I have a system of algebraic PDEs that is overdermined. I am trying to solve some of the equations in the system with respect to some function, and equate in another equation, just to reduce the system. For instance,

X1:=solve(eq1=0,f1);

X2:=solve(eq2=0,f1);

Now X1-X2 should be zero. So I would like to simplify X1-X2 to be able to use it in the system. Note that there are lots of parameters in the system, and X1-X2 will not result in zero. Was thinking of using factor() instead if it's any better?

@Thomas Richard Thanks Thomas. This does the trick.

@Thomas Richard I know I can suppress output by a colon, but I don't know how to import a file and assign its content to a variable.

For example, my text file system.txt contains the following:

{Derivative[1,0,0][F][x,y,t]+Derivative[2,0,0][F][x,y,t],Derivative[1,0,0][F][x,y,t]-Derivative[0,0,1][F][x,y,t]}

So I want to import the content of the file and assign it to a variable X, and then use pdes:= FromMma(X).

@Carl Love The result is assigned to a variable and supressed by (:). The memory usage is now 30%, but the CPU keeps fluctuating between 10% and 99% in short intervals. I guess the CPU usage is what to worry about here!? Does Maple make use of multiple cores?

@Carl Love OK, they seem to be moving now, increasing. Does that mean a solution will be found?

@Carl Love The time and memory counters seem not moving but the octagon around the exclamation mark is in red. The time shown is 1524423.5s and memory 26904.81M.

Yes I am on Windows and the task manager shows that Maple is consuming around 40% of memory (out of 256GB).

@Carl Love Thanks. It is clear now.

Another thing please. If I have a system of 5 PDEs (3rd order, overdetermined in 3 unkowns, equations are very large but the system should have a solution), and it takes very long to get an answer (been running for 2 days now) using pdslove, from your experience, would it be eventually resolved?

@Carl Love Thanks for that. Is there a way to extract a function argument? For example, if I have U(x,y,t), I would like to extract the first argument by using something like U[1] to get x, etc.

@Carl Love Many thanks!

@Carl Love If I want to find all functions in an expression, what do I do? Many thanks.

@Carl Love That works great. Many thanks!

@Carl Love Sorry for the late reply. I ended up changing my strategy and I am sure your code works. Thanks a lot for your help.

Just one more thing please. I know I can use has to find an expression in an expression. But it is a boolean function. Is it possible to find the full varaible/function instead? For example, if the expression has U(x,y,z) and I search for U, I get U(x,y,z).

@Carl Love Thanks but the code doesn't seem to work. I am getting the empty set for any order greater than 0.

e:=
     diff(P(x,y),x,y) + diff(P(r,s),r,r) + P(x,y) + diff(P(x,y),x) +
     diff(P(x),x) + diff(P(x),x,x): 

specdifforder(e,1,P)
                               {}

@subzero OK, adding coordinates = [X = (x, y, t)] sorted it out. Thanks again.

@ecterrab I had tried this. It gives the error message:

Error, (in Physics:-Define) expected indices of specific type - e.g.: spacetime, space, etc. - in the definition of Gamma[mu, alpha, beta], this is required when using the options symmetric = ... or antisymmetric = ... The indices of Gamma[mu, alpha, beta] are of no recognizable type.

When Gamma is defined.