When giving invlaplace an input with an Inert integral (becuase it can not be evaluated), it sometimes return 
              Error, (in depends) malformed integral

But sometimes it returns the inverse Laplace of the unresolved integral, which is the expected result.

In both cases, it should just return  inverse Laplace of the unresolved integral.

Below is worksheet showing such case.

Download malformed_intergal_dec_7_2024.mw

Just reported to Maple support also.

The determinant of a 10*10 matrix is solved, but the result is very long, like the numerical way to solve, but did not find the appropriate method, the Analytic solution is very slow, calculated for 5 hours has not been calculated.

question128.mw

Maple 2024.2 gives wrong inverse Laplace transform on expressions with exp(s) multiplied by Ei (the exponentional integral) with complex argument.

Below are two examples found so far. 

Inverse laplace of  exp(s)/2*Ei(1, s + I) gives exp(-I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(-I*(t + 1))/(2*(t + 1))

Inverse laplace of  exp(s)/2*Ei(1, s - I) gives exp(I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(I*(t + 1))/(2*(t + 1))

i.e. in both cases it gives 2*(t + 2) in denominator when denominator should be 2*(t + 1)

Below is worksheet

Download bug_in_inverse_laplace_transform.mw

Also Reported to Maple support.

Solved a "simple" dynamics problem involving the law of cosines... etc.  Part of the solution involves selecting the positive root from the resulting 2nd order equation in x(t)- below.  

eq1 := (r1 + r2)^2 = r1^2 + x(t)^2 - 2*r1*x(t)*cos(theta(t))  (law of cosines)

eq2:=diff(eq1,t)

eq3 := subs(diff(x(t), t) = v, diff(theta(t), t) = omega, eq2)  (remove xdot and theta dot)

assume(0 < x(t));
assume(0 < t);
assume(0 < theta(t) and theta(t) < 2*Pi);

xx := solve(eq3, v)  (creates an relationship between v, theta and x)

     xx := -r1*x(t~)*omega*sin(theta(t~))/(-cos(theta(t~))*r1 + x(t~))

Not clear what this t~ notation means?

when I solve eq1 above for x(t) there are two roots.  I select the positve root, but receive this warning...

eqx := solve(eq1, x(t))[1]

Warning, solve may be ignoring assumptions on the input variables.
        eqx := cos(theta(t))*r1 + sqrt(cos(theta(t))^2*r1^2 + 2*r1*r2 + r2^2)

How can I correct or address the warning message?

Finally,  to piece together the solution I perform this step

v := subs(x(t) = eqx, xx)

The result has a fairly obvious "simplification", but using "simplify" and "combine" only makes it worse...  Is there a combination of commands to accomplish a simplification.

Here is the entirety of the Maple...

restart;
with(Typesetting);
Settings(typesetdot = true);

eq1 := (r1 + r2)^2 = r1^2 + x(t)^2 - 2*r1*x(t)*cos(theta(t));
eq2 := diff(eq1, t);
eq3 := subs(diff(x(t), t) = v, diff(theta(t), t) = omega, eq2);
assume(0 < x(t));
assume(0 < t);
assume(0 < theta(t) and theta(t) < 2*Pi);
xx := solve(eq3, v);
eqx := solve(eq1, x(t))[1];
v := subs(x(t) = eqx, xx);

examine the result for v... easy to see the "simpificaion"... but not sure how to manipulate Maple to accomplish this...

JD

Hi!

I am working on a chemical engineering problem and trying to find a value (Ua) that does not result in a reactor temperature (T) exceeding 398.15 K.

I am employing a system of ode's, secondary functions, variables, starting conditions etc., and the dsolve function to determine these parameters.

Some values are given or calculated, UA is not. So for now I have just been guessing at the value (needed to preform the dsolve initially) and plotting to see relations to T and other parameters. My teacher has directed us to employ this trial and error apporach, which I find time consuming.

There is of course a smarter, more time efficient way of doing this and I was wondering how one could implement this? Moreover, how does one find the values of all the other variables at this Ua value? Is there a one-liner?

I tried implementing a loop to check for max UA values <= 398.15, but was not able to implement it..

Any help would be kindly appreciated.

FindingExtractingvaluesdsolvewithspecificconditions.mw

So my file got corrupted, i have no clue how to fix it. The file i was able to restore from OneDrive is 2 days old and is missing most of the information, i only have the backup files for the later version. Is there someone with expertice who can help me out? 

Can anyone explain me the reason of the last result?
Thanks in advance

Download What-does-happen-here.mw

Lb1 represents a number of lengths, but I don't want to use a number to replace it now, but directly using eval, the variable in it becomes Lb1, unlike the following values show, how to write it like a number?

Hi:

I want to copy some Maple output elsewhere in the form of Maple input.

Usually, if I highlight the output expression I can copy it with CTLR-C, and paste it elsewhere where it appears as Maple input.

Just like you'd expect and just like you'd want.

But if the expression is fairly long and complicated (it covers two lines on my screent this time), the highlight insists on including the > symbol on the next line and when I paste, all I get is the Maple output that I started with.

If I write the output expression name to a temporary file and read it in another worksheet, the same thing happens when I ask for the name of the output expression - it appears as Maple output. But I need the expression in the form of Maple input so I can modify it.

All this makes me think that there is a limit to the size of the copy buffer, but I can't find anywhere to change that.

Does anyone know how to do this very simple task which usually works reliably for small expressions?

Thank you.

Hi everyone!

I'm double checking a result from maple.  When I substitute maple's solution into the differential equation, left side does no equal right side.  Does anyone have some insight into this?

thanks

the maple file is below

is_this_correct.mw

Is it possible in maple to resume an asymptotic expansion from a specific order onwards.

To be more specific.

Let's assume that I have the asymptotic expansion to say Order 20 already calculated or can import it from file.

Is it possible for Maple to use the expansion I already have and immediately start calculating Order 21 onwards ?

This will save a lot of time for numerical  expansions that can take literally days to complete.

Hey guys, 

I am working with Maple 2024. I have to solve many systems of polynomial equations symbolically. I have 8 equations, 8 variables and 14 inequalities (which also implies that I only want real solutions). In my opinion the equations are not too difficult. However there is a maximum of up to 4 variables multiplied together which could be a problem. Since I have to solve thousand of those systems I need to reduce the amount of time needed. While many of the systmes only take a few seconds, there are a few systems (10%) that need way to much time (multiple houres, sometimes I stop the process before the computation is over). 

In my attached file you can see the kind of equations I have. While "equations_500 union inequalities" only needs a few seconds, "equations_1162 union inequalities" needs more than 2 houres (than I stopped). 
I also tryed a second approach. At first I just solved the 8 equations. Then I took every solution, combined it with the set of inequalities and solved it again. Not only does it not work for equations_1162 eather, but it also sometimes brings the warning "solutions may have been lost" which is not really convincing. For that process I also used "with(RealDomain) since I only want to find real solutions when solving the eight equations in the first step. 

I figured out, that for the normal and simpel solve command it cqn help to rename the variables so the lexigraphic order as the initial situation playes a role. But when I understood the pages explaining SolveTools or Groebner, this optimal order of the variables is completed automatically inside these environments. 

So my question is: Is there any way to accelerate the process (in this case for equations_1162)? Waiting some minutes isfine, but I cant wait houres for one solution. 

Thank you in advance. 

solve_system_of_polynomials_with_inequalities.mw

Suppose I want to run several systems of equations as below, however, the processing time exceeds 45 thousand seconds (reaching hours of calculations)

• What is better, buying a new processor (new notebook) or buying a new stick of RAM?
• Or does none of this affect Maple? Therefore, it is just a computational disadvantage (the delay time), characterizing the slowness of the program for very large systems as an imminent characteristic.
• Another question: The newer Maples (new versions) seem to be heavier to run. Is it just me? What seems to me is that the previous versions of Maple, because they contain fewer resources, are lighter and run certain calculations faster. Would this be correct?
• Last question: Is it possible to do parallel processing in Maple? So that calculations on huge systems can be run faster

Thank you so much! :)

Help me, I want to make this system be stable on graphs? How to make this system stable in plot?

This is my model:

dx/dt=\[Alpha]*
  x[t]*(1 - (x[t]/n)) - ((\[Beta]*x[t]*
     y[t])/(1 + (\[CapitalTau]*\[Beta]*x[t]))) - (x[
    t]*\[CapitalEpsilon]);
dy/dt=y'[t] == -\[Gamma]*y[t];

Prove: If a is an irrational number, then the function y = cos (ax) + cos x is not periodic.
Is it possible to graphically represent or calculate this fact using an example?