@patient For what it's worth (which I don't know at this point), the FindSingularity procedure that I gave will work for backwards integration, say using 0 as the initial point and integrating towards -1. No modification is needed---simply call FindSingularity(sol, -1).

@Preben Alsholm 

Try a time comparison of your procedural dsolve with my symbolic version of frem:

Frem:= (x,y)-> x - y*floor(x/y+1/2);

Ironically, Frem can be evaluated by evalhf, but frem can't be. For that reason, I think that it'll be faster.

@Axel Vogt 

What you called "acer's trick" was my trick. It seems that the setting of Digits determines whether declaring a method is needed. At Digits = 10, no method is needed. My guess is that the native Maple methods can't guarantee the accuracy at the higher setting.

Regarding the symbolic integration, see my new Answer about a symbolic equivalent to frem. It integrates easily.

@Markiyan Hirnyk What does it matter that neither you nor I understand the first part of the error message? All that matters is that the program stops because the time limit has expired, that the error is trapable, and that the user can continue from there.

@Markiyan Hirnyk The problem with using cpulimit is How do you continue the worksheet after the limit has expired? The timelimit command is more effective.

Please supply the complete code that leads to the error message, preferably in plaintext form. If you have difficulty with the plaintext form, or the code is too lengthy, then post a worksheet using the green uparrow tool that is the last item on the second row of the toolbar in the MaplePrimes editor.

Hello Raquel,

Please post a complete worksheet showing, at the least, the construction of Matrices K and M and the generation of the error message. To attach a worksheet to a post, use the green uparrow tool, which is the last item on the second row of the toolbar in the MaplePrimes editor.

What are Loading RealDomain; and solve; ? Are those commands that you gave? If so, they are meaningless. I think that you mean

with(RealDomain);
solve(LinearAlgebra:-Determinant(M), omega);

Personally, I would only use RealDomain after first trying to use solve without RealDomain.

It works for me. Perhaps your x has a value and you need to do a restart.

@testht06 

Yes, that is true. But the computation R^4 = newM is only done to verify for the reader that R was computed correctly; it's not a necessary part of the computation of R. If you want, I could explicitly show that R^4 = M (rather than newM) by converting the entries of R^4 from GF(2^16) back to GF(2^8). (This may be computationally intensive---I'm not sure.) None of this would change the computation of R itself, which is (I believe) the main goal.

@zmq 

The parameter of recurse is w, not v. If it was Departures(G,v), you'd be computing the departures of the root vertex repeatedly. Does that answer your question?

@testht06 

But I did compute the 1/4 power, not the 4th power! To say it explicitly, I computed Diag as the diagonal matrix of the 4th roots (also known as the 1/4 powers) of the eigenvalues of M. Here is the command that computes the 4th roots (ROOT = 4):

ROOTs:= map(lambda-> Roots(t^ROOT - lambda[1]) mod p, eigs);

The fact that R^4 = M proves that I computed the 1/4 power.

I request the assistance of my colleagues here at MaplePrimes to step in here and try to explain this better for you.

What is your native language? Perhaps someone else here speaks (or writes) it and is also fluent in English.

@Rouben Rostamian  

The difference in your two experiments is due to a very different (and more superficial) phenomenon called automatic simplification. The following example explains the behavior in your experiment #1, yet it has nothing to do with Vectors or other mutable objects. Note that automatic simplification cannot be delayed with unevaluation quotes, which is why the use of those quotes is used to prove that automatic simplification is occurring.

' '{a,a}' ';

a:= 1:  b:= 1:
' '{a,b}' ';

eval(%);

Please let me know if you understand why the example above explains your experiment 1 or if you have further questions.

@testht06 

I don't understand your problems with my implementation. Part of the problem is that I don't fully understand your English, and part is that I don't know if you understand the mathematical issues.

Regarding your point (1), "The matrix D is not take powers 1/4": I didn't use a matrix D (because D is a protected name in Maple); I used Diag instead of D. My matrix Diag is already constructed with the fourth roots of the eigenvalues; there is no need to compute Diag^(1/4). Do you want me to explicitly raise a matrix to the 1/4 power? That is superficial, but it can be acheived with operator overloading. 

Regarding your point (2): "Then the matrix R = P x D x P^(-1).": This is not even close to being a complete English sentence, and thus I can't figure it out. "Then elements of the received R will return to GF(2^8).": This is not mathematically possible! The only conceivable alternative is to present the entries of R as radical expressions over GF(2^8). This would be very messy visually, and would be an unusual presentation for a finite field. "The calculation of R^4 is performed in GF(2^8)/...": No! This is mathematically incorrect. The computation of R^4 is over GF(2^16).

@tomleslie Thanks for the research. Yes, spanning arborescence (see Wikipedia article "spanning arborescence") seems to be the correct concept in this situation. However, I don't think that Edmond's algorithm (see Wikipedia article "Edmond's algorithm") is the goal.

@zmq I don't understand what you're asking. Please explicitly ask a question as a complete sentence.

The syntax of GraphTheory:-Graph requires that the edges be given as a set---it's as simple as that. See ?GraphTheory,Graph. It doesn't have anything to do with edges being in pairs.