## How to produce a very accurate (and still reliable...

It says that one may specify the number of significant (decimal) digits when performing calculations. However, it appears that setting a higher precision does not yield more satisfactory results. Actually, the recommended solver (in the package) can report that a maximization succeeded, and yet the reported solution can be, in effect, incorrect.

 > restart;
 > kernelopts(version);
 Maple 2023.0, X86 64 WINDOWS, Mar 06 2023, Build ID 1689885
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 (1)
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 (2)
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It is said that the approximate supremum of  is 3e0 (under the assumptions).

```fun:=`assuming`((2*(x+y+z)*(sqrt(y*z*(z+x)*(x+y))/(z+2*x+y\
)+sqrt(z*x*(x+y)*(y+z))/(x+2*y+z)+sqrt(x*y*(y+z)*(z+x))/(y\
+2*z+x))-(9*x*y*z/(x+y+z)+2*(y*z+z*x+x*y)))/(sqrt(x*y*z/(x+y+z))*(x+y+z-sqrt(27*x*y*z/(x+y+z)))),[(x,y,z)>~0]):```

I am not sure if the toolbox performs better. But is there a way to obtain significantly accurate output natively?

## Three Questions: Function defined by derivative, f...

First Question

Let's define a function:

 (1.1)

now define a new function that is the derivative of f.

 (1.2)

g is not what I expected. I expect:

and if i try to calculate g(0), the result is:

 (1.3)

Second Question

I need to define an integral function in which the variable is an integration boundary:

 (2.1)

if I try to calculate :

 (2.2)

how can i do the calculation and display the explicit form of the function, and assign to a name ?

 (2.3)
 Third Question is there a way to write a system of equation in text mode (or math) in the usual math notation with a big curly bracket followed by the list of equation ? graphically similar to the piecewice operator that seems to be not useful for this purpose?

About the first and the second question i read on the web something but i don't understand deeply what is the reason of the behaviour. I would like to understand really that. Thanks a lot.

## Does the internal implementation of Maple keep tra...

In the end of numerics - Mathematica Stack Exchange,  claimed that "I don't know if it also has generalized precision tracking". (Another answer additionally claimed that Mma chooses "significance arithmetic" to track the precision.) So, the question is simple: Does Maple always (automatically) keep track of the accuracy of inexact numbers through a computation?

## This must be a bug in integration...

I beleave this must be wrong - plea

 (1)

 (2)

 (3)

se see attachment !

I am having problems in recreating in Maple Flow 2023 a worksheet I had created in MathCad. Any help greatly appreciated.

## How to display blank value table ?...

Hi,

I want to create two value tables for the functions: the first one with the values (and that's okay), but I want to display a second one that would be blank (without the outputs-Only the first row and first column should be displayed- ). Any ideas? Thanks

TableauValeursInterditesMaple.mw

## How to correctly perform numerical solutions for p...

Can someone kind help me? I encountered two issues when using the pdsolve function in Maple to obtain numerical solutions for partial differential equations. The first issue pertains to setting up the initial/boundary conditions correctly, and the second issue relates to configuring the plotting options. I'm wondering how to modify them in order to run the code correctly and generate the desired plots.

## How do I solve this problem ? Why the graph is not...

MAPLE.mw

 >
 > with(plots):
 > with(plottools):
 > with(DEtools):
 > N:=S(t)+C(t)+In(t);
 (1)
 > eqn1 := diff(S(t), t) = (b-mu*S(t)-beta*C(t)*S(t)+gamma*In(t)*S(t)-mu*C(t)-theta*S(t)), S(0) = ic1;
 (2)
 > eqn2:= diff(C(t),t) = rho*(beta*C(t)*S(t)+gamma*In(t)*S(t))-mu*C(t)-alpha*C(t),C(0) = ic2;
 (3)
 > eqn3 := diff(In(t), t) = (1 - rho)*(beta*C(t)*S(t) + gamma*In(t)*S(t)) - mu*In(t) - pi*In(t) + alpha*C(t), In(0) = ic3;
 (4)
 > b := 0.117852;
 (5)
 > mu := 0.035378;
 (6)
 > g := 0.11;
 (7)
 > rho := 0.05;
 (8)
 >
 > beta := 0.02;
 (9)
 > theta := 0.066;
 (10)
 > pi:=0.9;
 (11)

 > alpha:=0.5;
 (12)
 > ic1 := 2390000;
 (13)
 > ic2:=528;
 (14)
 > ic3:=753;
 (15)
 > dsol := dsolve([eqn1, eqn2, eqn3], numeric);
 (16)
 > odeplot(dsol,[[t,In(t),color=red],[t,C(t),color=yellow],[t,S(t),color=blue]],t=0..100,view=[0..0.001,0..2000000]);
 >

## How define functions with variable numbers of inpu...

Hi,

I think the title of the question speaks for itself.

But, to be more precise, here's an example with a real-valued function which, when it has two real numbers as input, gives the ratio of the first number to the second number, but if it has three real numbers as input, it returns the sum of the first number with the product of the next two numbers...

Thanks.

## Error, (in SolveTools:-Polynomial) too many levels...

I found another big problem.

In 2022, I get Error, (in SolveTools:-Polynomial) too many levels of recursion when using alias(seq(c[k] = _C||k, k = 0..10)); at the top of my code and the solution to the ode has c[2],c[3] etc.. as constants of integration.

This solution was given by Kitonum in this answer

I had this for years in the code (i.e. the alias) code.

In Maple 2022 the following gives the above exception error from odetest. I am using 2022, because in 2023 it just hangs on the same code.

If I remove the alias code, no error shows. (solution is wrong, but that is different story).

Also, If I remove the alias code, 2023 no long hangs!

 > restart;
 > #kernelopts('assertlevel'=2):
 > alias(seq(c[k] = _C||k, k = 0..10));

 > ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+12*y(x) = 80*sin(2*x); sol:=y(x) = -10*exp(-1/2*2^(1/2)*arctan(sin(2*2^(1/2)*x)/cos(2*2^(1/2)*x)))*(c[3]*cos(2*2^(1/2)*x)+c[2]*sin(2*2^(1/2)*x))*((-1/10*exp(4*I*2^(1/2)*x)+1/10)*c[2]-1/10*I*c[3]*exp(4*I*2^(1/2)*x)-1/10*I*c[3])/((exp(4*I*2^(1/2)*x)-1)*c[2]+I*c[3]*exp(4*I*2^(1/2)*x)+I*c[3])*c[1]-10*I*exp(-1/2*2^(1/2)*arctan(sin(2*2^(1/2)*x)/cos(2*2^(1/2)*x)))*(c[3]*cos(2*2^(1/2)*x)+c[2]*sin(2*2^(1/2)*x))*(cos(2*x)-sin(2*x))*exp(2*I*2^(1/2)*x)*exp(2*I*2^(1/2)*x)^(-1/2*I*2^(1/2))/((exp(4*I*2^(1/2)*x)-1)*c[2]+I*c[3]*exp(4*I*2^(1/2)*x)+I*c[3]); odetest(sol,ode);

Error, (in SolveTools:-Polynomial) too many levels of recursion

 >

Why using the alias line above causes this error?  If you remove the alias line, you will see it completes with no error.

But it hangs in 2023. I am no longer using 2023 but went back to 2022 due to too many hangs in 2023. I wonder now if it because of this alias line I had there all the time.  I will remove now and see if this solves some of the hangs I had in 2023.

Anyone can shed some more light on what is going on?

Windows 10.

## solve linear system ...

Dear all

I have a linear  system with four equations,  I used solve to get the result but unfortunately nothing returned

linear_system.mw

Thank you

## LibraryTools and obtaining list of all modules in ...

I can't figure how to obtain list of all modules inside my .mla file.

I can see all the modules using the command LibraryTools:-Browse("..../my_file.mla") then clicking EDIT then VIEW option at top right corner.  Member type is automatically set to MODULE in the lower left corner. So I can see the names of all the modules. And using the slider, I can scrol down. I see 73 modules listed.

But I want to do this in code. Not using GUI.

I tried the command

L:=LibraryTools:-ShowContents(my_file.mla):

And this gives L of lenght 15805. Looking at each entry in the above list, it shows things I do not understand and I do not want. It has names in there which I do not know where these came from.

There does not seem to be an option in LibraryTools:-ShowContents() to only return the names of the modules inside .mla. At least I can't find such option.

reference Maple help page

Any idea how to do this in code? Not using the maplet?

Maple 2022 on windows 10

ps. I know I can use the GUI and do EXTRACT to save the list to a file. But this is not good solution. I need the list of names of the modules be in a list so I can do this all in a function with no manual steps.

## guidance on how to write code?...

Hi,
Can someone guide me on how to write the code for this program?

sh.docx

## command to list names of all procs in module?...

Does Maple have a command to list all names of all procs (local and exported) given a name of module?

There is a question/answer here which shows how to list all procs in module. But I only want the names.

The reason I am asking, I am trying to see if I can code

trace(moduleA:-proc1,
moduleA:-proc2,
moduleB:-proc3,....,
moduleE:-proc1000,
statements = false)

Before running my programming in order to turn tracing on. The problem is that there are 1,000's of proc's in dozens of modules so I need a way to obtain a sequence of the names all such procs automatically each time.

Once I figure how to do it for one module (say moduleA), I will apply this to the other modules I have and collect all names in one long sequence and see if this will work.

Any suggestion how to do this?  I now have all my modules inside one .mla file if it helps. They are all build ito this .mla from source tree of dozens of .mpl files.

Maple 2022 on windows 10

## option trace, how to only display ENTER and EXIT m...

When adding option trace: inside a proc, Maple display trace of all assignments. I only want to see the --> enter  and <-- exit messages,.

I can't figure how to do that. Any suggestions?

Maple 2022 on windows

 > restart;
 > A := module()  export foo:=proc(n,m,k)       option trace:    local r;    r:=n:    B:-boo(r);  end proc: end module: B := module()  export boo:=proc(n)    option trace:    local k;    k:=n;    RETURN();  end proc: end module:
 > #kernelopts(tracelineinfo=2); #printlevel := 10: kernelopts(traceincidentalassign=false): kernelopts(tracesplitmulassign=false): kernelopts(traceshowspecassign=false): kernelopts(traceincidentalassign=false): kernelopts(tracesplitmulassign=false): kernelopts(traceshowspecassign=false): kernelopts(tracelineinfo=0): A:-foo(1,2,diff(y(x),x)=sin(x))

{--> enter foo, args = 1, 2, diff(y(x), x) = sin(x)

{--> enter boo, args = 1

<-- exit boo (now in foo) = }

<-- exit foo (now at top level) = }

 >