MaplePrimes Questions

*** 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

                         conjugatedSeries=conjugatePuiseux(generator,k) 

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)

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)

 

[(-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)]

(1)

sheet1 := puiseuxList[4]

-16*(-z)^(14/3)+(2/3)*(-z)^(13/3)+(1/3)*(-z)^(10/3)+2*z^3-(-z)^(4/3)

(2)

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"])

-16*(-1/2+((1/2)*I)*3^(1/2))^14*(-z)^(14/3)+(2/3)*(-1/2+((1/2)*I)*3^(1/2))^13*(-z)^(13/3)+(1/3)*(-1/2+((1/2)*I)*3^(1/2))^10*(-z)^(10/3)+2*(-1/2+((1/2)*I)*3^(1/2))^9*z^3-(-1/2+((1/2)*I)*3^(1/2))^4*(-z)^(4/3)

 

-16*(-1/2-((1/2)*I)*3^(1/2))^14*(-z)^(14/3)+(2/3)*(-1/2-((1/2)*I)*3^(1/2))^13*(-z)^(13/3)+(1/3)*(-1/2-((1/2)*I)*3^(1/2))^10*(-z)^(10/3)+2*(-1/2+((1/2)*I)*3^(1/2))^9*z^3-(-1/2-((1/2)*I)*3^(1/2))^4*(-z)^(4/3)

 

 

 

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

 

NULL

Download puiseuxPlotsVer2.mw 

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 :)

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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 

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Thank you for your help 

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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.

restart

``

with(Physics[Vectors])

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(1)

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

(2)

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

(3)

``

pdsolve([eq3, bc1])

NULL

Download laplacian.mw

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