Maple 16 Questions and Posts

These are Posts and Questions associated with the product, Maple 16

Anybody has a hint on how to solve a non-linear system with trigonometrics. I want to solve x, y and z.

If I have  the following..or different numbers, but 2 different arrays I need to calculate sample mean & variance

Array A:=([1,1,1,0,0,3,2,4])

and

Array B:=([2,1,0,1,3,3,4,1])

what formula do I use to force Maple 16 to calculate the sample mean and the sample variance?

I was thinking about the area problem, yet again, and found myself asking the question: why must we go through such elaborate means to get Maple to generate a plot of the region between two (or more curves)? I use the word elaborate to describe any process that would might become overwhelming, for, say a student, to go through to accomplish a task. Anyone with the most basic of backgrounds can understand the area problem, but yet, such an individual might not find it a trivial...

I want to solve 4 nonlinear equation using maple. I want to find many roots of this 4 nonlinear equation.

I have no idea about initial condition so I use 4 for initial condition. my program is as follow:

 

f1:=nonlinear equation1(include variable q1,q2,p1,p2);

f2:=nonlinear equation2(include variable q1,q2,p1,p2);

f3:=nonlinear equation3(include variable q1,q2,p1,p2);

f4:=nonlinear equation4(include variable q1,q2,p1,p2);

I have a very strange bug with Maple 16. When I try to start it, Maple loads its shell and starts to consume 100% CPU (maple.exe, not mserver.exe). If I try to calculate something, it throws something like "waiting for server connection". In 3 to 10 minutes Maple suddenly stops doing this and then works normally until I reboot Windows. What's this? Maple 16.0, Windows XP SP3.

PS. I do not have such bugs on my home PC with Windows XP SP2.

 

 

Dear Friends.   I solve a group of linear equations and the memory is not enough and i can't 
adding a new hardware to the computer.

i increase the virtual memory of the computer from some chose for the operating system 
but it seem to me the Maple use the memory from the hardware only.

I want to know is there any method to make the Maple using the virtual memory for 
the computer

Amr

I just encountered a very strange behavior when using DEplot. I want to generate a slopefield and solution curves. However, when I enter the command, only the arrows in the slopefield are showing. If I click on the plot where the solution curve should be, I see the outline of the curve. It's as if the curve isn't begin colored. I hope someone is able to replicate this behavior and suggest a fix. Thanks! (See attached file) 

I have three functions f,g,h and I want to create an n by 3 matrix with columns: 

[f(1), f(2), f(3), ..., f(n)] , [g(1), g(2), ..., g(n)] , [h(1), h(2), ..., h(n)]

I can do this for a particular positive integer n, but I would like be able to just input n and get the n by 3 matrix.  I am new to Maple and could not find an answer easily.  Thanks.

I have a set of 9 equations and 9 unkowns. These equations are massive 9th order polynomials. The equations themselves are contained in a vector called "C" in the .m file that follows:

Cvector_with_a.txt    (please rename the .txt file to .m since this forum doesn't seem to allow the upload of .m files)

In order to solve the eqautions, you must first set the values of two extra...

I am trying to save an array plot to an eps file. My code is the following:

restart: with(plots): currentdir("G:/"): plotsetup(default):
alpha := [.2, .25, .3, .35, .4]:
beta := -0.1e-1:mygamma := -1:delta := 0.1e-1:start := 0:finish := 20:

for i to 5 do
 eqn1 := diff(x(t), t)-x(t)*(alpha[i]-beta*y(t));
 eqn2 := diff(y(t), t)-y(t)*(mygamma-delta*x(t));
 
 solt[i] := dsolve([eqn1 = 0, eqn2 = 0, x(start) = 80, y(start) = 40...

Having read the above I decided to try it on a substitution problem I had last year on a set of equations. Work sheet containe an example. I successifuly applied algsubs to the problem. It can be slow and their is no easy way I see to know when the substitution is complete. so what I did go round the loop 2, 3, 4, 5 times. Crude!

Decided to try "side relations" with simplify here but it comes out with a totally different answer (not correct).

Could somebody explain why?

The following (downsized) images of Lyapunov fractals were each generated in a few seconds, in Maple 16.

 

I may make an interface for this with embedded components, or submit it in some form on the Application Center. But I thought that I'd share this version here first.

I'm just re-using the techniques in the code behind an earlier Post on Mandelbrot and Julia fractals. But I've only used one simple coloring scheme here, so far. I'll probably try the so-called burning ship escape-time fractal next.

 

 

 

 

Here below is the contents of the worksheet attached at the end of this Post.

 

 

The procedures are defined in the Startup code region of this worksheet.

 

It should run in Maple 15 and 16, but may not work in earlier versions since it relies on a properly functioning Threads:-Task.

 

The procedure `Lyapunov` can be called as

 

          Lyapunov(W, xa, xb, ya, yb, xresolution)

          Lyapunov(W, xa, xb, ya, yb, xresolution, numterms=N)

 

where those parameters are,

 

 - W, a Vector or list whose entries should be only 0 or 1

 - xa, the leftmost x-point (a float, usually greater than 2.0)

 - xb, the rightmost x-point (a float, usually less than or equal to 4.0)

 - ya, the lowest y-point (a float, usually greater than 2.0)

 - yb, the highest y-point (a float, usually less than or equal to 4.0)

 - xresolution, the width in pixels of the returned image (Array)

 - numterms=N, (optional) where positive integer N is the number of terms added for the approx. Lyapunov exponent

 

 

The speed of calculation depends on whether the Compiler  is functional and how many cores are detected. On a 4-core Intel i7 under Windows 7 the first example below had approximately the following performce in 64bit Maple 16.

 

 

Compiled

evalhf

serial (1 core)

20 seconds

240 seconds

parallel (4 cores)

5 seconds

60 seconds

 

 

 

with(ImageTools):


W:=[0,0,1,0,1]:
res1:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

memory used=46.36MiB, alloc change=65.73MiB, cpu time=33.87s, real time=5.17s


View(res1);


W:=[1,1,1,1,1,1,0,0,0,0,0,0]:
res2:=CodeTools:-Usage( Lyapunov(W, 2.5, 3.4, 3.4, 4.0, 500) ):

memory used=30.94MiB, alloc change=0 bytes, cpu time=21.32s, real time=3.54s


View(res2);


W:=[1,0,1,0,1,1,0,1]:
res3:=CodeTools:-Usage( Lyapunov(W, 2.1, 3.7, 3.1, 4.0, 500) ):

memory used=26.18MiB, alloc change=15.09MiB, cpu time=18.44s, real time=2.95s


View(res3);


W:=[0,1]:
res4:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

memory used=46.25MiB, alloc change=15.09MiB, cpu time=33.52s, real time=5.18s


View(res4);

 

 

Download lyapfractpost.mw

Lately as my computations become ever more intense, I have been having trouble with fsolve. Why exactly does fsolve sometimes return itself as in:

E:=fsolve({C1,C2,C3,C4},{c1,c2,c3,c4}}

returns--> fsolve({C1,C2,C3,C4},{c1,c2,c3,c4}}

and somtimes fsolve returns a blank.

 

What is going on internally here? Shouldn't it keep trying till it runs out of memory?

 

Thanks,

 

Pat

I have added a .mw file showing the problem. I wish to calculate the integral at the bottom of the post. unfortunately the function im using defined at he beginning of the file doesnt behave well for values k larger than 25/30...

The integral I need to evaluate therefore cant be evaluated if one wants to integrate from 0 to Infinity.

Also just integrating till 20 or so is not accurate enough...

Has anybody an idea about better implementation of the problem....

Today's SMBC strip by Zach Weinersmith is a silly math joke but it was pretty much begging for implementation.

So, here is a simple brute force Maple program to compute the Fouriest transform of an integer.

fouriest := proc(n::posint, ob::posint:=10)
local b,f,cap,i,rdx,fc;
...
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