I want to convert my code output into LaTeX format, but the current formatting isn't suitable for presentation. For example, when I use simplify, it sometimes introduces unnecessary fractions, making the expression look cluttered and less elegant on paper. I'm looking for a way to simplify expressions preferably by factoring terms, without introducing extra fractions, so the final LaTeX result appears clean and well-structured.

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How can we eliminate nonlinear terms involving two functions in a differential equation?

Download remove.mw

Hi!

Sorry if I am missing something or not following any implicit rules, I am really new to Maple and this forum.

For the sake of completeness, here the code that is given:

Ve := Vector([VeX, VeY, VeZ]);
with(LinearAlgebra);
Vh := Normalize(Vector([alphaX*Ve(1), alphaY*Ve(2), Ve(3)]), Euclidean, conjugate = false);
lensq := Vh(1)*Vh(1) + Vh(2)*Vh(2);
T1 := Vector([-Vh(2), Vh(1), 0])/sqrt(lensq);
T2 := CrossProduct(Vh, T1);
r := sqrt(x);
phi := 2*Pi*y;
t1 := r*cos(phi);
t2 := r*sin(phi);
s := 1/2*(1 + Vh(3));
t22 := (1 - s)*sqrt(1 - t1*t1) + s*t2;
Nh := t1*T1 + t22*T2 + sqrt(1 - t1*t1 - t22*t22)*Vh;
NULL;
Ne := Normalize(Vector([alphaX*Nh(1), alphaY*Nh(2), Nh(3)]), Euclidean, conjugate = false);
AV := (-1 + sqrt(1 + (alphaX^2*Ve(1)^2 + alphaY^2*Ve(2)^2)/Ve(3)^2))/2;
G1 := 1/(1 + AV);
DN := 1/(Pi*alphaX*alphaY*(Ne(1)^2/alphaX^2 + Ne(2)^2/alphaY^2 + Ne(3)^2)^2);

DVN := G1*DotProduct(Ve, Ne, conjugate = false)*DN/DotProduct(Ve, Vector([0, 0, 1]), conjugate = false);
PDF := DVN/(4*DotProduct(Ve, Ne, conjugate = false));

So far, so good. Now what I want to do is:

PDFint := int(PDF, [x = xInf .. xSup, y = yInf .. ySup]);

to calculate the symbolic integral of PDF over x and y. The issue is that I keep running out of memory after a few hours and my operating system (Linux Fedora) automatically shuts Maple down.

I am convinced that there must be a way to either preprocess PDF so that the int(...) command doesn't eat up all the RAM, or some different way to calculate an integral that maybe has a different structure?

I have tried codegen[optimize](PDF) and liked what it did, but I don't know how to progress with the result of it, if at all possible.

I know that there is also a way to calculate the integral numerically, but I need the analytic integral, so numerical solutions are of no use to me.

If there is really no way for me to obtain this integral, I would really appreciate an explanation of why, so that I can rest at night finally lol.

Thank you in advance,

Jane

I’ve successfully plotted this exercise, but I’m exploring ways to improve the visualization. Specifically, I’d like to know if it's possible to combine a 2D plot as a smaller inset within a 3D plot, positioned in a corner of the 3D graph.

Additionally, I’ve noticed that although the same data is plotted in different examples, the design and style of the plots can vary significantly, some look much more polished or professional. Are there recommended techniques, functions, or toolboxes in Maple that can help improve the visual design or aesthetic of the plots

Download plot.mw

Yes , i can ..a procedure for thiis?

Download can_we_plotthisin_3Dshapemprimes5-5-2025.mw

in here How we can seperate the coefficent of conjugate this conjugate sign how remove from my equation ?

Download conjugate.mw

according to what is new in Maple 2025, it says

• Maple 2025 introduces several important improvements to simplify regarding expressions containing exponential, trigonometric, hyperbolic, and/or inverse trigonometric functions, resulting in more compact results. Other commands in the math library also provide simpler results due to these improvements.

But I still see weakness in simplify. (see also recent question).

Here is an example, A and B below are equivalent mathematically. But A is almost twice as big. So one would expect simplify(A) to return B. right? But it does not. Also using size option has no effect.  

Does one need more tricks in Maple to make it simplify this? Is this not something that a powerful CAS software like Maple should have been able to do?

Download why_can_not_simplify_may_4_2025.mw

Using another software, all what is needed is call to Simpify to do it:

I also tried my most power full_simplify() function in Maple, and it had no effect

full_simplify:=proc(e::anything)
   local result::list;
   local f:=proc(a,b)
      RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
   end proc;

   #add more methods as needed

   result:=[simplify(e),
            simplify(e,size),
            simplify(combine(e)),
            simplify(combine(e),size),
            radnormal(evala( combine(e) )),
            simplify(evala( combine(e) )),
            evala(radnormal( combine(e) )),
            simplify(radnormal( combine(e) )),
            evala(factor(e)),
            simplify(e,ln),
            simplify(e,power),
            simplify(e,RootOf),
            simplify(e,sqrt),
            simplify(e,trig),
            simplify(convert(e,trig)),
            simplify(convert(e,exp)),
            combine(e)
   ];   
   RETURN( sort(result,f)[1]);   

end proc:

Calling full_simplify(A) did not simplify it.

I wanted to search for all files with some extention in directory tree. But when adding depth=infinity and also adding 'select'="*.log" (or whatever the extension I want is), then it returns an empty list even though there are files with this extension but deep in the tree.

If I remove select, then it does work, but it returns list of the files in the tree. Which I do not want. I want to filter these by select.

If I remove depth=infinity then select works but only finds such files at top level of the directory and does look down the tree where there are more such files.

It seems select and depth conflict with each others.  Adding 'all' option makes no difference.

I do not remember now if I reported this before or not.

Here is worksheet showing this problem

Download listdirectory_may_3_2025.mw

How can one get list of files with specific extension in the whole tree? And why is adding select makes it not work? Help does not say anything about select does not work when adding depth=infinity.

I suppose I can get list of all files in tree, then iterate over the list and remove all entries that do not end with the extension I wanted. But this is what select is supposed to do. For example

folder_name:="/home/me/maple2025/"; #works but this finds everything
L:=FileTools:-ListDirectory(folder_name,depth=infinity):
map(X->`if`(FileTools:-Extension(X)="wav",X,NULL),L);

Gives list of only files with extension "wav". So the above is workaround for now.

I’m currently trying to collect terms in an expression f^G(xi), but the result is not behaving as expected. I attempted two different coding approaches, but both resulted in errors. This particular case of collecting terms seems to be different from what I’ve encountered before, and I’m unsure how to resolve it.

Could you please advise on how to properly collect the terms in this situation and avoid the errors? Any insight into why this case behaves differently would also be appreciated.

Thank you for your help.

collect_term.mw

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

1. Properly formulating the ODE.

2. Understanding the role of f in the context of exponential functions.

3. Finding the correct and complete solutions.

4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw

These are the same (i.e. mathematically equivalent for real x)

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

But can't see how to use Maple to show this, other than numerically and by plotting.

Any one knows of a trick? Below is worksheet. Using another software, it was able to show they are same:

Here are my attempts in Maple 2025
 

>  interface(version); >  restart; >  A:=-x*(x - 4*exp(x/2) + 2); B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4); >  plots:-display(Array([plot(A,x=-3..3),plot(B,x=-3..3)]))   >  Digits:=16; seq(MmaTranslator:-Mma:-Chop(A-B),x=-2..2,.1) >  simplify(A-B); >  simplify(A-B) assuming real; >  simplify(evala(A-B)) assuming real; >  simplify(normal(A-B)) assuming real; >  simplify(A-B,exp) assuming real; >  simplify(evalc(A-B)) assuming real;

Download show_same_may_3_2025.mw

Syntax to find KKT Condition, only one constrain is there? Need help
KKT_Condition.mw

Manually factoring each equation in this system one by one is time-consuming and inefficient. Is there a way to automate the factoring of expressions into two multiplicative terms—some of which may be single-term factors—using code?

Download by_hand!.mw

Substituting the solutions into the ODE doesn't yield zero, despite the code appearing correct—suggesting either complexity, symbolic limits, or an implementation issue.

17-ode.mw

also in this ode why solution is like this how i can fixed this too

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