Consider the following system of differential equations

sys := diff(y(x), x) = z(x)*f1(i), diff(z(x), x) = y(x)*f2(i)

where f1 and f2 are functions that depend on the current iteration. Ultimately, I'd like to index into an array that has the length of the number of iterations, to obtain a value that will be part of the differential equations. It's an array of random numbers, but I'd rather not have to generate them on the fly while dsolve is working.

I've been investigating the use of Events for this, but the documentation is quite atrocious and outdated (and I only know this because, for example, when I try to use certain arguments to dsolve some error messages show that the arguments have changed name)

I've read the documentation on events, and as far as I can tell after an hour or two, I am doing exactly what is in the documentation but not getting the expected result.

Here is a worksheet illustrating the issue: dsolve_events.mw

Basically there is a very simply system of two differential equations and I would simply like to see an event triggered when the dependent variable is above 2. 

This event has no useful interpretation, it was just my attempt at trying to get something to trigger (I have tried multiple things). As far as I can tell from the docs I am using an event specification of form 

[0, c(t,y(x)) < 0]: discrete event with a conditional trigger

ie, [0,2-x<0]

and when that is triggered I set i(x) to something like i(x)+1 (but even something as simple as assigning it to some constant like 7, given that the initial value i(0)=0, would allow me to check when the event is being triggered), where i(x) is defined as a discrete variable (my ultimate goal is to trigger the event on every iteration and have i be the iteration counter. I want to use this iteration counter in the equations)

I run the dsolve command, assign the result to a variable p and then call, for example p(3). I would expect to see the event triggered and i(3) not equal to the initial value i(0). But the value of i(x) doesn't change.

The following example shows clearly that timelimit is still broken in Maple.

I tried this 10 times, and it hangs each time. I could wait 30 minutes and it still hangs. timelimit simply does not work. I set timelimit to 20 or 30 seconds.  This really makes developing software in Maple very difficult when timelimit itself hangs as it means the whole program comes to halt and becomes frozen and I see no workaround this problem.

Does this hang on your version of Maple? I am using 2022.2 on windows 10.

I was hoping this problem with timelimit has finally been fixed in Maple 2022.2. From this post almost 2 years ago!  it says

"You will also be pleased to know that Maple 2021 addresses the timelimit() issue that you mentioned."

But it is clearly not yet fixed.

Some important observations

1) sometimes I noticed if timelimit is small (say 5 or 10), it does not hang. So it the above does timeout for you, please try with larger time out, say 40 or 60 seconds. Since it depens on how fast the PC is.

2)sometimes I  noticed if I close Maple and start new sesstion, the very first time it could timeout OK, but the second time it is called, it hangs. May be because the server caches something to cause this.

All this means, it is completely not predictable what wil happen when starting the maple run. I have no idea how long it will take from one time to another, or even if it will hang or not. For all the years I used Maple, I never had one single time where one run completed without having to restart it at least 2 or 3 times in order to reach the finish line.  This is in addition to all those server.exe crashing on its own many times in between. I noticed more and more of these in Maple 2022.2.  But that is for another topic.

The following screen shot showing one instance when I run the above timelimit (been wainting now for 15 minutes, using timeout of 30 second)., It shows Maple server taking 81% of the CPU

And the following is screen shot of the worksheet itself when I took the above screen shot

Download timelimit_hangs_on_odeadvisor.mw

I have an expression and I want to find its maximum value.

expr:=sin(sqrt(3)*t)*cos(sqrt(3)*t)*(sqrt(3)*cos(sqrt(3)*t) - sin(sqrt(3)*t))/3

It is easy to find its maximum value in a numerical form.

Optimization:-Maximize(sin(sqrt(3)*t)*cos(sqrt(3)*t)*(sqrt(3)*cos(sqrt(3)*t) - sin(sqrt(3)*t))/3)

[0.324263244248023330, [t = 1.39084587050767]]

The images of the expression is as follows.

But does it exist an acceptable maximum value in symbolic form?  As the function maximize seems to take a lot of time, I don't see any hope so far. Perhaps the expression is indeed complex.

maximize(expr)# it runs long time.

We try to find the derivative of expr and get some points where thier derivatives are 0.

s:=[solve(diff(expr,t),t)]
evalf~(s) # Some solutions seem to have been left out.

[0.7607468963 + 0.*I, -0.4229534936 - 0.*I, 0.2668063857 + 0.*I]

ex:=convert(expr,exp):
s:=[solve(diff(ex,t)=0,t)]:
s1:=evalf~(s);# choose the 6th item: 1.390845877 + (4.655829150*10^(-9))*I
fexpr := unapply(ex, t);
evalf(fexpr(s1[6]));
fexpr (s[6]); # a very long expression that is not quite acceptable.

-I/6*(-sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44))/(6*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)) + 6*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)/sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44)))*(-sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44))/(12*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)) - 3*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)/sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44)))*(sqrt(3)*(-sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44))/(12*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)) - 3*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)/sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44))) + (-sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44))/(6*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)) + 6*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)/sqrt(-(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3)*((1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3)*sqrt(3)*I - 2*I*sqrt(3)*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) + (1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(2/3) + 36*I*sqrt(3) + 2*(1404*I*sqrt(3) - 1396 + 36*sqrt(-3018 - 3018*I*sqrt(3)))^(1/3) - 44)))*I/2)

An interesting problem is that an acceptably concise expression (although it is very subjective) for the maximum value may not exist mathematically. But knowing this in advance is difficult.

Download compute_zlc.mw

During my reaserch on diffusion I am arrived at the integral with argument

exp(-1/sqrt(x^2 + 1)) which Maple is not able to solve.

If some experts in solving integrals is able to solve it please keep me informed.

The file in Maple 2022 is below

primes_integral_diffusion.mw

Procedure returns two values. I would like to print a comment after them if possible, without it being a returned value

foo := proc(a, b) 
local x, y; 
x := a^2 - b; 
y := b^2 - a; 
# return x,y, "test on foo"  # returns 3 values
return x, y, print(" tests on return"); end proc;

A, B := foo(6, 3);
                       " tests on return"

                         A, B := 33, 3  #would like "tests on return here"

I was trying New-Display-Of-Arbitrary-Constants-And-Functions- but found a small problem.

in my code I build the constants of integrations using parse("_C"||N); where N is an integer that can go up to as many constants of integration are needed. For example, for 4th order ode, there will be 4 of them.

I noticed only the first 2 come out using the nice c__1,c__2 notation, but anything after 2 ,they come out using old notation _C3, _C4.

Here is a MWE

So now my solution comes out with mixed looking constants. Why does this happen for N>2?

Download problem_with_C.mw

So for now, I went back to using the old method of using alias as follows

Download problem_with_C_alias.mw

conjcl := proc(k, p, n) local t, L, q; L := []; t := 0; q := p^n - 1; while k*p^t <> k mod q do t := t + 1; L := [op(L), t mod q]; end do; return L; end proc

I'm fairly new to coding with Maple / in general, but basically for my course I need to do the following:
For each t=0,1,... I need to first check if kp^t = k mod (p^n-1), and if it isn't, I compute t mod (p^n-1) then add it to my list. The problem I have is I just can't seem to get it to work. I incliuded both the screenshot of the code and typed it out. Thanks in advance

The attached worksheet contains expressions that cause a warning message to appear in my worksheet.  In another post it was suggested that the variable i should be explicitly declared local in the definition of the arrow expression. However, as shown in the same worksheet, this gives rise to an error message. Subsequently, I found a statement in help that suggested this approach would not work in 2-d math notation.  Are there any other ways of eliminating these warnings in 2-d math notation?

warningmessage.mw

In a Maple session I have several worksheets open. When I click on the close cross of a worksheet tab the following can happen:

Closing the worksheet next to it works as normal

This occurs irregularly. For far I could not make it reproducible to report it to Maplesoft support. Anyone has seen something like this or ideas what the cause could be? 

Is this new in Maple 2022.2 or was it there before? I have no way now to verify. Could someone please check? I am not using assuming anywhere, so this must be internal.
 

Maple 2022.2 on windows 10

Download dsolve_nov_10_2022.mw

This integral produces very large result and division by zero when simplified. I do not have earlier version of Maple to check if this is a new problem or not

f:=1/(3*u^(2/3)+3*((-4*u^(1/3)+1)*u^(4/3))^(1/2)-12*u);
anti:=int(f,u);
MmaTranslator:-Mma:-LeafCount(anti);
simplify(anti)

For reference, this is Mathematica's results with leaf count only 35 instead of 41,385 and no problem when simplifying.

f=1/(3*u^(2/3)+3*((-4*u^(1/3)+1)*u^(4/3))^(1/2)-12*u)
anti=Integrate[f,u]
LeafCount[anti]
Simplify[anti]

Could someone please check if this fails same way on earlier Maple version?

Here is a worksheet with a system of differential equations

Maple_DE_Example.mw

The system is

where g(x) is a random number generator seeded by x. That is, for the same x, g gives the same result. 

Using the classical method as an option to dsolve, a solution is plotted. Using rkf45, however, there is pretty much always an error that says

Warning, cannot evaluate the solution further right of ...

Why does it work with classical but not rkf45?

I have to take my equations for velocity, acceleration, and height and evaluate them in 4 second intervals and combine them into one table or columns.

The procedures "getCP" which uses "cpsub" (not exported) acts differently inside the package as opposed to them outside it.
In the package it returns a column matrix which is incorrect. Should return a 2 row matrix. They dismantle a polynomial into it's powers and coefficients. I know one cant run the package here. Included are the two procedures and the text of the notepad file to make the package.

Download 6-11-22_Procedures_acting_differently_in_Package.mw