with your help i solved ODE for Elziki transform ...but now i am facing some issues for PDE...elziki transform is like laplace ...but having 1/v in product...if any one can solve pde for laplace ... then please help me out.pde_elziki.mw

I was tasked updating an old maple program (written +20 years ago using Maple version 3 I believe) and came across a line I'm unsure the meaning of. The line is: beta := [rhobar2$rowdim(A)]:

rhobar2 is the square of the mean of a data set and A is a Matrix with 3 columns and 12 rows. I'm just unsure what the $ operator is or is doing to the data. Any help would be appreciated. I'm new to this, sorry if this seems trivial.

hi, do you know how can we smooth this ellipse and make it more clear?

thickness, grid, numpoints don't help

restart;
with(plots);
f := (x, y) -> x^2 + y^2 - 12*x + 16*y;
display(plot3d(f(x, y), x = -9 .. 9, y = -9 .. 9), pointplot3d([[6, -8, f(6, -8)]], color = red, symbol = solidcircle, symbolsize = 18), view = [-4.2 .. 8.2, -8.2 .. 4.2, -100 .. 100], plot3d([cos(t), sin(t), 1 - 12*cos(t) + 15*sin(t)], t = 0 .. 2*Pi, orientation = [-15, 68, 5]));
 

Let (C):f(x)=1/(x^2-2x).Find the equation of the circle touching the graph  at three points?

Hi 

As the titel states: It is possible to create a asymptotic bode plot in maple?

I know how to do a normal bode plot with the DynamicSystem package. But is it possible to get a straight line approximation/ asymptotic bode plot instead?

I discovered the MRB constant (CMRB) while using Maple. Since then, I've found many formulas related to it, including its integrated analog the MKB constant (MKB). They're both found in Google scholar!

However, I am stuck on proving the following.

Also prove the above equation, ReMKB+NoMKB-CMRB=0.

All my similar proofs are found at

https://www.mapleprimes.com/posts/214522-Formulas-For-The-MRB-Constant?sp=214522

Dear Users!

Hope everything going find with you. I want to generate sequence of Spline[i,p], p=1…M as given bellow

restart; M := 3;
for p while p <= M do
(x-x[i])*B[i, p-1]/(x[i+p]-x[i])+(x[i+p+1]-x)*B[i+1, p-1]/(x[i+p+1]-x[i+1]);
B[i, p] := collect(%, [`$`(B[i+s, 0], s = 0 .. M)]);
B[i+1, p] := eval(%, i = i+1)
end do;
for p while p <= M do
Spline[i, p] := B[i, p]
end do

The expression for Spline[i,1] and Spline[i,2] are fine but the expressions of Spline [i,p] p>2 is not in simplified form I got the its simplification like given bellow for Spline[i,3]

Spline[i, 3]:=(x-x[i])^3*B[i, 0]/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+1]-x[i]))+(((x-x[i])*(x-x[i]))*(x[i+2]-x)/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+2]-x[i+1]))+(x-x[i])*(x[i+3]-x)*(x-x[i+1])/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1]))+(x[i+4]-x)*(x-x[i+1])^2/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1])))*B[i+1, 0]+((x-x[i])*(x[i+3]-x)^2/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+(x[i+4]-x)*(x-x[i+1])*(x[i+3]-x)/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+((x[i+4]-x)*(x[i+4]-x))*(x-x[i+2])/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+3]-x[i+2])))*B[i+2, 0]+(x[i+4]-x)^3*B[i+3, 0]/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+4]-x[i+3]));

I am waiting for positive respone. Please take care and thanks in advance

timelimit() has improved in Maple 2021, and I thought it works now for everything. 

https://www.mapleprimes.com/maplesoftblog/213986-Introducing-Maple-Learn-officially#comment204444

But unfortunately,, it still hangs on some dsolves when I was testing something. Here is an example

restart;
ode:=(y(x)^4-a^2*x^2)*diff(y(x),x)^2+2*a^2*x*y(x)*diff(y(x),x)+y(x)^2*(y(x)^2-a^2)=0;
timelimit(60,dsolve(ode,y(x)))

The above has one minute timeout. But its been running for 20 minutes now. Here is another example that hangs

restart;
ode:=(diff(y(x),x) = (-y(x)^2+4*a*x)^3/(-y(x)^2+4*a*x-1)/y(x));
timelimit(60,dsolve(ode,y(x)))

I have found many more dsolve examples that hang with timelimit. Will update later. May be they will help find the cause.

Hopefully this timelimit issue will be fixed in some future release.  hangs in Maple commands even when using timelimit makes it very hard to run long scripts that run over many problems, since do not know when/where it will hang and have to restart and clean things manually each time.

Window 10. Maple 2021

Update March 15,2022

Here is another example of timelimit taking so much longer than asking for, it is pretty much useless.

I will use this question to collect such examples in one place. Here I asked for one minute (60 seconds, CPU time) timeout. Maple actually timedout after using 1381 CPU seconds which is 23 times as much as requested.

Download timelimit_example_march_15_2022.mw

Help says

The timelimit function evaluates the expression x, but gives up if the evaluation takes longer than the number of seconds specified by t.
Note: In some cases, the execution may not abort at exactly the time limit imposed, but will abort as soon as it can do so safely.  This can happen when execution is in critical sections of certain built-in routines.

For me, the above makes no sense at all. What does "as soon as it can do safely"? I am not running the code to control an airplane flight full of people here. This is some code running on my PC at home to do some calculation. It can abort right away. It will not hurt me physically or hurt my PC to do so. 

So what does "do so safely" actually mean? Safety of what exactly?

Compare the above example to Mathematica where it times out at almost exactly to the requested timeout. Here I ask for 3 seconds timeout

I am not asking for exact timeout. But asking for 1 minute timeout and getting 8 minutes is not good at all.

1.5 minutes is OK. even 2 minutes is OK. 

I have more examples to add. But will do that later.

Update

Quick try with Maple 2022 shows timelimit has much improved. Here are 3 examples from above. First one asks for 60 seconds limit, it finishes in 288 seconds.   Second one asks for 60 seconds, it finishes in 96 seconds. Third one asks for 60 seconds and finishes in 73 second.

This is much much better than in Maple 2021. Thanks for the Maple engineers who improved this.

Download better_time_limit_with_maple_2022.mw

Download system.mw

Download system.mw

Solving a system of equations

I want to solve the following system (please see the code) for small even N=4,8,16. They said that the roots lie on the lines Im x_i = ±π/2 and they are symmetric with respect to the imaginary axis. For N=4, I tried with fsolve directly but the roots are:

 x[1] = -3.799588601-1.570796327*I,

 x[2] = -3.799588601-1.570796327*I,

 x[3] = .1196098914-1.570796327*I,

 x[4] = 1.110549099-1.570796327*I

these solutions are not valid because half of them should have +π/2 as an imaginary part, and they should be mutually distinct and also symmetric with respect to the imaginary axis. Therefore, for N=4  I am expecting solutions of these form :

x[1] = a_1-I* π/2,

x[2] = -a_1-I* π/2,

x[3] = a_1+I* π/2,

x[4] = -a_1+I* π/2,

I tried with fslove({system}, {Im(x[1]) = .5 .. 1, Im(x[2]) = .5 .. 1, Im(x[3]) = -1 .. -.5, Im(x[4]) = -1 .. -.5}) but it does not work! I do not know what should I do to make Fsolve locate the wanted solutions. Thanks in advance!

I found a big problem.

When adding kernelopts('assertlevel'=2): which I like to have it on all the time to catch (actual) errors, but now Maple server hangs then crashes on what should be no issue at all. 

This happens when I am using an object, which is used at global type. Here is a MWE

restart;

interface(warnlevel=4);
kernelopts('assertlevel'=2);

local ode_type:=module()
    option object;
    export ode;
    local ModuleLoad::static:=()->
           TypeTools:-AddType(':-ode_type', ode_type);
    ModuleLoad()       
end module:

A:=module()
  export foo:=proc()
    C:-foo();
  end proc;

  local B:=module()
    export foo:=proc()
      local ODE::ode_type;
      return ODE;
    end proc;
  end module;

  local C:=module()
    export foo:=proc()
      local the_ode::ode_type;  #THIS CAUSES the hang
                                #using the_ode::':-ode_type'; makes no difference
      #DEBUG
      the_ode:=B:-foo();
    end proc;
  end module;
end module;

There is nothing wrong with the above code as far as I can see. But now A:-foo(); crashes the Maple server.

If I change the line local the_ode::ode_type; to local the_ode; i.e. remove the type on the local variable, it works.

So assert thinks the type being returned is not ode_type

It also works if I remove the assert and keep the type there. Like this

restart;

interface(warnlevel=4);

local ode_type:=module()
    option object;
    export ode; 
    local ModuleLoad::static:=()->
           TypeTools:-AddType(':-ode_type', ode_type);
    ModuleLoad()       
end module:

A:=module()
  export foo:=proc()
    C:-foo();
  end proc;

  local B:=module()
    export foo:=proc()
      local ODE::ode_type;
      return ODE;
    end proc;
  end module;

  local C:=module()
    export foo:=proc()
      local the_ode::ode_type;  #NOW IT WORKS
      the_ode:=B:-foo();
    end proc;
  end module;
end module;

In my actual code, when I remove the kernelopts('assertlevel'=2); I do get correct final output. So it is not like I am bypassing some wrong code or something. The code works as expected.

Now now I have two choices, either remove  kernelopts('assertlevel'=2); or remove the type from the defintion of the local variables, when the type of object defined as above.

edit

another version below. When I copied the code above from my .mpl files to the worksheet to make a MWE, there was a local next to the object module (because that is how it is in my main code), and I did not notice it at first.

When I removed it to make new MWE in the worksheet, an error still shows up. But now Maple server do not hang/crash but it still does not like the assignment being made. So here is another version

restart;
interface(warnlevel=4);
kernelopts('assertlevel'=2):


ode_type:=module()  #note that local ode_type:=module()  crashes Maple.
    option object;
    export ode; #can be list      
    local ModuleLoad::static:=()->
           TypeTools:-AddType(':-ode_type', ode_type);
    ModuleLoad()       
end module:

A:=module()
  export foo:=proc()
    C:-foo();
  end proc;

  local B:=module()
    export foo:=proc()
      local ODE::ode_type;
      return ODE;
    end proc;
  end module;

  local C:=module()
    export foo:=proc()
      local the_ode::ode_type;
      #DEBUG();
      the_ode:=B:-foo();
    end proc;
  end module;
end module;

And now A:-foo(); do not crash the server, but still gives error

     Error, (in foo) assertion failed in assignment to the_ode, expected ode_type, got ODE

Why? since ODE is of type ode_type, and I am returning. Can one not return Object like this? 

Is there something I am doing wrong?

is it possible for a string such as "res:=boo()" to be evaluated after calling parse, and have res have the value that the function boo() returned?

Now, it does not work. I must do   res:=eval(parse("boo()")) , meaning the result of the call to boo() is outside the string.

Here is an example of what I mean

boo:=proc()
   return 99;
end proc;  

foo:=proc()
  local s,res,i;
  s:="res:=boo()";
  eval(parse(s)):
  print(res);
end proc;

foo();

The above does not work. It displays res but this works

boo:=proc()
   return 99;
end proc;  

foo:=proc()
  local s,res,i;
  s:="boo()";
  res:=eval(parse(s)):
  print(res);
end proc;

foo();

The above works, and prints 99.

The reason I am asking, is that I was thinking of storing in a data base the complete Maple command as string, along with the LHS of the call, and just load the string the evaluate it, and it will have res automatically set.

It is no problem if this can't work, I could always just eval the command itself, without the assignment being there. Just thought to ask if there is a way.

I have about 30 modules under one root common module.  The total code is about 25,000 lines.

Currently during development, when I change a line of code and want to run a test, I just do

interface(warnlevel=4);
kernelopts('assertlevel'=2):
read   "my_root_module.mpl";
#run some test 

From a worksheet. This works fine, but it is very slow. it takes now about 8-10 minutes to finish each time.

So each time I make small change to the source code, which all sit in separate .mpl plain text files, I have to wait and wait for the read to complete.

This is way too slow. 

The thing is, my my_root_module.mpl files includes child modules (using the $include directive), and each child module might also have $include to pull in its own child modules, if any. Each module is onbe separate .mpl file.

So at the end my_root_module.mpl will end up reading all the code, which is now about 25,000 lines over 30 or so modules. Here is an example of the layout I have

my_root_module.mpl
=======
export my_root_module:=module()
$include  "B.mpl"   
$include  "C.mpl"                            
$include  "D.mpl"   
   export foo:-proc()....     B:-foo().... end proc;
end module:

B.mpl
=======
local B:=module()
$include  "B1.mpl"   
$include  "B2.mpl"                            

   export foo:=proc()..... end proc;
end module:

C.mpl
=======
local C:=module()
$include  "C1.mpl"   

   export foo:=proc()..... end proc;
end module:

etc...

There must be faster way to do this. Having to wait about 10 minutes each time to test one small code change each time is not practical.

What do others do when they develope large code in Maple? Is this a typical time?

I do not want to break my main modules into separate name spaces again in order to  use separate mla for each module, so that my changes only affects one mla file.  This will speed things, as I would then only have to rebuild one small modules, the one I changed.

But I want to put all my modules under one common module, which acts just as a common name space, and have only one mla file.

Are there ways to speed  reading mpl file?

Edit

Thanks to all the answers. It turned out indeed to be the slow Maple GUI again. The option interface(prettyprint= 0) did not help in the worksheet to speed the GUI.

I wrote the commands to read the mpl file and build the mla in a file, and used the DOS command line, and turned off the warning messages using DOS option, and now it finished almost instantly.

"C:\Program Files\Maple 2021\bin.X86_64_WINDOWS\cmaple.exe" UPDATE_MLA.mpl 1> nul

    memory used=18.6MB, alloc=73.3MB, time=0.52

Notice, in the above 1>nul will not even display the warning messages on the terminal. 2>nul does not work, since these are not error messages. Here are the different redirection options from the net

But even without using this redirection, and keeping the messages scroll on the terminal, it was still very very fast from the command line

I complained about how slow the Maple Java GUI when it comes to scrolling and how it can can cause  slow down many times before, so will not complain again about. May be one day Maplesoft will fix this.

Hi MaplePrimes team,

I want to create two 3d surfaces with plot3d command in Maple, one of which represents a light-emitting diode (LED).

For that, my idea is simple: Just to disable the shade on a specific surface (representing the LED-like) among other surface. So, whatever the direction of the light, the LED surface keeps a constant luminosity.

Unfortunately, the glossiness = 0 option is still dependent of light direction.

I looked at all the options for plot3d and display commands, but I couldn't find anything for disable light on special surface.

Maybe in PLOT3D command?

If not, is there an option to add a second light source?

Simple example I would like create:

- 1. A surface with regular light:

BALL := plot3d(<cos(t)*cos(s), cos(t)*sin(s), sin(t)>, s = 0..2*Pi, t =-Pi/2..Pi/2, color = "Blue"):

- 2. An illuminated surface representing the LED:

LED := plot3d((<2 + cos(t)*cos(s), cos(t)*sin(s), sin(t)>, s = 0..2*Pi, t =-Pi/2..Pi/2, color = "Yellow", What option to insert?):

Then, the assembly will give:

display(BALL, LED);

My Advanced Applications Tests in Maple

Figure 1: Aisle LED light and LED-screens of first-class seats in an illuminated cabin on board of an aircraft.

Figure 2: Here is the problem in the darkness. The aisle LED light and LED-screen must be stay constantly illuminated for any direction of light.

To better understand my objectives, here is another image using lights. Note that the LEDs (pale yellow strip shapes) stay constantly illuminated whatever the daylight and therefore allowing the aircraft to be visible.

Figure 3: Exterior lighting systems and dazzling jet engine afterburner of a military transport aircraft concept.

Thank you for your time.

Best.

Guy.

Please help to find the exact solution of any ODE by the >sinh or cosh method. I have attached arbitrary ODE here:

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0

I need to get more tickmarks in my plots by reducing the size of fractions produced by Maple.
For example, instead of (3*Pi)/10, Maple gives me (3/10)*Pi. Any help would be appreciated.
I can actually convert all there Maple numbers to fractions, but Maple will not accept these conversions as tickmarks.
Thank you.
mapleatha