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Series of Complex Analysis Worksheets

by: Paras31 225 Maple 2025
complex-analysis series convergence
2 hours ago
0  0

Hello everyone,

I am creating this post to begin a thread where I will share a series of worksheets on important topics in Complex Analysis, written as part of my notes for my classes. Complex_Analysis_Notes.pdf

The planned sections include:

  • Section 1: Infinite Series

  • Section 2: Power Series

  • Section 3: The Radius of Convergence of a Power Series

  • Section 4: The Riemann Zeta Function and the Riemann Hypothesis

  • Section 5: The Prime Number Theorem

Each worksheet will include calculations, plots, and examples using Maple to illustrate key ideas.

✅ I plan to upload one worksheet every week to keep a steady pace and allow time for discussion and feedback between posts.

I hope this thread will be helpful both for learning and for deeper exploration.
Feel free to comment, suggest improvements, or ask questions as I post the materials.

Thank you!

> 

restart; interface(imaginaryunit = 'I'); z := I*(1/3); S_N := proc (n) options operator, arrow; sum(z^k, k = 0 .. n) end proc; limit(S_N(n), n = infinity); S_N(10); S_N(100); S_N(1000); with(plots); points := [seq([Re(evalf(S_N(n))), Im(evalf(S_N(n)))], n = 0 .. 50)]; pointplot(points, connect = true, symbol = solidcircle, symbolsize = 10, color = blue, labels = ["Re", "Im"])

proc (n) options operator, arrow; sum(z^k, k = 0 .. n) end proc

  

9/10+(3/10)*I

  

53144/59049+(5905/19683)*I

  

 
> 

restart; interface(imaginaryunit = 'I'); z := I*(1/2); S_N := proc (n) options operator, arrow; sum(z^k, k = 0 .. n) end proc; limit(S_N(n), n = infinity); S_N(10); S_N(100); S_N(1000); with(plots); points := [seq([Re(evalf(S_N(n))), Im(evalf(S_N(n)))], n = 0 .. 50)]; pointplot(points, connect = true, symbol = solidcircle, symbolsize = 10, color = blue, labels = ["Re", "Im"])

proc (n) options operator, arrow; sum(z^k, k = 0 .. n) end proc

  

4/5+(2/5)*I

  

819/1024+(205/512)*I

  

 
> 

NULL
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; sum(((1/2)*I)^n, n = 0 .. N) end proc; fullsum := sum(((1/2)*I)^n, n = 0 .. infinity); realpts := [seq([n, Re(S(n))], n = 0 .. 30)]; imagpts := [seq([n, Im(S(n))], n = 0 .. 30)]; limit(Re(S(n)), n = infinity); limit(Im(S(n)), n = infinity); horiz_reallimit := plot(4/5, k = 0 .. 30, color = black, linestyle = 2, thickness = 2); horiz_imaglimit := plot(2/5, k = 0 .. 30, color = black, linestyle = 2, thickness = 2); plots[display]([pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Value"], legend = "Real Part"), pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Value"], legend = "Imaginary Part"), horiz_reallimit, horiz_imaglimit], axes = boxed, labels = ["n", "Partial Sum Value"])

4/5+(2/5)*I

  

4/5

  

2/5

  

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); H := proc (N) local n; sum(1/n, n = 1 .. N) end proc; limit(H(n), n = infinity); limit(Re(H(n)), n = infinity); limit(Im(H(n)), n = infinity); harmonic_pts := [seq([n, H(n)], n = 1 .. 100)]; harmonic_plot := pointplot(harmonic_pts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum Value"], axes = boxed)

infinity

  

infinity

  

0

  

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; sum(I^k/k, k = 1 .. N) end proc; realpts := [seq([n, Re(S(n))], n = 1 .. 100)]; imagpts := [seq([n, Im(S(n))], n = 1 .. 100)]; complex_pts := [seq([Re(S(n)), Im(S(n))], n = 1 .. 100)]; S_infinite := sum(I^k/k, k = 1 .. infinity); Re(S_infinite); Im(S_infinite); horiz_reallimit := plot(-(1/2)*ln(2), k = 0 .. 100, color = black, linestyle = 2, thickness = 2); horiz_imaglimit := plot((1/4)*Pi, k = 0 .. 100, color = black, linestyle = 2, thickness = 2); real_plot := pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum Value"], axes = boxed, legend = "Real Part"); imag_plot := pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Partial Sum Value"], axes = boxed, legend = "Imaginary Part"); plots[display]([real_plot, horiz_reallimit, imag_plot, horiz_imaglimit]); plots[pointplot](complex_pts, symbol = solidcircle, style = pointline, color = blue, axes = boxed, labels = ["Re", "Im"])

-(1/2)*ln(2)+((1/4)*I)*Pi

  

-(1/2)*ln(2)

  

(1/4)*Pi

  

 

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; sum((-(2/3)*I)^n, n = 0 .. N) end proc; fullsum := sum((-2*I*(1/3))^n, n = 0 .. infinity); realpts := [seq([n, Re(S(n))], n = 0 .. 30)]; imagpts := [seq([n, Im(S(n))], n = 0 .. 30)]; limit(Re(S(n)), n = infinity); limit(Im(S(n)), n = infinity); horiz_reallimit := plot(9/13, k = 0 .. 30, color = black, linestyle = 2, thickness = 2); horiz_imaglimit := plot(-6/13, k = 0 .. 30, color = black, linestyle = 2, thickness = 2); plots[display]([pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Value"], legend = "Real Part"), pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Value"], legend = "Imaginary Part"), horiz_reallimit, horiz_imaglimit], axes = boxed, labels = ["n", "Partial Sum Value"])

9/13-(6/13)*I

  

9/13

  

-6/13

  

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; sum((I*Pi)^n, n = 0 .. N) end proc; realpts := [seq([n, Re(S(n))], n = 0 .. 100)]; imagpts := [seq([n, Im(S(n))], n = 0 .. 100)]; complex_pts := [seq([Re(S(n)), Im(S(n))], n = 0 .. 100)]; limit(S(N), N = infinity); limit(Re(S(n)), n = infinity); limit(Im(S(n)), n = infinity); real_plot := pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum (Real Part)"], title = "Real Part of Partial Sums of (Pi i)^n", axes = boxed); imag_plot := pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Partial Sum (Imaginary Part)"], title = "Imaginary Part of Partial Sums of (Pi i)^n", axes = boxed); complex_plot := pointplot(complex_pts, symbol = solidcircle, style = pointline, color = blue, labels = ["Re", "Im"], title = "Partial Sums in Complex Plane (Pi i)^n", axes = boxed)

undefined

  

undefined

  

undefined

  

 

 

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; sum(2*I^k/k, k = 1 .. N) end proc; realpts := [seq([n, Re(S(n))], n = 1 .. 100)]; imagpts := [seq([n, Im(S(n))], n = 1 .. 100)]; complex_pts := [seq([Re(S(n)), Im(S(n))], n = 1 .. 100)]; S_infinite := sum(2*I^k/k, k = 1 .. infinity); Re(S_infinite); Im(S_infinite); horiz_reallimit := plot(-ln(2), k = 0 .. 100, color = black, linestyle = 2, thickness = 2); horiz_imaglimit := plot((1/2)*Pi, k = 0 .. 100, color = black, linestyle = 2, thickness = 2); real_plot := pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum Value"], axes = boxed, legend = "Real Part"); imag_plot := pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Partial Sum Value"], axes = boxed, legend = "Imaginary Part"); plots[display]([real_plot, horiz_reallimit, imag_plot, horiz_imaglimit]); plots[pointplot](complex_pts, symbol = solidcircle, style = pointline, color = blue, axes = boxed, labels = ["Re", "Im"])

-ln(2)+((1/2)*I)*Pi

  

-ln(2)

  

(1/2)*Pi

  

 

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; add(exp(Pi*I*n)/n, n = 1 .. N) end proc; realpts := [seq([n, Re(S(n))], n = 1 .. 100)]; imagpts := [seq([n, Im(S(n))], n = 1 .. 100)]; complex_pts := [seq([Re(S(n)), Im(S(n))], n = 1 .. 100)]; S_infinite := sum(exp(Pi*I*n)/n, n = 1 .. infinity); limit_Re := Re(S_infinite); limit_Im := Im(S_infinite); limit_Re; limit_Im; real_plot := pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum Value"], title = "Real Part of Partial Sums", axes = boxed); imag_plot := pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Partial Sum Value"], title = "Imaginary Part of Partial Sums", axes = boxed); complex_plot := pointplot(complex_pts, symbol = solidcircle, style = pointline, color = blue, labels = ["Re", "Im"], title = "Partial Sums in Complex Plane", axes = boxed); plots[display]([real_plot, imag_plot]); plots[display](complex_plot)

-ln(2)

  

-ln(2)

  

0

  

-ln(2)

  

0

  

 

 
> 

restart; with(plots); interface(imaginaryunit = 'I'); S := proc (N) local n; add(exp(2*Pi*I*n), n = 0 .. N) end proc; realpts := [seq([n, Re(S(n))], n = 0 .. 100)]; imagpts := [seq([n, Im(S(n))], n = 0 .. 100)]; complex_pts := [seq([Re(S(n)), Im(S(n))], n = 0 .. 100)]; S_infinite := sum(exp(2*Pi*I*n), n = 1 .. infinity); limit_Re := Re(S_infinite); limit_Im := Im(S_infinite); real_plot := pointplot(realpts, symbol = solidcircle, style = pointline, color = blue, labels = ["n", "Partial Sum Value"], title = "Real Part of Partial Sums", axes = boxed); imag_plot := pointplot(imagpts, symbol = solidbox, style = pointline, color = red, labels = ["n", "Partial Sum Value"], title = "Imaginary Part of Partial Sums", axes = boxed); complex_plot := pointplot(complex_pts, symbol = solidcircle, style = pointline, color = blue, labels = ["Re", "Im"], title = "Partial Sums in Complex Plane", axes = boxed); plots[display]([real_plot, imag_plot]); plots[display](complex_plot)

infinity

  

infinity

  

0

  

 

 
 

``

Download infinite_series.mw

why such different result from integrate when pull...

Asked by: nm 11048
integration int indefinite-integration
21 hours ago
2  3

These two expressions are the same, just pulled minus sign out

But look what happens when integrating them. the anti derivative of one is much more complicated than the other and contains complex numbers and logs. And no matter what I tried, I could not convert the complicated one to look same as the simpler result. Also could not verify the complicated one by back differentiating.

> 

integrand_1:=x^2*(-arctan(x) + x)*exp(-arctan(x) + x)/(x^2 + 1);

x^2*(-arctan(x)+x)*exp(-arctan(x)+x)/(x^2+1)

> 

integrand_2:=evala(integrand_1);

-x^2*(arctan(x)-x)*exp(-arctan(x)+x)/(x^2+1)

> 

simplify(integrand_1 - integrand_2)

0

> 

anti_1:=int(integrand_1,x);

(-arctan(x)+x)*exp(-arctan(x)+x)-exp(-arctan(x)+x)

> 

anti_2:=int(integrand_2,x);

-(1-x+((1/2)*I)*ln(1-I*x)-((1/2)*I)*ln(1+x*I))*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

> 

simplify(diff(anti_1,x)-integrand_1);

0

> 

simplify(diff(anti_2,x)-integrand_2);

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

> 

simplify(anti_1 - anti_2)

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

> 

simplify(anti_2);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

> 

simplify(anti_2,ln);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

 

 

Download int_strange_result_april_27_2025.mw

I would have expected same anti derivative to show.  To check, I used another software, and that one gave same anti-derivative for both integrands.

The questions I have: Why Maple gives such different result for same integrand? And how could one convert the one with the logs and complex numbers to the first one?

Maple 2025

Plotting contour integral diagrams...

Asked by: Paras31 225
integration contour plotting
Yesterday at 3:32 PM
1  5

 I am writing notes on complex analysis, I need to use figures of contour paths to integrate on them, i want to create something like this

I tried to plot the contour for 
\oint_{|z|=2} \frac{1}{z^2+1}\,dz
I need to have connecting lines all around because the poles can not be isolated

> 

with(plots); circle1 := plot([2*cos(t), 2*sin(t), t = 0 .. 2*Pi], color = blue, thickness = 2); circle2 := plot([(1/2)*cos(t), 1+(1/2)*sin(t), t = 0 .. 2*Pi], color = "Green", thickness = 2); circle3 := plot([(1/2)*cos(t), -1+(1/2)*sin(t), t = 0 .. 2*Pi], color = "Red", thickness = 2); sing1 := plottools[disk]([0, 1], 0.2e-1, color = white); sing2 := plottools[disk]([0, -1], 0.2e-1, color = white); label1 := textplot([.1, 1.1, "z = i"], font = [Arial, Bold, 12]); label2 := textplot([.1, -1.1, "z = -i"], font = [Arial, Bold, 12])
> 

display(circle1, circle2, circle3, sing1, sing2, label1, label2, scaling = constrained, labels = ["Re", "Im"])

 
> 

``

 

 
> 

restart; f := proc (z) options operator, arrow; 1/(z^2+1) end proc; z := 2*exp(I*t); dz := diff(z, t); integrand := f(z)*dz; simplify(integrand); value(Int(integrand, t = 0 .. 2*Pi))

0

 (1)
> 

``


 

Download CIF.mw

about updating the Physics Package...

Asked by: Jean-Michel 35
update physics
Yesterday at 3:12 PM
0  2

Hello all,

After updating the Physics package I have this error :

Physics:-Version();
The "Physics Updates" version "1862" is installed in the

   directory C:\Users\jm\maple\toolbox\2025\Physics Updates but

   is not active. The active version of Physics is within the

   library C:/Users/jm/maple/toolbox/2025/Physics Updates/lib\Ph\

  ysics Updates.maple.

What am I supposed to do next?

Thanks a lot and kind regards to all,

Jean-Michel

bug report. Maple 2025 server crash on call to ode...

Asked by: nm 11048
ode differential-equations crash
Yesterday at 3:07 PM
0  0

FYI;

 

You might have to try the command more than one time to see the above crash. Here is the worksheet

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 13 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

> 

restart;
> 

ode:=x^2-2*x*y(x)+5*y(x)^2 = (x^2+2*x*y(x)+y(x)^2)*diff(y(x),x);

x^2-2*x*y(x)+5*y(x)^2 = (x^2+2*x*y(x)+y(x)^2)*(diff(y(x), x))

> 

sol:=y(x) = (-1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2+3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))-6+2*(exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-6*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))+9)^(1/2))/(1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6)))*x:
> 

odetest(sol,ode);
> 

 

Download crash_maple_2025_april_27_2025.mw

Hopefully a fix could be found for this.

new regression in Maple 2025 found. in solve ident...

Asked by: nm 11048
solve recursion
April 26 2025
1  4

Just found new regression in Maple 2025. This internal error can not be cought and was not there in Maple 2024.2. This is new from the ones reprted earlier in Collection-Of-Problems-In-Maple-2025 

Here it is , using latest SupportTools

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 13 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

> 

restart;
> 

#17593
eq:=2*A[6]*exp(-2*t)*cos(t)+2*A[3]*exp(-2*t)*sin(t)-2*A[4]*exp(-2*t)*cos(t)-4*A[7]*exp(-t)*sin(2*t)+4*A[8]*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*sin(t)+4*A[2]*exp(-t)+4*A[1]*t*exp(-t)+4*A[3]*exp(-2*t)*cos(t)+4*A[4]*exp(-2*t)*sin(t)+2*A[9]*exp(-t)*cos(2*t)-8*A[9]*t*exp(-t)*sin(2*t)+2*A[10]*exp(-t)*sin(2*t)+8*A[10]*t*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*cos(t)+2*A[5]*t*exp(-2*t)*sin(t)-2*A[6]*exp(-2*t)*sin(t)-2*A[6]*t*exp(-2*t)*cos(t)+4*A[5]*t*exp(-2*t)*cos(t)+4*A[6]*t*exp(-2*t)*sin(t) = 3*t*exp(-t)*cos(2*t)-2*t*exp(-2*t)*cos(t):


trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8], A[9], A[10]]:
> 

try
     timelimit(30,[solve(identity(eq,t),trial_solution_constants) ]);
catch:
     print("OK cought error");
end try;

Error, (in type/trig) too many levels of recursion

 

 

Download regression_maple_2025_april_26_2025.mw

Here is the same code in Maple 2024.2 but using windows. No internal error and timeout was cought as expected.

> 

restart;
interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862. The version installed in this computer is 1849 created 2025, March 12, 12:37 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

> 

#17593
eq:=2*A[6]*exp(-2*t)*cos(t)+2*A[3]*exp(-2*t)*sin(t)-2*A[4]*exp(-2*t)*cos(t)-4*A[7]*exp(-t)*sin(2*t)+4*A[8]*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*sin(t)+4*A[2]*exp(-t)+4*A[1]*t*exp(-t)+4*A[3]*exp(-2*t)*cos(t)+4*A[4]*exp(-2*t)*sin(t)+2*A[9]*exp(-t)*cos(2*t)-8*A[9]*t*exp(-t)*sin(2*t)+2*A[10]*exp(-t)*sin(2*t)+8*A[10]*t*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*cos(t)+2*A[5]*t*exp(-2*t)*sin(t)-2*A[6]*exp(-2*t)*sin(t)-2*A[6]*t*exp(-2*t)*cos(t)+4*A[5]*t*exp(-2*t)*cos(t)+4*A[6]*t*exp(-2*t)*sin(t) = 3*t*exp(-t)*cos(2*t)-2*t*exp(-2*t)*cos(t):


trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8], A[9], A[10]]:
 
> 

try
     timelimit(30,[solve(identity(eq,t),trial_solution_constants) ]);
catch:
     print("OK cought error");
end try;


Download no_problem_in_maple_2024_april_26_2025.mw

strange warning message from mint which do not sho...

Asked by: nm 11048
mint module
April 25 2025
1  5

everytime I run mint I get hundreds of messages coming from child modules, saying

           These names were used as global names but were not declared:  A

Where A above is the name of the top level module.

This only shows from commnd line mint, and not from maplemint used in the GUI.

The set I have is 

A:=module()
    export module foo_type()
       option object;
       ....
    end module;

     export B := module()  #child module
       .....
     end module;
end module;

  In the child module B above, whever I do 

                 o:=Object(A:-foo_type);

mint gives the above warning.

It is clear the name A should not be declared, as the module B is child to it so it can see it.

The workaround is to add  global A inside each child module to remove this warning. 

But why is this needed?

Here is a worksheet showing maplemint does not show this warning, and below example using command line mint on same exact code, which does

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

A:=module()

    export module foo_type()
       option object;
       export name::string:="";
    end module;

    export B := module()
       export step := proc()::A:-foo_type;                 
       local o::A:-foo_type;   
          o:=Object(A:-foo_type);
          o:-name:="x";
          return o;
       end proc;

    end module;

end module;

_m128759219362528

> 

maplemint(A)

Nested Module foo_type() on lines 1 to 2
  These exported variables were never used:  name::string

 

 

Download mint_isse_april_25_2025.mw

Here is A.mpl 

A:=module()

    export module foo_type()
       option object;
       export name::string:="";
    end module;

    export B := module()    
       #global A;     why is this needed for mint??
       export step := proc()::A:-foo_type;                 
       local o::A:-foo_type;   
          o:=Object(A:-foo_type);
          o:-name:="x";
          return o;
       end proc;

    end module;
end module;

And now the command

>/home/me/maple2025/bin.X86_64_LINUX/mint A.mpl
    |\^/|      Maple 2025 Diagnostic Program
._|\|   |/|_.  Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2025
 \  MINT   /   All rights reserved. Maple is a trademark of
 <____ ____>   Waterloo Maple Inc.
      |        
Nested Procedure step() on lines 10 to 15
  These names were used as global names but were not declared:  A
Module A() on lines 1 to 18
  These exported variables were never used:  foo_type
>

You see the difference. mint complains that A is not declared.

Is this a bug in mint?

Some questions about MapleCloud ...

Asked by: C_R 3222
browser gui
April 24 2025
0  2

MapleCloud opend from Maple2025 and 2024.

Has this extended scrollbar always been like this?
Maybe it is a browser thing.
Which browser is Maple using?
Are there any settings I could adjust?

Announcing the Maple Customer Support Updates...

by: aroche 650 Maple 2025
maplecloud update physics
April 22 2025
12  12

Maplesoft now has a new approach to providing customer support for Maple users! The Maple Customer Support Updates allows Maplesoft to provide important updates to our customers as fast as possible. These updates contain a series of improvements and fixes to any area of the Maple library, enabling a rapid response for customer reports and requests. When a Maple user reports a bug or weakness, or requests some missing functionality that can be addressed with an update to the Maple library, such an update can now be provided immediately after the fix or improvement is developed. Furthermore, the update will not just be available to that customer who reported it, but also to any other Maple users who wishes to use them. Of course, not all reports will be able to be addressed quickly, and for those that are, it will be up to the developer's discretion whether to make the fix or improvement available via these new Maple Customer Support Updates. Please note that these Updates may contain experimental elements that could change in subsequent official releases.

The updates are available as a workbook containing a Maple library file that can be downloaded and installed from the Maple Cloud. To install the Maple Customer Support Updates from the Maple Cloud,

  • Click the MapleCloud icon in the upper-right corner of the Maple GUI window and select Packages.
  • Find the Maple Customer Support Updates package and click the Install button, the last one under Actions.
  • To check for new versions of Maple Customer Support Updates, click the MapleCloud icon and select Updates. If the cloud icon in the Actions column of Maple Customer Support Updates has the word Update beside it, then you can click on it to download a new update.

To make the process of installing and maintaining the Maple Customer Support Updates as smooth as possible, we've also introduced a new Maple library package, SupportTools, with 3 commands, Update, Version, and RemoveUpdates.

Load the SupportTools package:
with(SupportTools)

[RemoveUpdates, Update, Version]

 (1)

Check which version is currently installed:
Version()

`The Customer Support Updates version in the MapleCloud is 10. The version installed in this computer is 9 created April 22, 2025, 15:14 hours Eastern Time, found in the directory C:\Users\Austin\Maple\toolbox\2025\Maple Customer Support Updates\lib\Maple`

 (2)


Update to the latest version (you could also call Update(latest)):

Update()

Warning, You have just upgraded from version 9 to version 10 of the Customer Support Updates. In order to have this version active, please close Maple entirely, then open Maple and enter SupportTools:-Version() to confirm the active version.

  


Check the version again:

Version()

`The Customer Support Updates version in the MapleCloud is 10 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

 (3)


Remove all updates for this release of Maple (except for those installing the SupportTools package itself):

RemoveUpdates()RemoveUpdates()

Warning, You have just reverted to version 4 of the Customer Support Updates. This version contains no actual updates other than the SupportTools package itself. In order to verify this, please close Maple entirely, then open Maple and enter SupportTools:-Version() to verify that the version number is 4.

  


Note: You can also specify which version to install by supplying the version number as the argument to the Update command:

Update(10)

Warning, You have just upgraded from version 4 to version 10 of the Customer Support Updates. In order to have this version active, please close Maple entirely, then open Maple and enter SupportTools:-Version() to confirm the active version.
 

Download SupportTools.mw

In Maple 2025.0, the SupportTools package is not installed by default. For the first installation, you can also run the command
PackageTools:-Install(4797495082876928); instead of installing it from the Maple Cloud.

The Maple Customer Support Updates were inspired by and modelled after the existing Physics Updates which many Maple users may be famiilar with already. Going forward, Physics Updates will only contain changes to the Physics package itself. All other library updates will be available via the Maple Customer Support Updates. For compatibility with the pre-existing Physics:-Version command, calling SupportTools:-Version(n) is equivalent to calling SupportTools:-Update(n), and similarly SupportTools:-Version(latest) and SupportTools:-Update(latest) are both equivalent to the single call SupportTools:-Update().

Plotting a simply connected domain and multiple p...

Asked by: Paras31 225
plotting incomplete-question connected
April 22 2025
1  10

I am trying to create a diagram in Maple using its plotting tools and simulate a simply connected domain and multiple paths between two points.

My first try is the following

> 

with(plots); with(plottools)

 

 
> 

curveDomainPts := [[-1, 0], [-.7, 1.2], [0, 1.5], [.7, 1.2], [1.2, 0], [.7, -1.2], [0, -1.4], [-.7, -1.2], [-1, 0]]; domain := polygon(curveDomainPts, color = "LightBlue", transparency = .4); z0 := [-.8, .6]; z := [.9, -.4]; curve1_pts := [[-.8, .6], [-.3, 1.0], [.4, .5], [.9, -.4]]; curve2_pts := [[-.8, .6], [-.7, 0.], [.2, -.6], [.9, -.4]]; curve1 := pointplot(curve1_pts, color = red, linestyle = dot, thickness = 2, connect = true); curve2 := pointplot(curve2_pts, color = green, linestyle = dot, thickness = 2, connect = true); pt1 := pointplot([z0], symbol = solidcircle, symbolsize = 15, color = black); pt2 := pointplot([z], symbol = solidcircle, symbolsize = 15, color = black); label1 := textplot([z0[1], z0[2]-.1, z__0], font = [Helvetica, Bold, 14]); label2 := textplot([z[1], z[2]-.1, "z"], font = [Helvetica, Bold, 14]); display(domain, curve1, curve2, pt1, pt2, label1, label2, scaling = constrained, axes = none, title = "Curved Domain with Arbitrary Paths")

 
 

NULL

I would like to ask if I could create something like that in Maple or should I use another software to draw it?

Download curved_domain.mw

collection of problems in Maple 2025. Looking for ...

Asked by: nm 11048
simplify int odetest
April 20 2025
4  3

To save space, I've decided to show problems found so far in Maple 2025 in one worksheet.

Hoping someone will figure the cause. The big problem is that these internal errors can not be cought using try/catch. Which means there is no user workaround. If they can be cought, then it is not a big problem.

Some from odetest, some from int and some from simplify and some from symgen.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1861 and is the same as the version installed in this computer, created 2025, April 10, 15:58 hours Pacific Time.`

> 

restart;
> 

#18573
e:=(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)-1/2*(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)^2/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2-16)^(1/2))*x:
> 

try
    timelimit(60,simplify(e));
catch:
    print("OK, cought error");
end try;
> 

 

Error, (in anonymous procedure called from depends) too many levels of recursion

> 

restart;
> 

#12178
ode:=diff(y(x),x) = lambda*arctan(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arctan(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

> 

restart;
> 

#12181
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arctan(x(y))^m*a*y^2+x(y)^n*arctan(x(y))^m*b*y+arctan(x(y))^m*c-n*y):
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

> 

restart;
> 

#12187
ode:=diff(y(x),x)=lambda*arccot(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arccot(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

> 

restart;
> 

#12190
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arccot(x(y))^m*a*y^2+x(y)^n*arccot(x(y))^m*b*y+arccot(x(y))^m*c-n*y):
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

> 

restart;
> 

#10708
e:=2/(ln(x)-exp(1/x))*x*diff(diff(u(x),x),x)-(-2/(ln(x)-exp(1/x))^2*x*(1/x+1/x^2*exp(1/x))+2/(ln(x)-exp(1/x))+8*x^3/(ln(x)-exp(1/x))^2)*diff(u(x),x)-4/(ln(x)-exp(1/x))^3*x^2*(-2*x^3+ln(x)-exp(1/x)-2*x)*u(x):
e:=evala(e):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

Error, (in anonymous procedure called from property/ConvertRelation) too many levels of recursion

> 

restart;
> 

#6764
e:=1/2/x^(7/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x)*(1+x):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/common_factors/do) too many levels of recursion

> 

restart;
> 

#19337
> 

sol:=-y+Intat((_a*((_a^2+1)/_a^2)^(1/2)+_a^2+1)*exp(-1/2*(arctanh(1/(_a^2+1)^(1/2))*((_a^2+1)/_a^2)^(1/2)*_a^3+2*_C3*(_a^2+1)^(1/2)*_a^2+(_a^2+1)^(1/2)*((_a^2+1)/_a^2)^(1/2)*_a+(_a^2+1)^(1/2))/(_a^2+1)^(1/2)/_a^2)/((_a^2+1)/_a^2)^(1/2)/_a^5,_a = RootOf(x(y)-exp(-1/2*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*_C3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/(_Z^2+1)^(1/2)/_Z^2)))+_C4 = 0:
ode:=-1/2/(diff(x(y),y)^2+1)^(1/2)*(diff(x(y),y)*(arctanh(1/(diff(x(y),y)^2+1)^(1/2))*diff(x(y),y)^2+(diff(x(y),y)^2+1)^(1/2))*((diff(x(y),y)^2+1)/diff(x(y),y)^2)^(1/2)+(diff(x(y),y)^2+1)^(1/2))/diff(x(y),y)^2 = ln(x(y))+_C3:
try
    timelimit(60,odetest(sol,ode));
catch:
    print("OK, cought error");
end try;
 

Error, (in unknown) too many levels of recursion

 

 

Download collection_of_problems_maple_2025.mw

Below is worksheet showing output in Maple 2024.2. It shows NO internal error is generated in any one. Either a result is returned, or it timedout as expected.

This shows all the above cases are regressions in Maple 2025.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1861. The version installed in this computer is 1849 created 2025, March 12, 12:37 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

> 

restart;
> 

#18573
e:=(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)-1/2*(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)^2/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2-16)^(1/2))*x:
> 

try
    timelimit(60,simplify(e));
catch:
    print("OK, cought error");
end try;
> 

 

(1/4)*(RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2-((RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2-16)^2/RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2)^(1/2)*RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))+16)*x/RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))

> 

restart;
> 

#12178
ode:=diff(y(x),x) = lambda*arctan(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arctan(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

> 

restart;
> 

#12181
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arctan(x(y))^m*a*y^2+x(y)^n*arctan(x(y))^m*b*y+arctan(x(y))^m*c-n*y):
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

> 

restart;
> 

#12187
ode:=diff(y(x),x)=lambda*arccot(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arccot(x)^n:
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

> 

restart;
> 

#12190
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arccot(x(y))^m*a*y^2+x(y)^n*arccot(x(y))^m*b*y+arccot(x(y))^m*c-n*y):
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

> 

restart;
> 

#10708
e:=2/(ln(x)-exp(1/x))*x*diff(diff(u(x),x),x)-(-2/(ln(x)-exp(1/x))^2*x*(1/x+1/x^2*exp(1/x))+2/(ln(x)-exp(1/x))+8*x^3/(ln(x)-exp(1/x))^2)*diff(u(x),x)-4/(ln(x)-exp(1/x))^3*x^2*(-2*x^3+ln(x)-exp(1/x)-2*x)*u(x):
e:=evala(e):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

> 

restart;
> 

#6764
e:=1/2/x^(7/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x)*(1+x):
try
    r:=timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

> 

restart;
> 

#19337
> 

sol:=-y+Intat((_a*((_a^2+1)/_a^2)^(1/2)+_a^2+1)*exp(-1/2*(arctanh(1/(_a^2+1)^(1/2))*((_a^2+1)/_a^2)^(1/2)*_a^3+2*_C3*(_a^2+1)^(1/2)*_a^2+(_a^2+1)^(1/2)*((_a^2+1)/_a^2)^(1/2)*_a+(_a^2+1)^(1/2))/(_a^2+1)^(1/2)/_a^2)/((_a^2+1)/_a^2)^(1/2)/_a^5,_a = RootOf(x(y)-exp(-1/2*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*_C3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/(_Z^2+1)^(1/2)/_Z^2)))+_C4 = 0:
ode:=-1/2/(diff(x(y),y)^2+1)^(1/2)*(diff(x(y),y)*(arctanh(1/(diff(x(y),y)^2+1)^(1/2))*diff(x(y),y)^2+(diff(x(y),y)^2+1)^(1/2))*((diff(x(y),y)^2+1)/diff(x(y),y)^2)^(1/2)+(diff(x(y),y)^2+1)^(1/2))/diff(x(y),y)^2 = ln(x(y))+_C3:
try
    r:=timelimit(60,odetest(sol,ode));
catch:
    print("OK, cought error");
end try;
 

-(1/2)*RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))*arctanh(1/(RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2+1)^(1/2))*(1+1/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2)^(1/2)/(RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2+1)^(1/2)-ln(x(y))-c__3-(1/2)*(1+1/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2)^(1/2)/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))-(1/2)/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2

Download collection_of_problems_maple_2024_version.mw

why Maple 2025 hangs on this separable ode?...

Asked by: nm 11048
ode dsolve differential-equations
April 20 2025
2  1

This looks like regression in dsolve.

In Maple 2024.2, dsolve solves this with no problem and very quickly. 

In Maple 2025 it just hangs.

Any one could find why this is the case? infolevel does not show why. Below is Maple 2024.2 worksheet and Maple 2025 worksheet.  This is Maple 2024.2 NO HANG

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

ode:=diff(y(x),x)+((y(x)+1)*(y(x)-1)*(y(x)-2))/(x+1)=0;
IC:=y(1)=0;

diff(y(x), x)+(y(x)+1)*(y(x)-1)*(y(x)-2)/(x+1) = 0

y(1) = 0

> 

DEtools:-odeadvisor(ode);

[_separable]

> 

infolevel[dsolve]:=5;
dsolve([ode,IC])

5

 -> Computing symmetries using: way = 3

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

<- separable successful

y(x) = RootOf(-2048+(x^6+6*x^5+15*x^4+20*x^3+15*x^2+6*x+257)*_Z^18+(-6*x^6-36*x^5-90*x^4-120*x^3-90*x^2-36*x-1542)*_Z^12+(9*x^6+54*x^5+135*x^4+180*x^3+135*x^2+54*x+3081)*_Z^6)^6-1

 

 

Download dsolve_2024_no_hang_april_20_2025.mw

This is Maple 2025. HANGed. Had to terminate it after 15 minutes. It seems to hang on resolving initial conditions. 

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

ode:=diff(y(x),x)+((y(x)+1)*(y(x)-1)*(y(x)-2))/(x+1)=0;
IC:=y(1)=0;

diff(y(x), x)+(y(x)+1)*(y(x)-1)*(y(x)-2)/(x+1) = 0

y(1) = 0

> 

DEtools:-odeadvisor(ode);

[_separable]

> 

infolevel[dsolve]:=5;
dsolve([ode,IC])

5

 -> Computing symmetries using: way = 3

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

<- separable successful

 

 

Download dsolve_2025_on_linux_hangs_april_20_2025.mw

unable to evaluate the function...

Asked by: Mapleliquid 20
syntax plotting
April 20 2025
1  3

Hello everyone,

How I get a plot for this function ? What means numeric values ? 

Thanks !

 
> 

restart
> 

T[S] := 290
> 

eta := 17; lambda := 24
> 

h := .2; `&ohm;` := 2*Pi*10; R := 2
> 

T(x[2]) := eta*`&ohm;`^2*R^2*[x[2]/h-(1/2)*(x[2]/h)^2]/lambda+T[S]

eta*`&ohm;`^2*R^2*[x[2]/h-(1/2)*(x[2]/h)^2]/lambda+T[S]

 (1)
> 

plot(T(x[2]), x[2] = .1 .. .2)

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  

 


Download TSL_bung_9.mwTSL_bung_9.mw

Bug of "MatrixExponential" Function in t...

Asked by: MathGuru 5
linearalgebra matlab matrixexponential
April 19 2025
1  7

Dear Maple Support Team and Community,

    I would like to report what seems to be a bug in Maple's MatrixExponential function in the LinearAlgebra package.

    Consider the following 8×8 skew-Hermitian matrix B:
 

B := Matrix(8, 8, [[0, I, 0, -I, 0, I, 0, -I], 
                   [-I, 0, I, 0, -I, 0, I, 0], 
                   [0, -I, 0, I, 0, -I, 0, I], 
                   [I, 0, -I, 0, I, 0, -I, 0], 
                   [0, I, 0, -I, 0, I, 0, -I], 
                   [-I, 0, I, 0, -I, 0, I, 0], 
                   [0, -I, 0, I, 0, -I, 0, I], 
                   [I, 0, -I, 0, I, 0, -I, 0]]);

    Now compute the matrix exponential exp(I*t*B) using MatrixExponential

H := LinearAlgebra:-MatrixExponential(I * t * B);

However, this result is inconsistent with the matrix exponential computed using MATLAB and SageMath, both of which give the same result, different from Maple's.

I would appreciate it if someone from the development team could look into this.

Error, (in PatternMatching:-AlgStruct:-Match) stri...

Asked by: nm 11048
patmatch
April 19 2025
0  1

Encountered this error using patmatch with condition. I have changed my code since then  to avoid such cases.

But do you think this is valid error? It only happens when adding conditional. 

> 

interface(version);
> 

restart;
> 

RHS:=1/2/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a+1/2/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b-1/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y-1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*b+1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*y+1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b*y-1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y^2;

(1/2)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a/lambda(y)+(1/2)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b/lambda(y)-f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y/lambda(y)-(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*b/lambda(y)^2+(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*y/lambda(y)^2+(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b*y/lambda(y)^2-(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y^2/lambda(y)^2

> 

patmatch(RHS,F::anything*lambda(y)^(n::anything)+H::anything,'la')

true

> 

patmatch(RHS,conditional(F::anything*lambda(y)^(n::anything)+H::anything, not (_has(H,lambda(y)) or _has(n,y))),'la')

Error, (in PatternMatching:-AlgStruct:-Match) string or symbol expected for substring

 

 

Download error_patmatch_april_18_2025.mw

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