Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

*** Edited to make more clear ***

The function algcurves.puiseux creates generator series for an algebraic function at a point.  The code below generates a few terms of each of the five generator series for the 1,2,3,4 and 5-cycle branch of  w(z) at the origin written implicitly as f in the code below.  Consider the 3-cycle branch:  I extract the 3-cycle generator and plot the imaginary sheet.  Note that's only one surface of a 3-valued function..  In order to plot the other two surfaces the generator series has to be conjugated.   The documentation doesn't appear to have a option to do this.   

If there's no procedure for doing this already and some are interested in this, we need to conjugate each individual monomial separately and  multiply each power of z expressed in terms of p/3 by the root of unity raised to the power p.   Not hard to do manually  for a few terms (see updated notebook below)  but I would like to generates several hundred terms.  Note in my updated notebook below how each monomial is multiplied by (exp(2k Pi i/3))^p (for k=1,2) where p is the numerator of the exponent in this case over 3 for the associated power of z.  We can graphically check if this is correct by stitching the sheets together as a Riemann surface via plots:-display(convert({sheet1Plot, sheet2Plot, sheet3Plot}, list)) which shows a 3-valued analytically-continuous surface wraping  around the z-plane three times.   I'll try to write a procedure but I'm brand new to Maple so might take a while.  Maybe call it as


for sheet k.

with(algcurves); f := 6*w^14+z^30+z^32+w^15*(z^2+2)+w^12*(z^3+z)+w^9*(z^9+z^5)+w^5*(z^20+z^14); puiseuxList := convert(puiseux(f, z = 0, w, 5), list)



[(-z)^(9/4), -(-z)^(16/5), -3-(350887/472392)*z^4-(4381/52488)*z^3+(365/243)*z^2-(1/18)*z, -16*(-z)^(14/3)+(2/3)*(-z)^(13/3)+(1/3)*(-z)^(10/3)+2*z^3-(-z)^(4/3), (35663903797/2166612408926208)*(-6*z)^(9/2)-(3407/944784)*z^4-(28431487/69657034752)*(-6*z)^(7/2)-(310547/104976)*z^3-(62285/26873856)*(-6*z)^(5/2)-(1/972)*z^2-(5/15552)*(-6*z)^(3/2)+(1/36)*z-(1/6)*(-6*z)^(1/2)]


sheet1 := puiseuxList[4]



sheet1Plot := plot3d([Re(r*exp(I*t)), Im(r*exp(I*t)), Im(eval(sheet1, z = r*exp(I*t)))], r = 0 .. .15, t = 0 .. 2*Pi, colorscheme = ["Red"])


sheet2 := -16*(exp((1/3)*(2*Pi*I)))^14*(-z)^(14/3)+(2/3)*(exp((1/3)*(2*Pi*I)))^13*(-z)^(13/3)+(1/3)*(exp((1/3)*(2*Pi*I)))^10*(-z)^(10/3)+2*(exp((1/3)*(2*Pi*I)))^9*z^3-(exp((1/3)*(2*Pi*I)))^4*(-z)^(4/3); sheet3 := -16*(exp((1/3)*(4*Pi*I)))^14*(-z)^(14/3)+(2/3)*(exp((1/3)*(4*Pi*I)))^13*(-z)^(13/3)+(1/3)*(exp((1/3)*(4*Pi*I)))^10*(-z)^(10/3)+2*(exp((1/3)*(2*Pi*I)))^9*z^3-(exp((1/3)*(4*Pi*I)))^4*(-z)^(4/3); sheet2Plot := plot3d([Re(r*exp(I*t)), Im(r*exp(I*t)), Im(eval(sheet2, z = r*exp(I*t)))], r = 0 .. .15, t = 0 .. 2*Pi, colorscheme = ["Blue"]); sheet3Plot := plot3d([Re(r*exp(I*t)), Im(r*exp(I*t)), Im(eval(sheet3, z = r*exp(I*t)))], r = 0 .. .15, t = 0 .. 2*Pi, colorscheme = ["Green"])







plots:-display(convert({sheet1Plot, sheet2Plot, sheet3Plot}, list))




I have tried to translate the Mathematica-Code of OEIS (A219954):

with MmaTranslator. In the translator occurs an error message with the IF-Statement ...

I will be happy to have this in Maple. I am interested in the digitCount in the above Code.

Sequence is:


Thanks for help :)

My maple froze while it was running. I saved and closed it and now it gives me this message when i try to open it "There was a problem in the loading process, you worksheet may be incomplete.". 

There is only one backup file and it is corrupted as well. I tried to see if i could work it out in the text file, but im not very good at doing this.

If anyone knows how to uncorrupt it pls help me 

Dear all
I have a boundary value problem, 
How can I solve the problem using maple or maybe we can introduce serie expansion to solve it or something else.

Thank you for your help 

I have problem to calculate the max value for 3d  phase potret for each period. Thank You

How could one reduce this equation int(x^2*diff(y(x), x)/(x^2 - 1), x) = int(y(x)^(1/2), x)^(-2/3)down to a first order ordinary differential equation? Maple can solve this equation, namely, 9*(1/x^(5/3) - 1/x^(11/3))*x*(sqrt(y(x))*x)^(8/3)/(8*(x^2 - 1)) - 3*x*(4*x^2 - 1)*(1/x^(5/3) - 1/x^(11/3))/(8*(x - 1)*(x + 1)) + _C1 = 0 , however I could not understand how this equation was arrived at, leading me to go to 'odeadvisor', which responded with y = G(x,y'(x)) labelled as the 'patterns' method, which appears to require a first order ode - that is why I raised the reduction question.

Please pardon the poor format below.  I'm new to Maple and cannot figure out how to cut and paste worksheet code which includes  Maple prompts.  

I would like to create a list of funtions in a set and then select one and plot its real or imaginary surface.  I'm able to do this with a single function below:

h := z -> z^(1/2);
    h := proc (z) options operator, arrow; z^(1/2) end proc

plot3d(Im(h(x + y*I)), x = -1 .. 1, y = -1 .. 1);

This plots the Imaginary surface of z^(1/2).  However I need to do this with a set of functions delimited with curly brackets such as:

functionList = {2 + z, z^2 - 3*z, -z^3 + 4};
                          /        2          3    \ 
          functionList = { 2 + z, z  - 3 z, -z  + 4 }
                   \                        / 

And if I now try and select the first function in functionList and attempt to plot it, the plot is blank.

v := z -> functionList[1];
v := proc (z) options operator, arrow; functionList[1] end proc

plot3d(Im(v(x + y*I)), x = -1 .. 1, y = -1 .. 1);
Warning, expecting only range variables [x, y] in expression Im(functionList[1]) to be plotted but found name functionList[1]

 Can someone help me with this problem and also explain to me how to format this post nice like the others?

Thanks for reading.

I wanted to solve a pde of two variables in spherical coordinates with a boundary condition at a specific radius. I am doing something wrong because the pdsolve just evaluates for several minutes and does not actually give anything.

Could someone have a look and let me know what I am doing wrong.




Setup(mathematicalnotation = true)

[mathematicalnotation = true]


eq3 := Laplacian(Phi_out(r, theta)) = 0

((r^2*(diff(diff(Phi_out(r, theta), r), r))+2*r*(diff(Phi_out(r, theta), r))+diff(diff(Phi_out(r, theta), theta), theta))*sin(theta)+(diff(Phi_out(r, theta), theta))*cos(theta))/(r^2*sin(theta)) = 0


bc1 := eval(Phi_out(r, theta)-Omega*mu*(-1+cos(2*theta))/(2*r), r = R) = 0

Phi_out(R, theta)-(1/2)*Omega*mu*(-1+cos(2*theta))/R = 0



pdsolve([eq3, bc1])




How to generate different letters? I've tried the 'exclude' option, which doesn't work in this context. Thank


I want to provide my students with a series of exercises involving radicals, but I don't want the final simplification to display rational exponents. I only want a solution in simplified form with radicals. Ideas? Thanks

how to make a phaseportrait curves with animation? so i can see how the curve going on. Thank you

Optimization code for mathematical model with nine compartments,

How can I generate a code to plot the optimals; h, chi and psi?


I am experiencing difficulties using my old Maple programs with the newer version. I tried changing the types of inputs and the typesetting level, but it just doesn't work. I would appreciate it if someone could help me overcome my ignorance.

Some simple input is attached with the output.

Hi everyone, I am trying to draw horizontal and vertical line on the graph. Command is working but vertical line is not displayed. Looking for help in this regrads.

Hi everyone, I am trying to draw bar graph for my expression, but received error. Could anyone please help me in this regard.

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