This seems like a serious limitation of Maple module, unless I am missing something.

I am trying to refactor one of my module, putting some code in separate .mpl file, say B.mpl,  and then do, from the main module

   $include  "B.mpl"; 

 But Maple complain now that, since B.mpl has export in it, that I can't do that. 

But the code inside B.mpl works fine if I copy it back and paste it inside the module, in the same location where the $include  "B.mpl";  is

Here is an example. (Since I can't use $include  "B.mpl";  in worksheet, Maple does not like it, I replaced it in this example by read "B.mpl";

(btw, both the syntax  module A()   and A:=module() seem to be equivalent), the problem shows up with either form)

I also tried with ";" and witout ";" at the end of the $include , it still gives same error.

restart;

currentdir("....."); #set directory to where the folder is


module A()

read "B.mpl";

 export foo:=proc()
  0;
 end proc;
end module;

Where the file B.mpl is

export boo:=proc()
return 0;
end proc; 

How is one supposed to refactor long file to separate files if can't leave export on those proc's?  

If I put everything in one .mpl file, it works

module A()

#read "B.mpl";  

export boo:=proc()  #this proc was in B.mpl
return 0;
end proc; 

 export foo:=proc()
  0;
 end proc;
end module;

I did more testing, and found that this seems to be an issue in Maple 2020.2. Because I just tried the same thing in Maple 2019 and it worked there ! i.e. no error.

Any one knows what is going on? 

Maple 2020.2, Physics 884.   Windows 10.

Here is screen shot. Same code. Works OK in Maple 2019.2 but gives error in 2020.2

I'd like to define a proc, which takes first argument to be either an ode (i.e. type `=`) or set of ode's, or list of ode's.

However, I do not know how to tell Maple that the list or set, if that is the type, to be a list of `=` and no other type.

Here is what I tried to make it more clear

If I do this

restart;

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


foo:=proc(ode::{`=`, set,list},func::`function`,$)
   print("ode=",ode);
   print("func=",func);
end proc:

Then Maple will check that the first argument is ANY one of `=`, set or list. 

But does not check if the list or set contains only equations of type `=`.  So I am able to call the above like this

ode1:=diff(y(x),x)=1:
ode2:=diff(y(x),x)=x:
foo(ode1,y(x));  #this is OK
foo([ode1,a],y(x))  #this is wrong

Which is wrong, since `a` is not of type `=`.

Next I tried this (I also wanted to check that if first argument is list or set, that it is not empty, so added extra check)

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

foo:=proc(ode::{`=`, 
                   And(set,satisfies(x-> (numelems(x)<>0 and type(x,`=`))  )),
                   And(list,satisfies(x-> (numelems(x)<>0 and type(x,`=`))  ))
                   },
                   func::`function`,$                                   
                   )

  print("ode=",ode);
  print("func=",func);
end proc;

But the above gives an error

ode1:=diff(y(x),x)=1:
ode2:=diff(y(x),x)=x:

foo([ode1,a],y(x))  

I also tried

foo:=proc(ode::{`=`, 
                   And(set,satisfies(x-> type(x,`=`)  )),
                   And(list,satisfies(x-> type(x,`=`) ))
                   },
                   func::`function`,$                                   
                   )

   print("ode=",ode);
   print("func=",func);

end proc;

Also gives erorr when called 

foo([ode1,ode2],y(x))

Ofcourse, I can just leave the check as in first case above, and in the proc itself, do the check myself manually by going over each entry in the list or set to make sure each entry is of type `=`. 

But I wanted Maple to do this work for me, if possible.

What is the correct syntax for doing so?

Maple 2020.2

why setting interface(warnlevel=0); makes dsolve change the form of the final solution to an ODE?

Is this to be expected? Help on warnlevel 0 says to just suppress all warnings. 

In this example, both solutions are equivalent. One is just simpler than the other.

But now I am worried if this setting could affect dsolve in other ways not yet anticipated.
 

Download warnlevel_difference.mw

btw, the same thing happens with warnlevel 2. i.e. answers look different.

But with warnlevel 3 and 4, now dsolve gives the same answer. 

SInce it seems default is warnlevel 3, it seems internally, dsolve takes different path depending on warnlevel setting? 

Edit

Here is a movie. I am using windows 10.

Edit: Here is another video. Tried now with fresh start of Maple. i.e. closed Maple and started it again.  Using worksheet. No other worksheet was open. This is what I found. Initially it gives the longer solution. After couple of tries, it then changed to the simpler one

Hello Maple experts;

We've talked about this subject before. odetest not verifying dsolve output. And very useful input was given:

https://www.mapleprimes.com/questions/227546-How-To-Make-Odetest-Verify-Dsolve

https://www.mapleprimes.com/questions/227638-How-To-Make-Odetest-Give-Zero-On-Its

Here, I thought to give a collection from my ode database of ode's that are solved by Maple, but odetest does not give zero, all in one place. 

I know this is a hard problem to get odetest to always verify its own solution. May be each case needs custom solution?

It would be nice if this area in Maple could be improved on more if possible (Maple is already a CAS leader in solving ODE's).

If some of the experts here like to see if they can get odetest to give zero on some of these examples, they are welcome to and will be useful to see. I only tried just simplify().

I depend on odetest to tell me if my solution is correct or not, and getting false negative makes me spend more time trying to find where my error in my solution, where there might be no error there, and it is just that odetest could not verify it.

These are all from different text books. I put the reference on each ODE where it was obtained from.

Two of these ODE can also hang or take very long time. I indicated that there so one might want to skip these two.

edit added new one, #1822, uploaded new worksheet

edit 12/23/2020

Found one more.

#3647
restart;
ode:=diff(y(x),x)=2*(x*sqrt(y(x))-1)*y(x);
ic:=y(0)=1;
sol:=dsolve([ode,ic]);
odetest(sol,ode);

The above becomes zero only for x>-1 

ps. I added this to the worksheet, but since upload now does not work, did not re upload so not to lose the display above. Will do that later when it is working.

edit 12/25/2020

Found one more.

#3607
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 19.

restart;
ode:=1/2*diff(y(x),x) = (y(x)+1)^(1/2)*cos(x);
ic:=y(Pi)=0:
sol:=dsolve([ode,ic],y(x)):
res:=odetest(sol,ode);

edit 12/26/2020

Found one more

#3613
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 26.

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
res:=odetest(sol,ode);

PDEtools:-Solve(res=0,x) assuming real;

edit 1/10/2021

Found one more

#2406
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Problem number: 406.

restart;
ode:=(x^3+1)^(2/3)*diff(y(x),x)+(y(x)^3+1)^(2/3) = 0;
sol:=dsolve(ode,y(x));

check:=simplify(odetest(sol,ode));  #tried other simplication, can't get it to zero. But sol is correct

Download examples_of_odes_that_do_not_odetest.mw

What do folks think about adding \, space automatically after Maple's Latex output for sqrt command?

This is all using the new Latex command. Not the orginal latex() command.

For me, it looks much better. I did some tests, and see no negative effect by always adding \, at the end of \sqrt{}

The reason is this: If there is a symbol after sqrt(.....)<HERE> then the math looks like the symbol is almost inside the integral, when it should be out. By adding \, this makes it more clear and better looking.

It is possible to write macro in Latex to do this in preamble I suppose. But if it can be done in the source, then that will be much better as it will always be there without the need to write complicated macro to change it later in Latex. 

Here are 4 expressions to compare

One can see the current problem area and the effect of adding \, automatically. The space was added for each case above in the second column, even for those where it was needed (second and third expressions) to show that adding space has no negative side-effect even when not needed.

Here is the above raw latex used, compiled on Tex Live 2020 on Linux,  and the Maple worksheet below that.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{longtable}
\usepackage{mleftright}  
\mleftright

\begin{document}

\begin{longtable}{|p{3in}|p{3in}|}\hline
Default. No space after & With space added after\\\hline 
\[
\sqrt{\left(3+x \right)^{2}+1} a +\sin \left(x \right)
\]
&
\[
\sqrt{\left(3+x \right)^{2}+1}\, a +\sin \left(x \right)
\]\\\hline 
\[
\frac{\sqrt{\left(3+x \right)^{2}+1}}{5}+b
\]
&
\[
\frac{\sqrt{\left(3+x \right)^{2}+1}\,}{5}+b
\]\\\hline 
\[
\frac{\sqrt{x}}{5}+b
\]
&
\[
\frac{\sqrt{x}\,}{5}+b
\]
\\\hline 
\[
\frac{\sqrt{x^{2}+6} c}{5}+b
\]
&
\[
\frac{\sqrt{x^{2}+6}\, c}{5}+b
\]\\\hline 
\end{longtable}

\end{document}

(typo, should be sqrt, not int)

Download space_after_int.mw