## Geometric and algebric generation of Pythagorean t...

How to show that any Pythagorean triplet can be obtained from <3,4,5> ? Thank you.
Can we simplify this program?

#Génération Géométrique et Algébrique des triplets Pythagoriciens
restart;
with(geometry);
with(LinearAlgebra);
_EnvHorizomtalName = 'x';
_EnvVerticalName = 'y';

with(plottools);
P := point([0, 0], color = black, symbol = cross, symbolsize = 25);
Oo := point([1/2, 1/2], color = black, symbol = cross, symbolsize = 25);
A := point([1, 1/2], color = black, symbol = cross, symbolsize = 25);
with(plots);
c1 := circle([1/2, 1/2], 1/2, color = blue);
NULL;
PA := line([0, 0], [1, 1/2], color = red);
eqC := (x - 1/2)^2 + (y - 1/2)^2 = 1/4;
eqPA := y = 1/2*x;
sol := solve({eqC, eqPA}, {x, y});

t1 := textplot([0, 0, 'typeset'("P"), font = [Times, Bold, 14]], 'align' = 'above');
t2 := textplot([1, 1/2, 'typeset'("A"), font = [Times, Bold, 14]], 'align' = 'right');
t3 := textplot([1/5, 1/10, 'typeset'("A'"), font = [Times, Bold, 14]], 'align' = 'above');
A1 := point([1 - 1/5, 1/10], color = black, symbol = cross, symbolsize = 25);
diff(A, x) := point([1/5, 1/10], color = black, symbol = cross, symbolsize = 25);
t4 := textplot([1 - 1/5, 1/10, 'typeset'("A1"), font = [Times, Bold, 14]], 'align' = 'right');
A2 := point([1 - 1/5, 1 - 1/10], color = black, symbol = cross, symbolsize = 25);
t5 := textplot([1 - 1/5, 1 - 1/10, 'typeset'("A2"), font = [Times, Bold, 14]], 'align' = 'right');
A3 := point([1/5, 1 - 1/10], color = black, symbol = cross, symbolsize = 25);
t6 := textplot([1/5, 1 - 1/10, 'typeset'("A3"), font = [Times, Bold, 14]], 'align' = 'right');

poly := Matrix([[1/5, 1/10], [1 - 1/5, 1/10], [1 - 1/5, 1 - 1/10], [1/5, 1 - 1/10]], datatype = float);
pol := polygonplot(poly, color = blue, transparency = 0.95);

display(c1, P, Oo, A, PA, seq(A || i, i = 1 .. 3), seq(t || i, i = 1 .. 6), pol, scaling = constrained, axes = none, size = [600, 600]);

R1 := Transpose(<<1, -2, 2> | <2, -1, 2> | <2, -2, 3>>);
R2 := Transpose(<<1, 2, 2> | <2, 1, 2> | <2, 2, 3>>);
R3 := Transpose(<<-1, 2, 2> | <-2, 1, 2> | <-2, 2, 3>>);
V := <3, 4, 5>;
MatrixVectorMultiply(R1, V);
MatrixVectorMultiply(R2, V);
MatrixVectorMultiply(R3, V);
t1 := <2225, 3648, 4273>;
t2 := MatrixVectorMultiply(1/R1, t1);
t3 := MatrixVectorMultiply(1/R3, t2);
t4 := MatrixVectorMultiply(1/R2, t3);
t5 := MatrixVectorMultiply(1/R1, t4);
t6 := MatrixVectorMultiply(1/R3, t5);
MatrixVectorMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(MatrixMatrixMultiply(R1, R3), R2), R1), R3), V);
% - t1;
NULL;

## How does Maple perform in this comparison?...

As I learned here Maple is also a multi-paradigm programming language.

I was wondering how Maple compares in this chart.

Even though I am not a computer scientist, I would say that Maple is on a par with the number one (not sure about pipelines).

Would this claim be correct?

## Status bar: Memory - What memory is displayed...

I have noticed a substantial difference between the memory Maple displays per worksheet

and what the task manager (red arrow) indicates. After kernel restart it looks like this

What Maple displays does not seem to correlate with the physical memory used/allocated.

What is actually displayed and how can we make use of this information?

Also: Is the displayed Time the total process time or the time the Gui waits for the server to reply? Hard to tell.

## Avoiding the "roots of complex number"...

Hello,

I'm encountering an issue with the "roots of complex number" message while running my Maple code. Maple seems unable to solve this problem for me.

I would greatly appreciate any ideas or suggestions that could help me resolve this error.

Vib-code.mw

## Trouble with AI Formula Search...

Every last query I make in the AI Formula Assistant returns this message...

This happens even when I use a basic canned query shown in use-case examples (e.g., surface area, sphere).

I have accepted the Terms of Use.  Is there some other setting I need to enable? Thanks.

## Icons dissapearing...

What might be the reason for the GUI loosing icons during a session? It looks like this

Mouse over let the icons reappear.

This problem is not new to me and only happens from time to tim

The only thing I can say is that I didn't see it after restarting Maple.
And: Only the icons on the left-most disappear.

Everything under Windows 10

Has anyone seen the same thing?

Any idea how to fix this?

## solutions of solve command does not fit to given i...

I want to solve a big system of equations. There are 32 equations and 32 variables. Furthermaore there are a few restrictions to 8 of those variables, for example 0<t, t<1. I put the restrictions into the set of equations I want to solve. Normaly its works quite well, but today, one of the solutions was t=-2.0000000000. But this does not fit to the inequalitys I gave into the programm. Why is that? Is there a diffrence if I mark a set of inequalitys as restrictions and put them as a further property into the solve command comparded to use those inequalitys as additional equations?

Hi,

I am the administrator of Maple in my school, and all the students use Maple in part of their exams. Is it possible  to block the access to ChatGPT thru eg. the firewall or otherwise during exams.

The reason for this question is that the students must have access to some internet sources during exams, but definately not CharGPT.

Kind regards

Per Kirkegaard

## solve the equation of the odometric model...

Hello, I try to solve the equations of the odometric model with the Maple 2024 but I have not the answers as with the hands, can you help me to verify it ?

dsolve(diff(phi(t), t) = tan(10*t)/5)

dsolve(diff(x(t), t) = V*cos(ln(1 + tan(10*t)^2)/100))

dsolve(diff(y(t), t) = V*sin(ln(1 + tan(10*t)^2)/100))

Best regards, Edern Ollivier.

## Need to Obtain Bifurcation Points and Bifurcation ...

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance.

123.mw

 >
 >
 >
 (1.1)
 >
 (1.2)
 > bif_eq1 := eq1 = 0;

 > bif_eq2 := diff( eq1, V) = 0;

 > bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

as the solutions, which are then expressed as the points  via

## what is the right way to rearrange this equation...

I have solution to system of equations that results (I assign it to) in:

```I2sol := -I*omega0*k*L*vin*1/(L^2*k^2*omega0^2 + R^2)
```

I then try to solve it for k by doing

```solve(I2sol = I2, k)
```

but that doesn't work.  What is the "right" Maple way to rearrange I2 such that the expression is the solution(s) for k?

## HELP WITH A CORRUPTED FILE ASAP!...

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

## why mapleprimes removes tags from post?...

I noticed tags on the post

https://mapleprimes.com/questions/238161-Why-Maple-Gives-Solution-To-Euler-Ode

keep disappearing.

I added tags "differential equation" and "dsolve" and so on.

Later on when I visit this site again I found the tags are all gone.

Why does Mapleprimes remove the tags on post?

Or is someone else removing the tags? If so, why? is something wrong with the tags I've added?

This happend twice on this one post. I noticed earlier today the tags were gone, so I added them again. And now I see the same thing. They are all gone.

## Kernel Issues in Maple Flow...

I am new to Maple Flow and am constantly having issues like the one shown below. A cell will become corrupted somehow, and the kernel will crash or freeze. I can save and quit, but if I re-open the file, the crash will happen again before I can diable evaluation. My questions:

1. Has anyone else had this issue? Was it solvable?
2. Can evaluation be disabled by default? Its possible in Maple but I don't see how in Flow.
3. Can the kernel be restarted and reconnected (like Jupyter Lab)?

I cant expand the cell in question because of the crash, but this cell isn't the issue. This is happening all the time.

## Problem bug in Maple Primes with Replys ...

I have noticed over a few questions I have asked recently.
I ask a question.                   It goes to top of active converstaions

A bit of time passes  so slides  of the top six/seven that show

Another Reply/Answer from someone                possibly does not show in active conversations.  I catch this by the orange flag or email notification

I reply                                 Does not appear in active conversations..

This can kill the conversation chain.

I have even tried changing one of me replys to an answer but did not go to top active conversations again.

Has anyone else expperienced this?

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