I am looping over a list of functions to calculate various properties of the said functions. some of these calculations take too long. I was wondering if there was a way to skip to the next element of the loop if a calculation takes more than a specific time.

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I need to solve a system of coupled partial differential equations. I would like to search for a function of 4 variables but such that two of the variables only appear in a particular combination.

F(theta,r, phi*(a^2+r^2)-at).

Is there a way to enforce this?

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I am trying to solve these two coupled PDE and am getting this error. Does anyone know what this mean?

I was wondering if there was a way to permute a list to get a list of sums of permutations.
for example,

list:=[a,b,c]
permute(list,2) gives me ([a,b] [b,c] [c,a])

I would like to get this instead: ([a+b],[b+c],[c+d])

I have defined several expressions that keep coming up in my calculations. 
Like :

Delta := -2*M*r+a^2+r^2;
Sigma := (a^2+r^2)^2-Delta*a^2*sin(theta)^2;

Is it possible to make maple recognize these objects whenever they appear in the result of a calculation?