MaplePrimes Questions

Objective: Solve a system of two equations.

Obstacle: Generating these two equations depends on millions of previous combinations as well as derivatives.

In other words, we've reached the maximum limit that Maple on my computer can handle.

What would be better, to leave the equations aside or to upgrade my computer?

restart

with(plots)

with(linalg)

H01 := -gamma11*S11-gamma12*S12-gamma13*S13-gamma14*S14-gamma15*S15-gamma16*S16-gamma17*S17-gamma18*S18-gamma19*S19-gamma110*S110-gamma111*S111-gamma112*S112-eta1*(S11^2+S110^2+S111^2+S112^2+S12^2+S13^2+S14^2+S15^2+S16^2+S17^2+S18^2+S19^2)-J1*(S11*S12+S12*S13+S13*S14+S14*S18+S18*S112+S112*S111+S111*S110+S110*S19+S19*S15+S15*S11+S16*(S12+S110+S15+S17)+S17*(S113+S111+S18))

H02 := -gamma21*S21-gamma22*S22-gamma23*S23-gamma24*S24-gamma25*S25-gamma26*S26-gamma27*S27-gamma28*S28-gamma29*S29-gamma210*S210-gamma211*S211-gamma212*S212-eta2*(S21^2+S210^2+S211^2+S212^2+S22^2+S23^2+S24^2+S25^2+S26^2+S27^2+S28^2+S29^2)-J1*(S21*S22+S22*S23+S23*S24+S24*S28+S28*S212+S212*S211+S211*S210+S210*S29+S29*S25+S25*S21+S26*(S22+S210+S25+S27)+S27*(S213+S211+S28))

Z01 := exp(-beta*H01)

Z01 := add(add(add(add(add(add(add(add(add(add(add(add(Z01, S11 = [-2, -1, 0, 1, 2]), S12 = [-2, -1, 0, 1, 2]), S13 = [-2, -1, 0, 1, 2]), S14 = [-2, -1, 0, 1, 2]), S15 = [-2, -1, 0, 1, 2]), S16 = [-2, -1, 0, 1, 2]), S17 = [-2, -1, 0, 1, 2]), S18 = [-2, -1, 0, 1, 2]), S19 = [-2, -1, 0, 1, 2]), S110 = [-2, -1, 0, 1, 2]), S111 = [-2, -1, 0, 1, 2]), S112 = [-2, -1, 0, 1, 2])

NULL

Z02 := exp(-beta*H02)

Z02 := add(add(add(add(add(add(add(add(add(add(add(add(Z02, S21 = [-2, -1, 0, 1, 2]), S22 = [-2, -1, 0, 1, 2]), S23 = [-2, -1, 0, 1, 2]), S24 = [-2, -1, 0, 1, 2]), S25 = [-2, -1, 0, 1, 2]), S26 = [-2, -1, 0, 1, 2]), S27 = [-2, -1, 0, 1, 2]), S28 = [-2, -1, 0, 1, 2]), S29 = [-2, -1, 0, 1, 2]), S210 = [-2, -1, 0, 1, 2]), S211 = [-2, -1, 0, 1, 2]), S212 = [-2, -1, 0, 1, 2])

NULL

G0 := -(1/24)*N*ln(Z01*Z02)/beta

NULL

m01 := -24*(diff(G0, gamma11))/N

m02 := -24*(diff(G0, gamma21))/N

NULL

beta := 11.605/T; gamma11 := 2*J1*m1+2*J2*m2; eta1 := Delta; gamma21 := 2*J1*m2+2*J2*m1; eta2 := Delta; gamma12 := J1*m1+2*J2*m2; gamma22 := J1*m2+2*J2*m1; gamma13 := J1*m1+2*J2*m2; gamma23 := J1*m2+2*J2*m1; gamma14 := 2*J1*m1+2*J2*m2; gamma24 := 2*J1*m2+2*J2*m1; gamma15 := J1*m1+2*J2*m2; gamma25 := J1*m2+2*J2*m1; gamma16 := 2*J2*m2; gamma26 := 2*J2*m1; gamma17 := 2*J2*m2; gamma27 := 2*J2*m1; gamma18 := J1*m1+2*J2*m2; gamma28 := J1*m2+2*J2*m1; gamma19 := 2*J1*m1+2*J2*m2; gamma29 := 2*J1*m2+2*J2*m1; gamma110 := J1*m1+2*J2*m2; gamma210 := J1*m2+2*J2*m1; gamma111 := J1*m1+2*J2*m2; gamma211 := J1*m2+2*J2*m1; gamma112 := 2*J1*m1+2*J2*m2; gamma212 := 2*J1*m2+2*J2*m1

NULL

eq1 := m1 = m01

eq2 := m2 = m02

fsolve(subs(J1 = 2*.83, N = 1, J2 = -2*.58, Delta = 0, m1 = 0.1e-1, {eq1, eq2}), {T, m2}, T = 0 .. 220, m2 = -.1 .. .1)

fsolve(subs(J1 = 2*.83, N = 1, J2 = -2*.58, T = 1, Delta = 0, {eq1, eq2}), {m1, m2}, m1 = -5 .. 5, m2 = -5 .. 5)

{m1 = 2.000000000, m2 = -2.000000000}

(1)

NULL

Download Maple_forum_test.mw

After system restart on Windows 11:

Maple 2026 was installed as usual with administrator rights and with import of preferences from Maple 2025. Other Maple versions are working on the same computer.

Does this never-seen-before output gives a hint what is wrong with my installation. Any suggestions what to do next?

That's the installed version:

On the same Windows 11 installation, Maple 2025 displays equation labels but Maple 2026 not. Maple 2025 settings were imported for the 2026 installation. (Crtl-l + number does return "invalid label". I assume that not labels have been generated)

Has anbody observed the same? Any suggestions what I could check/do?

Other observation: The output font does not look the same

 

Is there an easy way to read jld files in Maple?  Apparently JLD (Julia Data) and JLD2 files are binary formats primarily designed for saving and loading Julia variables, preserving types.

That's how it looks like in Maple 2026.0 for the Examples on the Help-page for topic solve, on Windows 11

For a fraction of a second I see output rendered in blue and Math-2D. Then it turns to the above.

Is this a regression or a new feature? How to get the output back to Math-2D and blue?

Glad that 2026 has been released now, and I will certainly use it as the default version in the future.

While there are a lot of new features, one thing that keeps annoying me is the inferior font quality, compared to other software.

Here's a screenshot of 4 different programs, all with font Arial 11pt and 100% zoom factor. Font AntiAliasing is set to enabled in Maple.

Judge it for yourself, but in my opinion it gives a clear picture that Maple is much worse to read than any of the other software packages (Word, LibreOffice, pdfXChange).

In the Maple 2025 release, the "old/former" user interface was provided under a menu entry called "Maple 2025 for Screen Readers". I used this version because of shortcommings of the new ribbon interface. Some of the shortcommings have been fixed in the 2026 release but it is still slow to use (I am missing functions in the quick access toolbar that I frequently use and no customization of the bar seems possible).

I could not find a similar menu entry in the 2026 release under Windows 11. Is the old unser interface still available?

I am solving a hybrid nanofluid flow problem in a bifurcated artery using Maple. The governing equations for velocity and temperature are solved using dsolve(..., numeric, method=bvp[midrich]).

My Maple code successfully produces for both the artery  parentartery_and_daughter_artery_error.mw.

The velocity profiles are obtained correctly using odeplot.

However, I want to compute additional physical quantities and generate plots similar to the velocity profiles.

Specifically I want to plot:

  1. Flow rate Q versus axial distance z

  2. Impedance (flow resistance) λ versus z

  3. Wall shear stress τ versus z

for different values of Hartmann number Ha.

The formulas I am using are

Flow rate:

Q=2π(R∫01ηw(η) dη+R2∫01w(η) dη)Q = 2\pi \left( R \int_0^1 \eta w(\eta)\,d\eta + R_2 \int_0^1 w(\eta)\,d\eta \right)Q=2π(R∫01​ηw(η)dη+R2​∫01​w(η)dη)

Wall shear stress:

τ=μ∣dwdr∣\tau = \mu \left|\frac{dw}{dr}\right|τ=μ​drdw​​

Impedance:

λ=∣dp/dz∣Q\lambda = \frac{|dp/dz|}{Q}λ=Q∣dp/dz∣​
Please help me to solve this question.

I am studying a nonlinear wave equation and trying to reproduce the energy balance method shown in a research paper. First, the original partial differential equation is reduced to an ordinary differential equation using a traveling wave transformation. After obtaining the reduced equation, the paper rewrites it in a form suitable for the energy balance method and derives the corresponding variational principle and Hamiltonian invariant. Then a trial periodic solution in cosine form is assumed. Using the Hamiltonian invariant and some initial conditions, the parameters of the trial function are determined and a periodic solution is obtained.

I would like to know how to implement this procedure in Maple. Specifically,  compute the Hamiltonian invariant from the equation, substitute the cosine trial function, and determine the unknown parameter in the trial solution using the energy balance method. I will attach images from the paper that show the derivation steps I am trying to reproduce. Any guidance on how to perform these symbolic steps in Maple would be very helpful.

f-s.mw

Hi,

For a pedagogical purpose, I am trying to illustrate the orthogonal projection H of a point A on to a plane P1

I constructed the line l1​ passing through A and perpendicular to the plane P1
However, in the graphical visualization, the line does not appear to be perpendicular to the plane. Visually, it gives the impression that the line is not orthogonal to the plane.

Do you have any idea what might cause this effect?

Thank you for your help.

Q_Espace.mw

While teaching a linear programming course I put together a worksheet to illustrate finding the largest disk inside a convex polygon as in section 2.6 of Understanding and Using Linear Programming by Jiří Matoušek and Bernd Gärtner.  I used both the Optimization[LPSolve] and the simplex[maximize] routines with the same objective and the same constraints.  Optimization[LPSolve] gives the correct answer but simplex[maximize] does not.  Is this a bug or did I do something wrong?

Below is the worksheet.

This is a worksheet I put together to illustrate finding the largest disk inside a convex polygon

as in section 2.6 of Understanding and Using Linear Programming by Jiří Matoušek and
Bernd Gärtner.

 

Load some packages

restart;
with(plots):
with(LinearAlgebra):
with(simplex);
with(Optimization);
with(plottools):

[basis, convexhull, cterm, define_zero, display, dual, feasible, maximize, minimize, pivot, pivoteqn, pivotvar, ratio, setup, standardize]

 

[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve]

(1)

This is the definition of the polygon with a plot.

constr := [x>=0,y>=0,y-x<=1,x+y<=5,2*x-y<=6];
Vector(%);
P1 := inequal(constr,x=-1..5,y=-1..5,optionsfeasible=[color=yellow]);

These are the outward normals for the polygon constraints and the "b" values.

C := [<-1,0>,<0,-1>,<-1,1>,<1,1>,<2,-1>];
b:= [0,0,1,5,6];

This is a check that a point is inside the polygon with plots of the circle that show the distance

from the pont to each defining line.

Pt := <1,.5>;
Pta := convert(Pt,list);
map(is,subs({x=2,y=1},constr));

DistV := [seq((b[i]-DotProduct(C[i],Pt))/Norm(C[i],2),i=1..5)]

P2 := NULL:
for i from 1 to 5 do
   P2 := P2,plottools:-circle(Pta,DistV[i],color=cat("Bright ",i),thickness=2);
   end do:
display([P2,P1],scaling=constrained);
display(map(display,[seq([P1,[P2][i]],i=1..5)]),insequence=true,scaling=constrained);

Now the distance from a point in the polygon to the boundary of the polygon is defined

and plotted over the polygon.

f := proc(x,y)
     local i;
      uses LinearAlgebra;
     min([seq(((b[i]-DotProduct(C[i],<x,y>))/Norm(C[i],2)),i=1..5)]);
     end proc;

plot3d(f(x,y),x=-1..5,y=-1..5,view=[0..4,0..4,0..2],grid=[151,151]);

 

This is the definition of the LP to solve the largest disk problem.

 

We maximize z, a variable less than or equal to the distance from the point x, y to each of the

constraining lines where x, yis in the polygon.

 

C := [<-1,0>,<0,-1>,<-1,1>,<1,1>,<2,-1>];
b:= [0,0,1,5,6];

Here are the constraints.

obj := z;
constr1 := [x>=0,y>=0,y-x<=1,x+y<=5,2*x-y<=6];
constr2 := [seq(z<=(b[i]-DotProduct(C[i],<x,y>))/Norm(C[i],2),i=1..5)];

This is the solution using LPSolve.

soln1 := LPSolve(z,[op(constr1),op(constr2)],maximize);

This is the same problem solved with simplex[maximize].

soln2 := simplex:-maximize(z,[op(constr1),op(constr2)]);
evalf(%);

The answer from the simplex package is wrong as the following plots demonstrate.

 

What, if anything, did I do wrong?

constr := [x>=0,y>=0,y-x<=1,x+y<=5,2*x-y<=6]:
P1 := inequal(constr,x=-1..5,y=-1..5,optionsfeasible=[color=yellow]):
Pt1 := subs(soln1[2],[x,y]);
C1 := disk(Pt1,soln1[1],color=red):
display(C1,P1);
Pt2 := subs(soln2,[x,y]);
r2 := subs(soln2,z);
C2 := disk(Pt2,r2,color=red):
display(C2,P1);

 

 

Download inscribe_circle.mw

I have generated the regional plot, but the boundaries between the regions are not clearly marked. How can I highlight the boundaries using a black line or a black dashed line, similar to the example image? What syntax should I use? I have attached my generated image file.

Regional_new.mw


how we solve x^(4)-12*x-12=0, 

mapple sent after solving: RootOf(_Z^4 - 12*_Z - 12, index = 1), RootOf(_Z^4 - 12*_Z - 12, index = 2), RootOf(_Z^4 - 12*_Z - 12, index = 3), RootOf(_Z^4 - 12*_Z - 12, index = 4)

sol:=ln( (y-1)^(1/3)* (y^2+y+1)^(1/3) ) - ln(y) = 2/5* ln(t^2+1)+_C1;
solve( sol,y);

in real domain is fine also. But all my attempts failed. I waited 3-4 minutes each time and stopped it.

Any one can find a trick? Below worksheet showing my attempts and also solution by Mathematica which took 0.3 seconds

Make sure to save all your work first. This problem is known to crash Maple !

restart;

sol:=ln( (y-1)^(1/3)* (y^2+y+1)^(1/3) ) - ln(y) = 2/5* ln(t^2+1)+_C1;
solve( sol,y) assuming real;

ln((y-1)^(1/3)*(y^2+y+1)^(1/3))-ln(y) = (2/5)*ln(t^2+1)+_C1

Warning,  computation interrupted

restart;

sol:=ln( (y-1)^(1/3)* (y^2+y+1)^(1/3) ) - ln(y) = 2/5* ln(t^2+1)+_C1;
RealDomain:-solve( sol,y);

ln((y-1)^(1/3)*(y^2+y+1)^(1/3))-ln(y) = (2/5)*ln(t^2+1)+_C1

Warning,  computation interrupted

restart;
sol:=ln( (y-1)^(1/3)* (y^2+y+1)^(1/3) ) - ln(y) = 2/5* ln(t^2+1)+_C1;
solve( sol,y,real);

ln((y-1)^(1/3)*(y^2+y+1)^(1/3))-ln(y) = (2/5)*ln(t^2+1)+_C1

Warning,  computation interrupted

 


 

Download solve_problem_march_7_2026.mw

 

I have attached a MapleFlow file that shows a result I don't quite understand.  For some reason the FinalValue result that I get using the DynamicSystems:-StepProperties is different than the steady state value from a DynamicSystems:-ResponsePlot to a unit step using a DifferentialEquation object.

You will notice that I played around a bit, including transforming the DiffEquation object to a TransferFunction object, to see if I could make sense of it.  All of the results are the same as the StepProperties result, it appears that only the ResponsePlot for the DifferentialEquation object is different.

Am I doing something wrong?  Does anyone have any ideas?

Dynamic_Systems_Final_Value.flow

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