nm

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These are questions asked by nm

I am translating old Maple code to run on Maple 2021.2. This code from 1985. I think it was Maple 3 then. I'll put a link to the paper and page number.

It uses this syntax

Btw, the " above is meant to be % in new Maple. I do not know what w='@W' is supposed to translate to.

The paper is

A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

by  Carolyn J. Smith.

Here is the link

https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf

The above is at page 67. Near the end.  The code also uses some old functions, which are not given in the listing, I searched but could not find these.. One is called Lsolve (to solve linear equations, but I can replace this with solve) and  on page 77 it uses these 

           Functions required: scanmap, expcontract, lncontract, explnsimp

These are not given in the source code in the paper. I assume these are old Maple function which no longer exist?. But I can just use simplify for now in their place.

My question is on the use of `@W` and what it could mean? This syntax @ is used in many places in this old Maple code.

I was trying Maple 2021.2 on this pde I saw on the net, and noticed it gives some error messages. 

Are these to be expected and known?  

interface(version);

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1127 and is the same as the version installed in this computer, created 2022, January 3, 14:33 hours Pacific Time.`

restart;

PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]);
bc := D[2](u)(t,0,y)=0,D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0;
ic := u(0, x, y) = f(x,y);
sol := pdsolve([PDE, bc,ic], u(t,x,y))

diff(u(t, x, y), t) = diff(diff(u(t, x, y), x), x)+diff(diff(u(t, x, y), y), y)

(D[2](u))(t, 0, y) = 0, (D[2](u))(t, 1, y) = 0, u(t, x, 0) = 0, u(t, x, 3) = 0

u(0, x, y) = f(x, y)

Error, (in assuming) when calling '`assume/NormalizeBoolean`'. Received: 'invalid input: type expects 2 arguments, but received 3'

restart;

PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]);
bc := D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0;
ic := u(0, x, y) = f(x,y);
sol := pdsolve([PDE, bc,ic], u(t,x,y))

diff(u(t, x, y), t) = diff(diff(u(t, x, y), x), x)+diff(diff(u(t, x, y), y), y)

(D[2](u))(t, 1, y) = 0, u(t, x, 0) = 0, u(t, x, 3) = 0

u(0, x, y) = f(x, y)

Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid input: has expects 2 arguments, but received 1

restart;

pde := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]);
bc := D[2](u)(t,0,y)=0,D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0;
sol := pdsolve([pde,bc], u(t,x,y))

diff(u(t, x, y), t) = diff(diff(u(t, x, y), x), x)+diff(diff(u(t, x, y), y), y)

(D[2](u))(t, 0, y) = 0, (D[2](u))(t, 1, y) = 0, u(t, x, 0) = 0, u(t, x, 3) = 0

Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid boolean expression: NULL

 

Download pde_error_messages.mw

In this example, i have a top module A. Inside it, I have module named my_RECORD (which happened to be option object) that I want to return back to caller when they call a proc.

Maple allows me to declare the proc to return my_RECORD. No problem., But when making a local variable inside the proc and using o::my_RECORD it complains  that my_RECORD does not exist. 

The solution is to change o::my_RECORD to o::A:-my_RECORD

My question why it did not complain the same way on the return value on the proc?   for me, they are both semantically the same. One says the proc returns this type, and the other says the local variable is this type. So why had to do A:-my_RECORD on one but not the other? 

Here is an example. Maple 2021.2 on windows 10.

restart;

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

3

A:=module()
 #this is the RECORD to return
  local module my_RECORD()
   option object;
   export data::string:="";
  end module;
   
  export do_analysis:=proc()::my_RECORD;   
    local o::my_RECORD; #error here. But this is the same above line above?    
    o:=Object(my_RECORD);
    o:-data:="test";
    return o;        
  end proc;
end module;

_m2642451182336

A:-do_analysis()

Error, (in do_analysis) type `my_RECORD` does not exist

#FIXED BELOW
restart;

A:=module()
    #this is the RECORD to return
    local module my_RECORD()
        option object;
        export data::string:="";
    end module;
   
    export do_analysis:=proc()::my_RECORD;
          local o::A:-my_RECORD;    
          o:=Object(my_RECORD);
          o:-data:="test";
          return o;        
    end proc;
end module;

_m2642339719872

A:-do_analysis()

module my_RECORD () export data::string; option object; end module

 

Download A_no_lib.mw

I do not understand why  simplify(eq,size,assume =t::real); gives an error but simplify(eq,size) assuming t::real; does not.

Which is the correct way to use assumptions with simplify? Inside or outside? And why would it make a difference?

Maple 2020.2 on windows 10.

interface(version);

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1122 and is the same as the version installed in this computer, created 2021, December 22, 16:3 hours Pacific Time.`

restart

eq:=t = 1/2*Int(1/ln(exp(t^2-2*t*y+y^2))^(1/2)/exp(t^2-2*t*y+y^2)/(exp(t^2-2*t*y+y^2)-1),exp(t^2-2*t*y+y^2))+c[1];
simplify(eq,size,assume =t::real);
 

t = (1/2)*(Int(1/(ln(exp(t^2-2*t*y+y^2))^(1/2)*exp(t^2-2*t*y+y^2)*(exp(t^2-2*t*y+y^2)-1)), exp(t^2-2*t*y+y^2)))+c[1]

Error, (in assuming) when calling '`anonymous procedure called from tools/recurse/indets`'. Received: 'invalid input: `simplify/int/simplify` expects its 3rd argument, r, to be of type {name, list({range, name = range}), name = anything}, but received exp((t-y)^2)'

simplify(eq,size) assuming t::real;

t = (1/2)*(Int(1/(ln(exp((y-t)^2))^(1/2)*exp((y-t)^2)*(exp((y-t)^2)-1)), exp((y-t)^2)))+c[1]

 

I know the above inert int looks strange, but this is why it is inert. Later on there will be change of variable to make the integration variable a single symbol again as in normal integration usage.

Download simplify_error.mw

Correction

Please ignore this question. dsolve does hang, but I had typo in the timelimit command itself when I wrote the test. Fixing this, now it timesout OK.

Maybe someone can look why dsolve hangs on this ode. But since timelimit does work, there is a workaround.

Original question

I was checking Maple's dsolve on this textbook problem

The book gives the answer in the back as

When using Maple's dsolve, I found it hangs. The stange thing, is that adding timelimit() also hangs. I can understand dsolve() hanging sometimes. But what I do not understand is why with timelimit it also hangs?

I've waited 20 minutes and then gave up. As you see, the timelimit is 20 seconds. May be if I wait 2 hrs or 20 hrs or 20 days, it will finally timeout. I do not know but can't wait that long.

Do others see same problem on this ode? Does it hang for you? How about on the mac or Linux?

During this time, I see mserver.exe running at very high CPU. I restarted Maple few times, but this did not help.

Maple 2021.2 on windows 10. May be one day Maplesoft will fix timelimit so it works as expected. 

interface(version)

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1122 and is the same as the version installed in this computer, created 2021, December 22, 16:3 hours Pacific Time.`

restart;

ode:=x*diff(y(x),x)=y(x)*cos(ln(y(x)/x));
try
   timeout(20,dsolve(ode));
catch:   
   print("timedout");       
end try;   
print("OK");

x*(diff(y(x), x)) = y(x)*cos(ln(y(x)/x))

 

Download test_ode_hang.mw

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