1], [1.969615506, .3672963554, 1], [0, 0.2e-1, 1]]

(1)

f   := k -> transform((x, y, z) -> [x, y+k, z]):
col := k-> COLOR(RGB, op(ListTools:-Rotate([1, 0, 0], -k))):
t   := TRANSPARENCY(0.5):
PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))

 

PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))

 

PLOT3D(f(2)(POLYGONS(p, t, col(2))), f(1)(POLYGONS(p, t, col(1))), POLYGONS(p, t, col(0)), AXESLABELS(2, 3, 1))

 

 


 

Download Background_Foreground.mw

Can anyone help me to frame the equations in Fractional Reduced Differential Transform Method 

system of nonlinear ordinary differential equations
ds/ dt = b−γ s(t)− (δ s(t)(i(t) + βa(t)) /N − ε s(t) m(t) 
de/ dt = δ (s(t)(i(t) + βa(t))/ N + ε s(t) m(t) − (1−ϑ) θ e(t) − ϑ α e(t) − γ e(t) 
di/ dt = (1−ϑ) θ e(t) − (ρ + γ) i(t)
da/ dt = ϑ α e(t) − (σ + γ) a(t)
dr /dt = ρ i(t) + σ a(t) − γ r(t)
dm /dt = τ i(t) + κ a(t) − ω m(t) 

choosing lightmodel=none and shading=none, produces a dark grey grided surface
plot3d(x*y, x = 0 .. 10, y = 0 .. 10, lightmodel = none, shading = none)

adding the style=wireframe option gives a blank plot.  Grid probably white?  Changing style to patchnogrid the surface is indeed white. However chosing both shading and style options to none regardless of the lightmodel will produce a plot that appears empty.  Is this to be expected?

However, just the style=wireframe option produces a colored grided wireframe as to expect
plot3d(x*y, x = 0 .. 10, y = 0 .. 10, lightmodel = none, style = wireframe)

Dear users

All my recent questions are removed by "mapleprimes" automatically. who knows the reason?

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0}, 

   /       l rho - 4 w                                        \ 
  { a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
   \          6 l m                                           / 
 

HOW TO WRITE BOX COUNTING DIMENSION IN FRCATAL

Hi.

I'm working on an electronics project currently. In that project I have been trying to solve a system of inequalities, as shown by the picture from Maple below:

restart;

R__1 := 1;
lign1 := V__i/(R__4*(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4)) = C*(k__1 - R/R__C + R);
lign2 := V__i*(1/R__1 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__2 - R/R__C + R);
lign3 := V__i*(1/R__2 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__3 - R/R__C + R);
lign4 := V__i*(1/R__3 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__4 - R/R__C + R);
lign5 := V__i*(1/R__1 + 1/R__2 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__5 - R/R__C + R);
lign6 := V__i*(1/R__1 + 1/R__3 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__6 - R/R__C + R);
lign7 := V__i*(1/R__2 + 1/R__3 + 1/R__4)/(1/R__1 + 1/R__2 + 1/R__3 + 1/R__4) = C*(k__7 - R/R__C + R);
solve({lign1, lign2, lign3, lign4, lign5, lign6, lign7}, [R__4, R__2, R__3, R__C, R, C, V__i]);

Here's a picture as well:

However, the solution is simply that V_i = 0 and C=0, which is not really helping me. Am I doing something wrong here or is my system of equalities simply unsolvabe?

 

Can you please post the procedure for interfacing maple with visual molecular dynamics (VMD) software. Thank you.

I want to do the following: Suppose we are given a linear recurrence operator with polynomial coefficients say (n+2)N^2+(2n^2-3n+5)+(n-4) where N is the shift operator with respect to n. I want to apply the following substitution:

(i) N-> (N+1)

(ii) n->n(N^(-1)+1)

and compute the corresponding equation. To do this, I want to use Maple's Ore_Algebra package. However, I could not define N and N^(-1), i.e N inverse, at the same time.

To sum up, I want to get something like

A := Ore_Algebra(shift= [N,n] , dual_shift=[Ninv,n]); however it is not allowed. 

Thanks, in advance.

 

 

This should be pretty simple. 

    with(Units:-Standard);
    local var::Unit(kg);     #generates a warning
    var := 1;
    var;                     #-> 1 kg... alas this doesn't work (it's just 1)

In other words, I want to declare a variable with an unknown quantity and known `Unit` at the outset similar to how things are done in C-style languages, and later set the numeric value. The goal is to make it easier to manipulate functions that deal with lots of different physics unit types without having to write them each individual line. For example on lines 10-13 I manually include the units when it would be more convenient if they were already tied to the variable they're associated with.

Solving a simple physics problem to find the radius of a planet with the universal gravitational constant & known density:

I know types exists in Maple, i.e. 

    evalfr := proc(expr, iexact::integer := 0) 
      if   0 < iexact   then  return convert(evalf(expr), rational, iexact); 
      elif iexact = -1  then  convert(evalf(expr), rational, exact); 
      else                    return convert(evalf(expr), rational); 
    end if; end proc

This just being a wrapper with `iexact` typed as an `integer` setting up a set of conditionals around `evalf` to rationalize an expression when using `ScientificConstants`.

I've considered using anonymous functions to emulate this behavior with setters and getters, but that seems like overkill for something that is probably builtin. For the time being I have configured my worksheet so it references secondary variables, 

    var := var2*Unit(kg)

This strikes me as somewhat inelegant. Also trying to use the same variable name in-line (i.e. `var := var*Unit(kg)`) gives `Error, recursive assignment`.

I am curious if there is a correct Maple way to do something like this. Or would I have to implement some sort of anonymous function to get the behavior I want? Appreciate any help!

  [1]: https://i.stack.imgur.com/ovZSB.png

I'm trying to upload a file to Maple Cloud for the first time, but I am getting an error due to the way I use libraries.

The first lines of the startup code in the sheet look like this.

libname := "S:/Maple/NODE_Library", libname;
with(NODETreMaterial);
with(NODETreTverrsnitt);

The libraries are on a network drive on our server.

The question is - how can I solve this? Would it be better to somehow upload those libraries to Maple Cloud (no idea how to do that by the way), or can it be solved in a different way?

When executing DEBUG within inline code (not within a procedure) the values displayed in successive debug windows (on clicking continue) are added to the end of my worksheet. How can the latter display be prevented?

Hello,

is it possible to solve the attached partial differential equation with zero initial boundary condition?

If not by assuming diff(u(sigma, tau, phi, t), t, t)=0 is there an answer for the equation?

Thanks

lapla.mw

Suppose two following Eqs.:

(1) du/dt+d(u*w)/dx=0

(2) dw/dt+wdw/dx=0

I want to expand u(x,t) and w(x,t) in the power series of epsilon

u=u0+epsilon*u1+epsilon^2*u2+…

w=w0+epsilon*w1+epsilon^2*w2+…

and change the variables x,t to X,T as follows

 X=(x-alpha*t) and T=beta*t,

and solving Eqs. (1) and (2) for different order of epsilon (epsilon, epsilon^2, epsilon^3,…) to finding u0,w0,u1,w1,…

How do I do that?

Thanks.

 

Maple 2018  has recently has  become sluggish to start up  -and very slow to respond to input. Can anyone suggest remedies?  I have plenty of space and CPU. Other apps seem to start fine.  Can any suggest a diagnosis and/or solution?

Melvin

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