dsolve accept system of first order ode's in the form x'=A x, where x' is vector, A is matrix of coefficients and x are the dependent variables. This is convenient since one does not have to convert things to a list.

But  dfieldplot and phaseportrait and DEplot do not accept this form. One must convert things to list first.

Here is an example

restart;
sys:=Vector([diff(x(t),t),diff(y(t),t)]) = Matrix([[1,2],[0,3]]).Vector([x(t),y(t)]);
dsolve(sys)

But

DEtools:-dfieldplot(sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

Error, (in DEtools/dfieldplot) system must have same number of dependent variables as DE's.

workaround is to write the system as list

new_sys:=[diff(x(t), t)=x(t) + 2*y(t),diff(y(t), t)=3*y(t)];
DEtools:-dfieldplot(new_sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

I know one can automate the conversion. But still, it would be better if dfieldplot would accept sys as dsolve did.

Same for 

DEtools:-phaseportrait(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);
#
DEtools:-DEplot(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);

They gives same error.

Since dsolve can do it, may be these other functions can also support taking a system of ode's in vector/matrix form? Any reason why not?

Maple 2021.1

I do not remember if there was a post on this before or not
Maple 2021.1

int(arcsin(x)/(1+(-x^2+1)^(1/2)),x)

gives

Error, (in Utils:-TransformAndApply) numeric exception: division by zero

The correct answer should be

((-1 + Sqrt[1 - x^2]) ArcSin[x])/x + ArcSin[x]^2/2 -  Log[1 + Sqrt[1 - x^2]]

I had to go back to Maple 2018, to get no exception:

May be this could be looked at for next Maple version?

I have plain text file generated, where each line has mixed numbers and strings. Some of the strings are latex. So they have "\" in them. The data is rectangle. same number of fields on each line, separated by commas.  I use CSV format to read the data to Maple.

I simply want to read this file using Import , which reads it into a matrix (using CSV format), and export it back right away using either ExportMatrix or Export and end up with the same exact file.

But Maple always adds extra "\" each time I export the matrix back to the file. So if I have initially "\sin x" in the file, after reading/writing the file 5 times without touching the data inside Maple, I end up with something like "\\\\\\\\\\\sin x" in the file at the end.

I could ofcourse not use ExportMatrix nor Export and write the data back to the file manually using fprintf using correct format for each field. But it is easier if I can get ExportMatrix to work since there are many fields some are integers, some are real and some are strings.

Here is a simple MWE which shows the problem. Originally I have this file on disk. Called test.txt and has 2 lines in it

1,"\sin x"
2,"this is second line"

Now after doing the following

data:=Import("test.txt",format="CSV",output=Matrix):  
ExportMatrix("test.txt",data,target=csv);

The file on disk now becomes

1,"\\sin x"
2,"this is second line"

And repeating the above one more time, the file becomes

1,"\\\\sin x"
2,"this is second line"

This ofcourse breaks all the latex strings in there.

Is there a way to prevent Maple from doing this? I looked at all the options in help, but do not see on so far.  I also tried Export but that did not work at all. So I'd like to see if ExportMatrix can do it, without adding an extra "\", otherwise, will have to use fprintf directly to export the data back to file.

edit

fyi, I ended up using fprintf to write the data back to disk. May be if there is a solution using ExportMatrix, will change back. This is what I ended up doing

File before

1,"\sin x"
2,"this is second line"

Now run this code

data:=Import("test.txt",format="CSV",output=Matrix):  
file_id := fopen("test.txt",WRITE):
nRows:=LinearAlgebra:-RowDimension(data);
for n to nRows do
    if n<nRows then
       fprintf(file_id,"%d,\"%s\"\n",data[n,1],data[n,2]);
    else
       fprintf(file_id,"%d,\"%s\"",data[n,1],data[n,2]);
    fi;
od;
fclose(file_id);

File after

1,"\sin x"
2,"this is second line"

Now the file is exactly the same as before reading it.

My actual data is more than the above two fields, but that makes the format string longer, that is all.

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

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?