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These are answers submitted by tomleslie

Nothing wrong with Carl's assessment, but his example could also be solved using only lists with something like

cols:=[red, green, blue, orange, black]:
plotlist:=[ seq(plot(x^k, x = 0..1, color = cols[k]), k = 1..5) ]:

Agree with Carl - sooooo many syntax errors

I took a chance, and tried to correct as many as possible - note that in many cases, I'm making an *educated guess* at what you intended, and may have got it wrong somewhere.

With that warning, the attached worksheet supplies plausible-looking results

If you type ExcelTools[Import]() without giving any arguments, then Maple will fire up an import wizard, which will allow you to navigate to the directory containing the file you want, select the file, and enter other options (sheet, cells etc).

I've just checked both versions (type command with arguments, use the wizard) and both seem to working just fine.

plot3d(1, theta=0..2*Pi, phi=0..Pi, coords=spherical);

Not sure this is going to help much, but here goes

PDEtools:-Solve cannot solve a system, if that system contains an equation in "arbitrary" parameters - in other words one which is completely irrelevant to the variables being solved. For example, as you observe


will work, but add an "arbitrary" equation to this,  such as

PDEtools:-Solve({eq3, a=b+c},H[xy])

and Maple errors.

In the case when you have a system of four equations in six unknowns, and you require a solution for only one variable, then it seems reasonable to suspect that one or more of the equations in the system will be arbitrary.

Note also that when asking for a solution to your system, if you specify four variables, then Maple will generally return a solution, so

PDEtools:-Solve({eq1, eq2, eq3, eq4}, H[xy])

fails, but

PDEtools:-Solve({eq1, eq2, eq3, eq4}, {H[xy],H[tt],H[tx],H[ty]})


I tried a few combinations of four variables and always obtained solutions, although there are 15 possible combinations of four from six variables and I didn't check all of them.

  1. Your question is not clear. When you say "what is the meaning of this statement", which statement are you referring to?
  2. You should use the big green up-arrow (right-hand end, second row of toolbar) to upload code. Using an image format such as png makes copy/paste almost impossible, and no-one wants to retype your code because it is time-consuming and error-prone
  3. If your problem is that fsolve() produces no answers, then (with a bit of work), I came up with the following solutions. There may be more solutions - I can't guarantee it either way

           sol={x = 256.2699202, y = 434.1099130}
           sol={x = 754.9656084, y = 1376.922255}
           sol={x = 1047.750388, y = 1090.143478}
           sol={x = 1594.603214, y = 304.6571162}

You can see my (distinctly experimental) method for doing this in the attached worksheet.

  1. I'm assuming that the 'grad' functions refers to the depreated linalg[grad] command, so need to load the (deprecated) linalg package
  2. OP's procedure doesn't return anything meaningful, because it defines globals C1, C2, C3, V1, V2, V3 and then assigns values to C[1], C[2}, C[3], V[1], V[2], V[3] - fixed this by assigining to C||j (ie cat the names)
  3. To use spacecurves need with(plots)
  4. Worksheet now runs (in Maple 2015) and produces plots (see attached), although I'm not sure that these are very interesting (I have no way of knowing)

Your requirements appear to be inconsistent:

your third requirement "K:=2 and m:=3" increments the first index, but

your fourth requirement "K:=1 and m:=4" shouldn't increment the first index, but your posted solution does. I'm assuming that this is a typo.

Assuming that it is a typo, try

genVec:= (x,y) -> [ seq
                             (  [ seq
                                   ( psi[k,j],
                                     k = 1..x
                                j = 0..y-1

If this isn't what you want then post requirements in a consistent fashion

  1. If you have 9 linear equations with 9 unknowns and numeric coefficients, then I would expect fsolve to breeze through it.
  2. If you have 9 non-linear equations with 9 unknowns and numeric coefficients then fsolve might find it a bit harder, but could probably be "persuaded" to work
  3. If you have 9 linear equations with 9 unknowns and "algebraic" coefficients, then solve might have difficulty, depending on the algebraic complexity of the coefficients
  4. If you have 9 non-linear equations with 9 unknowns and "algebraic" coefficients, then solve will almost certianly have difficulty, particularly if the coefficients are "complicated" algebraic expressions.
  5. If you upload a worksheet using the big green up-arrow (right-hand entry in the second row of the toolbar), then you might get some more useful comments





The attached worksheet "undefines" the spherical coordinate system in the Physics package and then "derives" it from first principles. You ought to be able to use it for any other coordinate system, provided that you know the transformation equations.

Remember that (according to the help page for the Physics[Vectors] sub-package)

"the Vectors subpackage is designed to work only with cartesian, cylindrical and spherical orthonormal basis and the related systems of coordinates"

so I advise caution if you are going to define your own coordinate system

Do you have something against fsolve which, for your example returns solution x1=6.000000000, x2=1.000000000, x3=-4.000000000?

If you want to use the Gauss-Seidel method for teaching/learning purposes, then you should be aware that it only works for linear equations, so is not appropriate for you example

If you still want to use the Gauss-Seidel method on a different (linear) example, then check out the Maple help page


One of the options available for the 'IterativeApproximate' command is to set method=Gauss-Seidel

Don't understand the issue you have with Carl's response, because when I try, it works just fine.

If you want another (less elegant) solution, try the attached

Well, in your worksheet Vr i a function of two variables r and theta - so you need to plot in 3D

As drawn, the vertical scale of your plot is completely dominated by the values as r->0 when Vr-> infinity. You might want to consider restricting the vertical range using the plot option/view

You might also consider the option coords=cylindrical

Not sure why you want a "recursive procedure" for this problem unless it is for teaching/learning pruposes.

Ignoring the "recursive" requirement there are many ways to achieve what you want, depending on whether you would like a user-defined error message, or are happy to receive a Maple-generated error message.

See the attached file for a few options

If I force a numerical evaluation of your final integral using

( int
  ( exp(-.3872983346*r*(2.*r-2.))/(r*HeunB(0., -.8801117368*I, -.1936491673, 0., (.8801117368*I)*r)^2),
    r = 0..1

then Maple returns Float(infinity)

If I plot the integrand over the integration range 0..1 using

( exp(-.3872983346*r*(2.*r-2.))/(r*HeunB(0., -.8801117368*I, -.1936491673, 0., (.8801117368*I)*r)^2),
   r = 0 .. 1

then it *seems* reasonably obvious that the integrand heads to infinity as r->0.

Given the expression(s) which you have entered, should Maple return infinity - probably yes, and I don't know why it doesn't. Either way I don't think you are going to have much luck evaluating these integrals, because the answer always seems to be infinite, and I'm pretty sure that is not what you want

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