@tomleslie Do you have kernelopts(assertlevel= 2) set, perhaps from an initialization file?

@acer I don't think lack of precision is the culprit leading to spurious roots in this particular case. Try this code and let me know what you think:

restart:
Digits:= 100:
JD:= int(6-sqrt(9+8*x-x^2), x= 0..L);
R:= solve(10=JD, L);
R2:= [allvalues](R);
R3:= select(type, evalf(R2), realcons);

The end result is the same 3 real roots (extended to 100 digits), 2 of which are very wrong.

I'm totally willing to accept that spurious roots may occur for purely symbolic reasons---as we learn in high-school algebra II when solving equations with variables under square roots. But I haven't found the actual symbolic culprit here yet,

@acer My Comment here has nothing to do with the Question; I'm just commenting on a curiosity in the prettyprinted output shown both in the Question and in your Reply above. Notice that Pi/2.2 appears two different ways in the output of the definition of piecewise function f. It appears twice as 1.427996661 and twice as Pi/2.2.

@lcz There is no specific command for numeric eigenvalues because LinearAlgebra:-Eigenvalues (and related commands) chooses an algorithm based on the datatype (such as hfloat) and the shape (such as symmetric) of the matrix. The Answer by @dharr shows how to use this feature.

@ecterrab You seem to be answering a question which is nearly the opposite of what was asked. The OP has set infolevel[dsolve]:= 2, has run dsolve twice on the same ODE, and has noticed that the 2nd run produces much shorter userinfo output. This is of course because of remember tables, and the OP now understands that. The OP wants to obtain only the userinfo from that second run without needing to obtain the userinfo from the first run as a preliminary step. (The OP does not want to "see again the previous user level information", so using Forget() doesn't help.) My Answer shows how only that second-run userinfo can be obtained efficiently.

@dharr But the OP wants to do this over finite fields. The diagonalization proceeds in a mostly similar manner to what you showed, although one often needs to create more-elaborate splitting fields for the eigenvalues (of degree possibly as large as the matrix order). The major stumbling block will be the finite-field equivalent of the solve, there being no good algorithm to solve for an exponent. This is the "discrete logarithm problem" that I referred to in my Reply above.

Even in the case of 1x1 matrices (i.e., scalars), it is a hard problem---called the discrete logarithm problem---for which no fast algorithm is known. See the Wikipedia article "Discrete logarithm".

@lcz I consider it a serious breach of "netiquette" to delete one's own Question after it has been Answered. That is NOT nm's habit. I've only noticed that user deleting material that has not been replied to.

@burgarth I thought this deserved to be a separate Question, so I moved it from the 7-year-old thread to which it was originally attached. And I gave it a title, which you're free to change if you want.

@dharr I'll be disappointed if any of those 3 are considered as "legitimate" solutions to the problem. If so, I'd consider it a "trick question" rather than a math/physics/engineering problem.

On the other hand, even if the total source-to-sink resistance is allowed to be anything, not necessarily 1, I can't imagine any possible way that all the currents are different. 

@ecterrab Sorry for causing confusion; my Reply wasn't directed solely to you. Parts of it were intended for @Axel Vogt , @janhardo , and @lcz each of whom questioned the general Moderation process on MaplePrimes.

I am virtually certain that @nm has on numerous occasions deleted their own material. Hopefully they will respond. I suspect that they are a perfectionist regarding their postings.

@ijuptilk The PDF contains a procedure my_pm that returns lambda and u. Use that procedure.

@vv Thanks, I was mistaken, but now I understand due to your example. 

@ecterrab The member @nm has a long-standing habit of deleting their own Questions (that haven't been Answered), Answers (once another Answer appears), and Comments. I've tried to discourage them from doing that, but I don't think they had any response. In my many years of being a Moderator here, I don't recall ever deleting anything by @nm nor seeing anything that I thought should be deleted. Indeed, I consider @nm to be the all-time most-prolific poster of good-quality Questions, and a substantial proportion of their 6000+ reputation points come from me voting up their Questions.

I suspect that the vast majority of cases where a Reader notices that a worthwhile Question has been deleted fall into one of these categories:

1. The author deleted their own Question.
2. The Question is a duplicate of (or substantially the same as) another recent Question that the Reader didn't notice.
3. The Question is a followup to an Answer to a recent Question by the same author, and the Reader hasn't noticed that (yet).

Note that there is no mechanism whatsoever on MaplePrimes for Moderators to do any of the following things; their options are only Edit, Reply, or Delete:

1. To move a Question into another thread (such as to the thread for which it is a followup) where it rightfully belongs;
2. To move material to a holding area for possible further review.

I'd be happy to use these things (or any other StackExchange-like features) if MaplePrimes implemented them.

@Alex0099 I suspect that the remaining errors are deeply dependent on the underlying mathematics, which I know nothing about unfortunately. The semicolon error that I corrected was just a simple syntax error.