Carl Love

Carl Love

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12 years, 300 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

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These are replies submitted by Carl Love

@ssgmckv Please post a worksheet that shows the syntax error.

My knowledge of this area is quite superficial, so please excuse me if this question is trivial.

It seems to me that there are numerous pairs (x,y) from the set {e1, e2, e3, e4, e5, e6} for which your operation [x,y] hasn't been specified. For example, what are each of these: [e1,e2], [e2,e5], [e2,e6]? Is it sufficient to say that these are to be defined such that Jacobi's identity is satisfied? or perhaps that that is sufficient provided that it yields a unique definition?

If you create additional fake usernames to repost duplicates of this Question (as you just did), those usernames will just be blocked and the reposts deleted.

If you have something more to say about this Question, you're welcome to say it here (in this thread).

Stop posting duplicates of this Question.

You've given no indication whether or not you understand the Answer that I gave over a week ago.

FWIW, your ODE system is linear. I doubt that this makes much practical difference for solution attempts, but you may want to edit the Question's title.

@max125 Don't delete the earlier Question. Instead, either edit it or Reply to it. Either of those will put it at the top of the Active Conversations giving it renewed visibility.

@dharr Impressive solution technique; I vote up.

@Tokoro Sorry, I misinterpretted your Question, particularly the phrase "point to point", which I took to mean from a point to the next point going around the circle. Yes, I knew that not every pair of points in my construction had integer distance.

@Kitonum I like your solution! Here's a variation that's even shorter, and, better yet, removes the code's dependence on the length of x.

x:= <1 | 2 | 3 | 4>; #row vector
k:= <seq(x +~ a, a= x)>;

The OP should note that in this case the a iterates over the entries rather than the indices of x

@lcz Your for loops do nothing other than waste time repeating the same calculation (1830 times in this case). Your procedure can be simplified to

ResistanceMatrix:= (g::Graph)-> 
    (M-> Matrix(
            upperbound(M), (i,j)-> M[i,i]+M[j,j], 'shape' = 'symmetric'
         ) - 2*M
    )(LinearAlgebra:-MatrixInverse(
          GraphTheory:-LaplacianMatrix(g), 'method'= 'pseudo'
     ))
:

 

@mehdibgh If a function such as x(t) appears in an expression ex both as an argument or part of an argument of another function, say F, and as elsewhere in ex as an ordinary polynomial term, then the concept of "coefficient" in its usual defintion doesn't make sense. For example, what is the coefficient of x(t) in 2*x(t) + sin(3*x(t))? In your example, the functions appear as arguments to diff. If you temporarily remove all the derivatives (by setting them to 0), then you can do the remaining coefficient extraction; like this:

CML:= eval(EqML, diff= 0);
KKNL:= Matrix((nops(EqML), nops(Var[4])), (i,j)-> coeff(CML[i], Var[4][j]));

@Harry Garst The distinction between the a's in the matrix and the a's returned by komb has nothing to do with types indexed or symbol. The a's returned by komb are local to komb because a is declared local there. When a local name (either indexed or symbol) continues to exist outside of the procedure where it was declared local, it's called an "escaped local" (as mentioned by acer). Escaped locals are not bugs--they are often useful--but they can lead to bugs if you're not aware of them. The a's in the matrix are of course not local to komb. They are globals that look the same as the local a's both as prettyprinted and via lprint. However, the command addressof will show that they're different. This is why acer rewrote komb so that var is passed in.

Ever since the keyword thismodule was introduced (many years ago), I've wanted an analogous keyword for "this module's parent". It'd even be more useful than thismodule itself. I guess that Python's super has this functionality. 

To me, there's nothing beautiful about digit patterns that are only apparent in the base-10 representation of a number.

It's trivial (because there's only about 3.3 million possible dates with a 4-digit year) to iterate through all possible digit sequences that represent dates and find those that you think are beautiful.

@max125 If you want to discuss some totally unrelated issue/bug regarding Maple's help system, please start a new thread.

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