Maple Questions and Posts

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Hi

The program below shows the plot3d of the function f1/its maximum, then contour plot at the value of the maximum point.

 

I applied  the same code to another function which is worked.

 

It might the issue with the optimization .

 

t:=Pi:

qp:=1/sqrt(2)*(Pi-I*(n+m)/2):

qm:=1/sqrt(2)*(-Pi-I*(n+m)/2):

pp:=1/2*(-Pi*I-(n-m)/2):

pm:=1/2*(Pi*I-(n-m)/2):

zp:=1/sqrt(2)*qp:

zm:=1/sqrt(2)*qm:

sum1:=0;for n from 0 to 3 do for m from 0 to 3 do if(n=m)then  sum1:=sum1+HermiteH(2*n,x)*HermiteH(2*m,y)*(erf(qp)-erf(qm))*exp(-1*(n+m)^2/8)*exp(-I/sqrt(2)*(n-m)*y)*exp(I/sqrt(2)*(n+m)*x)*exp(-I*(n-m)*t)*Pi:

else

sum1:=sum1+sin((Pi)*(n-m))/(n-m)*HermiteH(n,x)*HermiteH(m,y)*(erf(qp)-erf(qm))*exp(-1*(n+m)^2/8)*exp(-I/sqrt(2)*(n-m)*y)*exp(I/sqrt(2)*(n+m)*x)*exp(-I*(n-m)*t);fi;od;od; A:=sum1:

unassign('n','m'):B:=simplify(sum(sum((erf(zp)-erf(zm))*(erf(pp)-erf(pm))*exp(-n*m)*exp(-I/sqrt(2)*(n-m)*x)*exp(I/sqrt(2)*(n+m)*y),n=-5..5),m=-5..5)):

g:=(A*B*exp(-1/2*(x^2+y^2))):

f1:=(Re(g)^2+Im(g)^2):

f1:=simplify(f1) assuming real;

Optimization:-Maximize(f1,x=-5..5,y=-5..5);

Max:=%[1];

plot3d(f1/Max,x=-2..2,y=-2..2,axes=boxed,labels=["x","y","F(x,y)"],tickmarks=[3,3,2],style=surface,color=gold);

with(plots):contourplot(f1, x = -5 .. 5, y = -5 .. 5,view=[-5..5,-5..5], contours=[AT THE MAXIMUM POINT]);

Replies and comments are helpful 

Hello to all, does anyone create an example for me that how to calculate and plot streamline of fluid flow.

Hello

I solved these equations numerically but I need to solve it by Runge-Kutta fourth order Method. Kindly help me in the coding of the same.

 


restart;
N1 :=1:N2 :=1: N3 :=0.1 :R := -1:
EQ:={(1+N1)*diff(f(x),x$4)-N1*diff(g(x),x$2)-R*(-diff(f(x),x)*diff(f(x),x$2)+f(x)*diff(f(x),x$3))=0, N2*diff(g(x),x$2)+N1*(diff(f(x),x$2)-2*g(x))-N3*R*(f(x)*diff(g(x),x)-diff(f(x),x)*g(x))=0}:


IC:={D(D(f))(0)=0, D(f)(1)=0,f(0)=0,f(1)=1,g(0)=0,  g(1)=0}:

sol:= dsolve(EQ union IC, numeric,output=Array([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1])):
 

Hello,

I have a particular problem that I haven't managed to find the solution to by googling.

9/10 times that I open Maple 2020 I can't seem to open any of my saved documents. it opens the start tab, and I'm still able to open a new document or worksheet, but then when I try to change to text instead of math, it won't let me. I can type, but I can't press backspace or enter.

I have tried restarting and shutting down my computer, but every time I have to just force quit Maple because it won't respond half of the time and it won't quit normally.

I'm running the latest version of Maple and using macOS Catalina version 10.15.5.

 Suppose that A is an m×n real matrix. The function TA:ℝn→ℝm   defined by

TA(x)=Ax,  for all 𝕩∈ℝn

     is a linear transformation.

let A=<< 87, -66, -90, 12, 48>|<-36, -40, -82, -54, 15>|<99, 79, 76, -31, 27>|<-69, 15, -10, 45, -9>>

and x= <9,-4,2,-17>.

Then TA(x)=   Preview   

   Alternatively, you can copy your answer from your Maple worksheet and paste it to the answer box.

 

(b) Suppose now that the linear map T:ℝ2→ℝ3  is defined by, for all 𝕩=(x1,x2)∈ℝ2

 T(x)=  <<x1+6x2>|<−2x2>|<−4x1+2x2>>

    

     Enter the matrix M , in Maple syntax, in the box below such that T(x)=Mx  for all x∈ℝ2,  

  M=    Preview   

 

Can someone pls help me with this question. TIA.

   

 

 

I see this error once in a while

Error, (in SolveTools:-CancelInverses) assertion failed, simplify should not leak _Z variables out from RootOfs 

When I run a long script. Unfortunately, I have not been able to make a small example to reproduce it. So it is random. I've seen it about 5-6 times in the last 2-3 weeks, over 100 runs during this time.

Just wanted to see if anyone saw this before. The strange thing it is random. I can re-run the same script, or restart it from the point where it failed,  with no changes anywhere, and this error do not show up again for days, and suddenly it shows up again.

Must be related how to Maple internal cache memory happened to be arranged at that time. I noticed that a number of things in Maple seem to happen at random times, such as a random hang of the server at different times and places. I could never understand why this happens in Maple.

If there is only one thing Maplesoft could do for the next version, it will be to improve the robustness of its software.

Any chance to get a dataplot with units in one or both axis?

Or is this another thing where units are cause of trouble?

plotunits1.mw

Hello

I want to know if there is any option to convert the Maple code into MATLAB version to work across platforms. I have tried the code generation option in Maple and I could not understand how to use the single line code generated. I am working on an already written Maple code and conversion of code to use on both platforms is kind of important. Please advice me on the same.

Regards!

I'm willing to draw phase portrait for the equation of ode fifth order

u'''''+6(u'u'''+(u'')^2)-u'''(a+2b)=0

where a and b are arbitrary constant not equal to zero and (') represents derivative w.r.t  'x'.

We have just run into a problem (loss of data), when 2 users have opened the same workbook.

Does Maple support Multiuser access to a workbook, and if not - why isn't there any lock mechanism in place to prevent that?

I've asked about this 5 years ago

 

https://www.mapleprimes.com/questions/203628-Maple-2015-No-Longer-Autoscroll-As

And according to the reply there at the time, this is supposed to have been fixed in Maple 2015.1:

It appears that the scrolling issue has been fixed in the next version of Maple

But ever since then, whenever I use Maple, the worksheet do not auto-scroll as the program runs and prints outout to the screen. I have to keep using the mouse to move the bar down to see the latest prints.

Not only that, the bar itself (on the right side) shrinks in size as more outpout is printed.

It becomes smaller and smaller with time, and becomes very hard to grab it with the mouse since it become so thin.  Once all the output is deleted, the bar become long again.

So I think there is an option to enable autoscrolling somewhere.

But I am not able to find it. I looked at options, display, general and interface and see nothing there to turn it on.

Sometimes I get the feeling that the folks at Maplesoft do not use Maple interface the way we users use it, becuase this is such a basic interface problem and any one who uses Maple interface for more than one day must see these problems all the time.

So how come these are still not fixed?  Here is a screen shot showing the bar on the right after long print out, and showing how it was before.

I use only worksheet mode, not document mode. On windows 10.

 

 

 

 

Hi, I want to use Maple to derive the eigenvectors of a 3x3 matrix A. I can obtian the 3 eigenvalues correctly by using eigenvalues(A), and the results are "u, -a+u, a+u". But after inputing eigenvectors(A), I can only get "[-a+u, 1, {r}], [a+u, 1, {r}], [u, 1, {r}]". All the 3 eigenvectors are written as {r}, I dont know why...and how can I tranform {r} into visiable results? 

I would be very appreciate if anyone could give me some help!

How to draw a circle transfomed by orthogonal affinity to oblique line and k ration ? Thank you.

 Help me please.  How can i simulate murmuration in maple.

it took a while to track this. When I run these 3 ode's in this sequence, Maple gives 

Error, (in Engine:-Dispatch) too many levels of recursion

and it has to be this sequence.  I also found I might have to run the code 2 or 3 times to get this error if it does not show first time. 

Will show a movie below also.

Here is the code

restart;
ode1:=cos(y(x)) - x*sin(y(x))*diff(y(x), x) = sec(x)^2:
ode2:=y(x)*sin(x/y(x)) + x*cos(x/y(x)) - 1 + (x*sin(x/y(x)) - x^2*cos(x/y(x))/y(x))*diff(y(x), x) = 0:
ode3:=x/(x^2 + y(x)^2) + y(x)/x^2 + (y(x)/(x^2 + y(x)^2) - 1/x)*diff(y(x), x) = 0:

func:=y(x);
the_ic:={};
the_time_limit:=60;

advisor:=timelimit(the_time_limit,DEtools:-odeadvisor(ode1)):
solution_by_CAS := timelimit(the_time_limit,:-dsolve([ode1,y(0)=0],func,singsol=all)):
result_of_ode_test := timelimit(the_time_limit,:-odetest~([solution_by_CAS],ode1)):

advisor:=timelimit(the_time_limit,DEtools:-odeadvisor(ode2)):
solution_by_CAS := timelimit(the_time_limit,:-dsolve([ode2,y(0)=0],func,singsol=all)):
result_of_ode_test := timelimit(the_time_limit,:-odetest~([solution_by_CAS],ode2)):

advisor:=timelimit(the_time_limit,DEtools:-odeadvisor(ode3)):
solution_by_CAS := timelimit(the_time_limit,:-dsolve([ode3,y(1)=0],func,singsol=all)):
result_of_ode_test := timelimit(the_time_limit,:-odetest~([solution_by_CAS],ode3));


And here is a movie (this time it happend on second run) sometimes it happens on first run. so it is random.

 

Maple 2020.1

Why does it happen and is there a work around?

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