Is there a way to determine how we can construct a system of equations from this complex PDE? Also, moderator, you mentioned I could create a new question using the branch option, but you deleted my previous question, which led me to delete my earlier post. don't delete this one.

Download PDE-Hard.mw

The output  means that there is no real solution, but clearly, both and  satisfy the original equation: 

So, why does `solve` lose the real solutions without any warning messages? 
Code: 

restart;
eq := 9*(x^2 + 2*cos(x)) = Pi^2 + 9;
RealDomain:-solve(eq, [x]);
                               []

:-solve({eq, x >= 0}, [x]); # as (lhs - rhs)(eq) is an even function 
                               []

this equation will be solve by changing variable but when  i found the function and substitute the ODE is not zero where  is mistake?

Download problem.mw

I'm trying to solve system of ODE (Temperature changing with time) which are going to use the heat capacity obtained from thermophysical package (heat capacity is changing with temperature).

In the support page there is an example in which they were able to integrate the heat capacity from the package. So I wondering if it is possible to include it in an ODE system.

I used their same approach, I tried defining the call to the package as a function but I'm getting an error:

"Error, (in dsolve/numeric/process_input) input system must be an ODE system, found {ThermophysicalData:-CoolProp:-PropsSI(C,P,101325,T,T1(t),"hydrogen"), T1(t), T2(t), T3(t)}"

Attached question.mw

Hello sir, how are you?
Sorry to bother you, I needed your help. I have the script from your textbook "3D Graph Equation of Motorcycle run on Maple Software". It's not working. I'd appreciate it if you could take a look.

with(plots);
implicitplot3d(((49.80*x + 19.44*y + 133.2300 - 19.08*sqrt(x^2 + 8.30*x + 19.8469 + y^2 + 3.24*y) - 66.6150*abs(-3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + 0.5625*abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) = ((((((((((((2 + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(y^2 - 3.18)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24)) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24) + 0.42*abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) and ((((((((((((2 + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(y^2 - 3.18)) + abs(3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2))) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42) + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 8.30) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y - 2)*(x^2 + 3.24)) - 3.9*sqrt((x - 1.7)^2 + (y - 1.35)^2)) + 0.42 + abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2)*(y^2 + 3.24) + 0.42*abs(0.00390625*(x^8 + y^8) - 0.5*x + 2*y + 2) = 0, x = -7 .. 7, y = -4 .. 3, z = -3 .. 3, numpoints = 350000, style = surface, color = "Niagara Azure");

evalindets API says 

             evalindets( expr, atype, transformer, rest )

Where the transformer will be applied on any indents of atype.

But I want to be able to do the opposit, i.e. 

             evalindets( expr, except_this_atype, transformer, rest )

ie. apply the transformer on everything except those of atype.

Here is a concrete example and what I tried.

I get result of apply inverse Fourier transform which can have some terms in it which can not be evaluated. Like this

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);

Now I want to evaluate the above at some specific value of t, say t=0 but I do not want change/touch any "t" inside invlaplace(....) function. 

If I just do 

eval(expr,t=0)

So I tried evalindets with flat option and used for atype anything, then inside the transformer, check if op(0,X) is invlaplace (i.e the head), and if so, skip it. But it did not work

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);
evalindets[flat](expr,anything,X->`if`( evalb(op(0,X)='invlaplace'),X,eval(X,t=0)));
evalindets[flat](expr,anything,X->`if`( op(0,X)='invlaplace',X,eval(X,t=0)));

Currently what I do to make this to work, is to first replace the "t" inside invlaplace by another unused symbol, then do the eval to change t, then replace the symbol back to t.

Like this, and this works:

Y:=(s+1)/s^2+Int(sqrt(s^2),s);
expr:=inttrans:-invlaplace(Y,s,t);
expr:=evalindets[flat](expr,'specfunc(anything,invlaplace)',X->eval(X,t=T));
expr:=eval(expr,t=0);
expr:=eval(expr,T=t);

Is it possible to do the above using one call to evalindets?  Why did the check I had the above using `if`(...) not work?

It will be really useful if evalindets had option NOT atype,  in addition of just atype.

i.e. tell it to do the transformation on everything except the type given.

Maple 2024.2

I am trying to animate images generated in a do loop using display and insequence. I get an output but there is no flipping of the image even while I see the frames count flip through the frames. What am I doing wrong? See attached code. Thanks!

Why_cant_I_animate_still_images_like_this.mw

This is about delayed input after executing this file Campo_Médio_spin_7_2_-_Forum_optimize_02.mw

from annother question dealing with very large physics expressions (containing about 100000 exponential functions).

The GUI shows but when I place the cursor in an inputline and type, characters are sometimes displayed with a huge delay (about 20 seconds). This is from time to time, i.e. not always. All on Windows 10, 64 Gb memory and 4 Gb graphic card memory.

Can someone reproduce this?

Has anybody experienced the same (kernel with large expressions & GUI not responsive)?

Anything that I can test or try?

(I had a similar question about file size but this time the file size is small 150 kB and no big plots are made.

Only the kernel has to deal with the large expression. Output displayed on the GUI is negligible.)

Hey guys, 

in the attached file you can see my problem. Since Maple was not able to calculate my set with 8 equations, 8 variables and 13 inequalities I had to split in into two steps. Here you can see how I try to take one solutions of what I got with solve onto 8 equations with 8 variables and to solve this together with my inequalities. It never was a problem before. So ow I get a weird error I dont understand.

So my question is why does this error occur? And what does it mean? the "but received..." argument in the error makes no sense to me. Why does it happen when I add 0<s but 0<x,0<y is okay?

Thank you in advance

Download Why_this_error.mw

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.

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.

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

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.

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

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?