## MaplePrimes Questions

Search Questions:

## Turning points of 3d plane...

Dear all, I have the following issue:

Goal is to calculate saddle, turning point, etc.

As you can see in the code above only in case of a second restart x2 is calculated correctly.

Thanks for help.

I have created a document on my computer that runs normally in Maple 2024.1. However, when I upload this document to MaplePrimes, it shows an error or behaves unexpectedly. The document contains a system of differential equations, which I solved numerically and plotted, but the plots and equilibrium points do not display correctly after uploading.

When I run this code on my local machine, it works perfectly. However, after uploading the document to MaplePrimes, it does not run as expected. What could be causing this issue? Is there a known problem with Maple 2024.1 when uploading documents, or could there be a compatibility issue with MaplePrimes?

Any help or suggestions would be greatly appreciated. Thank you!

This project discusses the predator-prey system, particularly the Lotka-Volterra equations, which model the interaction between two species: prey and predators. Let's solve the Lotka-Volterra equations numerically and visualize the results.

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Now, we need to handle a modified version of the Lotka-Volterra equations. These modified equations incorporate logistic growth fot the prey population.

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## Improving the performance in series summation...

Hello, I am trying to evaluate the following series (summing up to 100), but due to the binomial factor, the summation is very slow, can anybody suggest some better code to speed up the summation?

n1 = 423; x = 16; n2 = 81; y = 35; s1 = 0.1; b1 = 7; beta1 = 2.1;

Mysum := (r, xx, k, b, s, beta) -> b*beta^s*sum(sum(binomial(k - xx, j)*(-1)^(j + h)*GAMMA(s + h + 1)*(beta - 1)^h/(h!*(r + xx + b*s + j + b*h)), h = 0 .. 100), j = 0 .. k - x)/GAMMA(s);

Mysum(0, x, n1, b1, s1, beta1);

## Combining standard font and Greek symbols in a plo...

I can't combine standard font and Greek symbols in a plot legend. I want to type:

"Limit of X_{i}^{\rho=0} (\alpha\mapsto+\infty)>0"

where I used LaTeX notation to emphasise that I want (1) superscript and subscript of X displayed as aligned exactly on top of each other, (2) rho, alpha, mapsto-style arrow, and infinity typed in their respective symbolic forms.

thanks!

## why dsolve gives division by zero on this ode? ...

I do not have earlier Maple version to check now. But Maple 2024.1 gives division by zero on this second order ode with missing x. This looks like new problem in Maple. Would someone who have access to earlier version of Maple be able to check if this problem shows there also? I solved this and get y=x+3 as solution which Maple verifies.

 > interface(version);

 > restart;
 > ode:=diff(y(x),x$2)=(diff(y(x),x))^3-(diff(y(x),x))^2; IC:=y(0)=3,D(y)(0)=1;  > dsolve([ode,IC]) Error, (in dsolve) numeric exception: division by zero  > sol:=y(x)=3+x; odetest(sol,[ode,IC])  > DEtools:-odeadvisor(ode);  > infolevel[dsolve]:=5;  > dsolve([ode,IC]) Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order --- trying a change of variables {x -> y(x), y(x) -> x} differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying differential order: 2; missing variables -> Computing canonical coordinates for the symmetry [0, 1] -> Rewriting ODE in canonical coordinates by means of differential invariants Try computing 1 more symmetries for ODE written in canonical coordinates -> Computing symmetries using: way = 3 Found another symmetry: Found another symmetry: Computing a convenient ordering to use the 3 symmetries available <- differential order: 2; canonical coordinates successful <- differential order 2; missing variables successful Error, (in dsolve) numeric exception: division by zero  > dsolve(ode) Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order --- trying a change of variables {x -> y(x), y(x) -> x} differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying differential order: 2; missing variables -> Computing canonical coordinates for the symmetry [0, 1] -> Rewriting ODE in canonical coordinates by means of differential invariants Try computing 1 more symmetries for ODE written in canonical coordinates -> Computing symmetries using: way = 3 Found another symmetry: Found another symmetry: Computing a convenient ordering to use the 3 symmetries available -> Calling odsolve with the ODE diff(_b(_a) _a) = _b(_a)^3-_b(_a)^2 _b(_a) HINT = [[1 0] [-_a+y -_b*(_b-1)]] *** Sublevel 2 *** symmetry methods on request 1st order, trying reduction of order with given symmetries: 1st order, trying the canonical coordinates of the invariance group <- 1st order, canonical coordinates successful <- differential order: 2; canonical coordinates successful <- differential order 2; missing variables successful Download divide_by_zero_maple_2024_1_august_5_2024.mw ## Clearing all Typesetting effect... Asked by: I set Typesetting:-Settings(prime=x,'typesetprime'=true); #this says to use y'(x) instead of dy/dx Typesetting:-Suppress(y(x)); # this says to use y' and not y'(x) So that y(x) and diff(y(x),x) display as y and y' and this works. But I am not able to clear this effect without doing restart. If I do Typesetting:-Unsuppress('all'); #clear all It still display derivative as y'(x) instead of diff(y(x),x) as expected. So the Unsuppress('all') had only partial effect. How to completely remove all typestting effects so that it returns to how it was and without doing restart? Worksheet below. Looked at help page, but it is still not clear. All what help page says is to use Unsuppress(all) and that is what I did. I am using typesetting level extended if it makes any difference.  > interface(version);  > restart;  > ode:=diff(y(x),x$2)+diff(y(x),x)*y(x)+3*y(x)=sin(x);

 > Typesetting:-Settings(prime=x,'typesetprime'=true); #this says to use y'(x) instead of dy/dx     Typesetting:-Suppress(y(x)); # this says to use y' and not y'(x)

 > ode

 > Typesetting:-Unsuppress('all'); #clear all
 > ode

 > Typesetting:-Unsuppress(y(x));

Warning, no depencency for function y has been declared => ignored

 > ode

## How do I simplify the representation/output of cod...

I want to substitute a variable r' =sqrt(x^2 + y^2 + z^2).

But how do I change my output so that r' is displayed instead of sqrt(x^2+y^2+z^2)?

E.g. line (5) D(g)(r')x/r' and not D(g)(sqrt(x^2 + y^2 + z^2))*/sqrt(x^2 + y^2 + z^2).

And one more question. How can I make sure that my output in (6) is only the result on the right side and the left side of the equal sign is not displayed?

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## 2D plot for same 3Dplot when parameter are change?...

for 2D plot of 3D plot when parameter change there is an idea for making something like that, i need some help about this

## Why does simplify command turn these three express...

In the code below, I define an expression, then turn it into a function of omega_d.

Consider the results (5) and (6) below.

I take the derivative of the function relative to omega_d, set the derivative to zero and ask Maple to solve for the critical point (ie, the omega_d at which the derivative is zero).

I get the correct result in (5), ie three different critical points. But when I simplify this result, Maple returns only one of the critical points.

Why?

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This was a problem for me just now because I used the command in (6) first and just could not figure out what the heck was going on. I did the calculations by hand to check, and then finally found out it was this simplify command.

## why 2024.1 now jumps to END of next execution cell...

Something seems to have changed.  I do not now have Maple 2024.0 to check or earlier Maple's as I have to reinstall windows since my C:\ drive died.

I installed Maple 2024.1 new on windows 10 home edition.

I noticed now when evaluating the current cell, the cursor automatically jumps to next cell, which is what I want and how Maple always worked.

But now the cursor jumps to the end of the command in the next cell. Before, I could swear that not how it worked and it used to jump to the start of the next cell.

This makes it very confusing, as I keep looking for where the cursor is now.

Why was this changed in 2024.1? I looked at option and see nothing to change this.

Here is worksheet and small movie.

This is my display options

 > interface(version);

 > x:=1;

 > y:=3;

 > z:=4;

 > h:=4;

 >

Update

I tried to change the cursor size and thickness in windows 10 itself (using settings->Ease of access->Text cursor) and made it much bigger and restarted Maple but this had no effect. Cursor inside Maple remained the same.

I was hoping if there is a way to make the cursor bigger then this will make it easier to see where it jumped to when hitting enter.

It is bad, since the Maple cursor jumps to random places in the next cell. sometimes it jumps to the middle of the code in the next cell when there are more than one line there.

Here is a movie. Notice how it jumped to the start of the second line now in next cell in one case and not to the end of the code.

I can't believe no one at Maplesoft have noticed this and is able to fix it. This is ridiculous behavior. I spend few seconds each time I hit enter looking for where the cursor has landed as I keep looking at start of the next cell and it is not there. I could have 10-20 lines of code in one cell and have too look to find where the cursor is hidden in these 20 lines.

It natural for one to look for where the cursor is when woking and this makes it annoying. Hopefully someone can find a way to tell Maple to bring the old behaviour back where cursor jumps always to the start of the next cell.

## How determine the complex region for 3D plot ?...

 > restart;
 > local gamma;
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 >

 > params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7,theta=0,gamma=1};
 (2)
 >
 (3)

 > sol1 := [U(xi), -k*x -(9*alpha*k^2*beta[4] + 2*beta[3]^2)/(9*beta[4])*t + theta];
 (4)

 > sol2 := eval(sol1, U(xi) = -beta[3]/(3*beta[4]) + beta[3]*sinh(xi)/(6*beta[4]*cosh(xi)) + beta[3]*cosh(xi)/(6*beta[4]*sinh(xi)));
 (5)

 > solnum :=eval(sol2, params);
 (6)
 > plots:-complexplot3d(solnum, x = -50.. 50, t = -50..50);
 >

if there is any other way for graph please share with me

## Why doesn't evalf work on data structures like Mat...

Why doesn't evalf work on the data structures below?

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## How to evaluate definite integral without substitu...

i am trying to solve definite integral but i want result in A,B form i dont want to assign numerical values to them can i get that  in maple? i have tried evalf, eval and simplify command but it is not working kindly help me out

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## File preview in File Explorer of Windows...

I was wondering if this has ever been discussed?

File preview would make life easier when searching an older document.

Since it seems to be a non trivial programming task, I was wondering whether generating a pdf document in parallel to a worksheet could be an option (in a subfolder). However, doing this by hand for all existing documents is not pratical.

Could this (generating pdf files) be done by a batchjob?