Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

This worksheet below has a very large test expression I use with Maple. It is just for testing.

Maple 2024.1 on windows 10. 128 GB RAM. Fast PC.

Someone in another question asked me to post this test worksheet for them to try also.

My question is: Why Maple expand hangs on it, even though I have timelimit?

I am not printing this at all. This is actually is run in .mpl file, but I am posting worksheet version here.

I am not asking about the printing of the expression. But about the timelimit hanging. This is the big problem for me. If timelimit hangs, my program hangs and no workaround.

Here is the worksheet below. The expression is 373,000 leave size, which is huge. Still, Maple should not hang and more important, timelimit should not hang as it was supposed to have been fixed in the year 2021.

Make sure to save all your work before running this.

Since expression is very large, I will only post link and not display the content here as well.

 

why_timelimit_hang.mw

 

At the bottom of the worksheet, there is one command that does print(e); which will hang Maple. so make sure to save your work if you want to run this command.

There is also second command after that, which is my question is about., It does

try
   timelimit(20,expand(e)):
catch:
   print("Timed out OK");
end try:

And this hangs.

My question is why and is there a workaround? I know it is large expression, but there is a timeout there. Maple should have timedout. Right?

 

I added radnormal(sol) to my solution to workaround bug in solve hanging

But now new problem showed up. sometimes radnormal gives internal error when there are _Z's in solution.

radnormal(sol);
Error, (in RootOf) _Z occurs but is not the dependent variable
 

Attached worksheet. Sorry that the solution is very large and has lots of _Zs and RootOf, but this is the first one I can see so far in the log file of my program running, so I left it as is:

Should I check in my code that solution does not contain _Z before calling radnormal on it?  Is this a bug or known limitation?
 

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1767 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

sol:=1/6*(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) + 1/6*(4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2 + 2*a*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2) + a^2)/(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) - 1/6*a + 1/3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2):

radnormal(sol);

Error, (in RootOf) _Z occurs but is not the dependent variable

 


 

Download bug_Z.mw

I have had this a few times this week since updating to 2024.1 on Windows 10.

I get sudden freezes in a worksheet. The !!! button greys out. The ! button is ok, so the worksheet can be run by using ctrl A and click !

Has anyone else experienced this?

I gave up trying to figure out why Maple sometimes generates solutions from my code that look different, running the same exact code. I know Maple is not deterministic and this can happen sometimes for reasons I will never know.

The following two solutions are the same, it just sometimes Maple shuffles terms a little around. For example SQRT(6) comes out SQRT(2)*SQRT(3).  I have no idea why this happens. It could be how memory inside Maple happened to be at the time and what happened before.

But my question is the following. Here is one ode, and two solutions that are exactly the same. I called one good_sol and one bad_sol.

If I do simplify(bad_sol - good_sol) I get  0 = 0 but here is the problem. When calling odetest on the good_sol, Maple returns 0 instantly,  But on the bad_sol it just hangs.

Even though the two solution are exactly the same. i.e. Mathematically the same.  

I'd like to know why does this happen? And if there is a permanent fix I could always use.

The following worksheet shows this problem.

After much trial and error, I found that if I do radnormal(bad_sol) then now odetest returns zero right away and the hang is gone!

I am just trying to understand why. And why odetest then itself does not use radnormal if this makes it work better?

Do I need to call randormal on every solution before calling odetest then? Will calling randormal on the final solution have any bad side effects on other computation after that?  It should not I would think.

This is all done in code without looking at the screen and having to decide. So I would need a solution that will work for all cases. But for now, I will change my code and add randormal to all solutions and see what happens.

Using 2024.1 on windows.   May be Maple behaves different on macOS, I do not know.

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1767 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

restart;

ode:=4*x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+3 = 0;

4*x*(diff(y(x), x))^2-3*y(x)*(diff(y(x), x))+3 = 0

bad_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))/sqrt(x)) + 1/2*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) + 1/2*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) = 0;

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))) = 0

good_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))/sqrt(x)) + 1/12*sqrt(3)*sqrt(6)*sqrt(2)*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))) + 1/12*sqrt(3)*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x)))*sqrt(6)*sqrt(2) = 0;
 

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/12)*3^(1/2)*6^(1/2)*2^(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/12)*3^(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))*6^(1/2)*2^(1/2) = 0

simplify(bad_sol-good_sol)

0 = 0

odetest(good_sol,ode); #instant answer

0

odetest(bad_sol,ode); #hangs

Warning,  computation interrupted

 

radnormal(bad_sol)

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((y(x)*x^(1/2)*3^(1/2)+x*(-(-3*y(x)^2+16*x)/x)^(1/2))/x)+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)-8*2^(1/2)*x)/(3*y(x)^2-16*x))+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)+8*2^(1/2)*x)/(3*y(x)^2-16*x)) = 0

odetest(%,ode); #instant answer

0

 


 

Download why_same_sol_hangs_july_7_2024.mw

 

Is there a way to apply Intc() and Fundiff() in spherical coordinates? If I initialize a spherical coordinate system X and then want to calculate the effect with Intc(), r, theta phi and t are integrated from -inf to inf but  thtea:(0, pi) phi:(0, 2Pi). I would also need a second spherical coordinate system Y, if I have understood Fundiff() correctly, but how can I define this Coordinates(X = spherical, Y = spherical) does not work.  

I would like to vary my Lagrange density (16) with respect to f_A(r). Where r is the radial coordinate of the spherical coordinate system.

YANG-MILLS-Theorie.mw

Hi all guys, I don't know how to simplify this easy expression? I have tried simplify command, and expand command, no use. Welcome to answer and thank you!

 

y1(x) = 2*sin(x)-sin(2*x)+cos(2*x); y2(x) = 4*sin(x)+sin(2*x)-cos(2*x); diff(y1(x), x); diff(y1(x), x); simplify*(1/2*((diff(y1(x), x))^2+(diff(y2(x), x))^2)+1/2*(3*y1(x)^2-y1(x)*y2(x)+y2(x)^2))

simplify*((1/2)*(diff(y1(x), x))^2+(1/2)*(diff(y2(x), x))^2+(3/2)*y1(x)^2-(1/2)*y1(x)*y2(x)+(1/2)*y2(x)^2)

(1)

 

Download simplify_expression.mw

There exists a new (?) checkbox  in the Interface tab of the Options dialog: 

But I cannot find any find any explanation about it in the corresponding help page. What is the purpose of this feature? 

I have a Dataframe of data, although I assume this question applies to any type of rTable-like structure.

What is a simple/elegant way to export the image of the data to a JPG file?  I would be happy to see it in the format when I ask it to print the Dataframe, or when I use DocumentTools:-Tabulate.

Is there a way to install 2024.1 and keep 2024 there also? i.e. install 2024.1 along side 2024? This way if I find a problem and want to check 2024 I still have it? 

i.e. install Maple 2024.1 in its own folder, separate from Maple 2024, and have its own icon on desktop. 

If I install 2024.1 using Tools->Check for update,  it will overwrite 2024 and not ask me if I want to keep it. At least this is what happened in Maple 2023 and earlier versions. So wanted to ask before I try to do this again, else it will be too late.

If I do not use Tools->Check for updates, and instead download 2024.1 manually from the product web page, will one then be able to install 2024.1 and keep 2024? Or will it also overwrite 2024? I have not tried because I do not know if it will ask me or not.

Maple 2024.

Dear all, in Maple Help exists the documentation of how to use the OpenMaple API Library. But I didn't found a link where to download the necessary libraries. I found e.g. the library maple-0.17.4.jar but it doesn't contain com.maplesoft.openmaple.*

http://www.java2s.com/example/jar/m/maple-index.html

Tahnks for help

We have just released an update to Maple. Maple 2024.1 includes improvements to the math engine, PDF export, the Physics package, command completion, and more. As always, we recommend that all Maple 2024 users install this update. In particular, please note that this update includes fixes to ODESteps and simplifying integrals, as reported on Maple Primes. Thanks for helping us, and other users, by letting us know!

At the same time, we have also released an update to MapleSim. MapleSim 2024.1.1 includes improvements to FMU import/export, plotting, co-simulation, and more, as well as enhancements to the Web Handling Library.

These updates are available through Tools>Check for Updates in Maple or MapleSim, and are also available from the Download Product Updates section of our web site, where you can find more details.

What is the command to stopat and showstat the proc  DEtools:-odeadvisor ?

I tried

ode:=y(x)*(2*x^2*y(x)^3+3)+x*(x^2*y(x)^3-1)*diff(y(x),x)=0;
DEtools:-odeadvisor(ode);

showstat(`DEtools/odeadvisor`);

showstat(`ODEtools/odeadvisor`);

And few other variations. It works on other proc's  such as

stopat(`ODEtools/symtest`); 
stopat(`ODEtools/test`); 
stopat(`ODEtools/normal/expanded`); 
stopat(`ODEtools/odepde`); 

But I was never able to figure the name for `DEtools:-odeadvisor`

Is there a general method to determine the correct name to use for printing or stopping at Maple command code to see it?

For me, it seems like trial and error process. For example DEtools:-command   becmes ODEtools:-command to stop at. Notice the extra O needed for tracing or printing. Do not know why extra O is needed. But showstat(`DEtools/symtest`); gives error, and showstat(`ODEtools/symtest`); works even though the command itself has no O.

So my question is, what would be the command to stop at DEtools:-odeadvisor? Is there a place to read more about how to find the correct path to give so do not have to guess?

Maple 2024

Maple gives type of this first order ode as _homogeneous, `class C`, but it is also dAlembert ode.

When asking it to solve as  dAlembert using the method option, it solves it.

But it returns singular solution which is wrong as it does not satisfy the IC. Singular solution should also satisfy IC like particular solutions do.

Is this a bug or Am I overlooking something?

Should not the solution returned satisfy the IC even though method used is not listed from odeadvisor?
 

29028

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1764 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

restart;

29028

ode:=diff(y(x), x) = (3*x - y(x) + 1)/(3*y(x) - x + 5);
ic:=y(0)=0;

diff(y(x), x) = (3*x-y(x)+1)/(3*y(x)-x+5)

y(0) = 0

sol:=dsolve([ode,ic],[dAlembert]); #this solution is singular solution.

y(x) = x-1

odetest(sol,[ode,ic]); #notice, solution do not satisfy IC

[0, 1]

sol2:=dsolve([ode,ic]):
odetest(sol2,[ode,ic]); #this is OK since used default method, not dAlembert

[0, 0]

DEtools:-odeadvisor(ode)

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

 


 

Download dsolve_dalembert_july_2_2024.mw

I want to simplify the attached expression by applying the relation \( k_1 + k_2 + k_3 = 0 \).

For instance, the terms \( k_3 + k_1 - k_2 \) become \(-2k_2\) and \( k_1 + k_2 - k_3 \) become \(-2k_3\), etc.

Instead of manually changing each term, I am looking for a systematic method to apply this relation to simplify the given expression.

aabb.mw

How to simplify the expression where each vectors k_i and q has real components, i.e., etc

Only W_i, U_i,j, V_i,j are complex numbers, so conjugate (bar) is applicable for them. How to make declaration, so that all other bars are removed and simplify the expression.

aa.mw

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