John Fredsted

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19 years, 48 days

MaplePrimes Activity


These are replies submitted by John Fredsted

@Christopher2222: Happy to be able to entertain once in while :-), although, of course, it may generally be considered bad style to do so at the expense of others. I am guilty.

@ecterrab: Thanks for that fix, now both situations work in both type settings, as you assert. With the two issues out of the way, and with the advantages of the extended typesetting that you give, I will of course use the extended type setting.

PS: I know that the standard setting is not the default; when I wrote " the Maple Standard setting" previously, I meant " the 'Maple Standard' setting" (note the single quotation marks), as 'Maple Standard' is what the standard setting is called under Options/Display. But, of course, that is nitpicking.

@ThU: Thanks a lot, that solved the problem.

PS: Unfortunately, this default extended setting does not work for me in another context, as reported in the thread Error for the Vector constructor; here, only the Maple Standard setting worked. So if both situations appear in the same worksheet of mine, what then?, I ask myself. Perhaps Maple 2018 will make it possible to run a worksheet in a quantum superposition!?

@ecterrab: My mistake. I actually knew that the correct syntax was and is

PerformOnAnticommutativeSystem(PDEtools:-ConservedCurrents,pde);

having at that point already read the help page. But I simply forgot to make the appropiate adjustments when I 'enclosed' PDEtools:-ConservedCurrents(pde) within PerformOnAnticommutativeSystem, having found that the former was not up for the job. I guess, I was at the time of posting prejudiced to thinking that the error lie with Maple, not with me, thus jumping to the wrong conclusion.

@Anyone: Why has the above post of mine been moved from being a reply to Edgardo to being a reply to my own original question? I have certainly not moved it myself.

@ecterrab: Thanks for your swift efforts. I have just downloaded, unzipped, and copied to some library folder of my own (the path to which is of course included in maple.ini) your Physics2017 fix. But for the same test example as above I still receive an error, now although the following different one:

"Error, (in PDEtools:-ReducedForm) unable to handle [[Y1(T)], [_F9(T)*_lambda5, _F10(T)*_lambda6]]"

 

Concening the command PerformOnAnticommutativeSystem: Although I did notice its name in the previous error message, I was not really aware of it; at least, I did not look up its help page. Doing

PerformOnAnticommutativeSystem(PDEtools:-ConservedCurrents(pde));

produces, though, the exact same error message as the one given above. Furthermore, the fix produces as well the error

"Error, (in simplify/do) invalid simplification command"

in some code of mine which was previously without error. So for the time being I will revert to the Physics version with which I installed Maple 2017.

PS: Please do not feel pressed; I have full understanding of you being elsewhere preoccupied for the time being. The issue is not absolutely critical to me. In the meantime, I think I will take a fresh look at my own procedure, totalDiv(), which can handle Grassmann-odd quantities as well, or at least almost: in the Grassmann-odd case, it often fails to perform a complete 'absorption' of terms into a divergence, a few terms being left behind, although they could be 'absorbed'.

@ecterrab: That is quite understandable, I had expected it. But luckily there is no need to present to you the whole shebang; the following simple test case, which I have just cooked up, exhibits the same problem:

pde := diff(psi1(x,y),x,y)*psi2(x,y) - psi1(x,y)*diff(psi2(x,y),x,y);
J := Vector([-psi2(x,y)*diff(psi1(x,y),y),diff(psi2(x,y),x)*psi1(x,y)]);
simplify(pde - (diff(J[1],x) + diff(J[2],y)));

0

the quantities psi1 and psi2 being Grassmann-odd. Applying ConservedCurrents yields

PDEtools:-ConservedCurrents(pde);

"Error, (in PDEtools:-ReducedForm) invalid input: Physics:-PerformOnAnticommutativeSystem expects its 2nd argument, list_of_decomposable_arguments, to be of type list(Or(algebraic, relation, list(Or(algebraic, relation)), set(Or(algebraic, relation)))), but received ..."

@ecterrab: Thanks a lot for that quite comprehensive comment, and apologies for my somewhat belated reply. My use of the words "almost gibberish", which could easily be perceived as being meant derogatively, was first and foremost a statement of my own inability to decipher the output, this no doubt being due to my zero experience with the application of Lie groups to differential equations. I had no real doubt concerning the correctness of Maple's result itself.

Update: As a reasonble simple test case, I have tried to apply ConservedCurrents to the variation of the Dirac Lagrangian resulting from performing an infinitesimal translation in the time direction, say, of the Dirac field. But it produces an error, the first part of which goes as

Error, (in PDEtools:-ReducedForm) invalid input: Physics:-PerformOnAnticommutativeSystem expects its 2nd argument, list_of_decomposable_arguments, to be of type list(Or(algebraic, relation, list(Or(algebraic, relation)), set(Or(algebraic, relation)))), but received ...

As for any translation, the resulting variation of the Lagrangian is, of course, a four-divergence. For the specific case here at hand, this fact is also born out by an explicit calculation with a function of my own pedigree, totalDiv(), developed some time ago.

@quo: I do not know whether that can be done. I have never had the desire to do any such thing. I have always used Worksheet Mode, never ever Document Mode which I think in certain respects can be more confusing than helpful. Anyway, I hope others can provide you with an answer.

@ecterrab: Thanks a lot for these pointers. I somewhat had a hunch that my problem belonged to the area of Lie groups applied to differential equations, unfortunately, one may say, as I have zero experience with such matters. But I will surely look into the details now.

Update: As a most simple, almost trivial example, let us consider, say, the following expression:

pde := diff(f(x,y),x)*g(x,y) + f(x,y)*diff(g(x,y),x);

Here the conserved current is given by

ConservedCurrents(pde,[f(x,y),g(x,y)],jetnotation = true);

Even in compact jet-notation, this seems to me almost gibberish, I am afraid. In this simple case, I do know how to write the expression for pde as a (two-)divergence:

J := Vector([f(x,y)*g(x,y),0]);
pde - (diff(J[1],x) + diff(J[2],y));

0

In my research, I am dealing with differential expressions that may contain several hundred terms; they arise by way of certain variations of the spinor field of the Dirac Lagrangian. In view of the difficulty I have in understanding the returned current for the most simple example above, I do not even dare to think what might be the returned output for such a much more complicated situation. But perhaps we are talking about two different things!?

@ecterrab: On grounds of what you write, I suddenly realize my mistake. Even though I actually know differently from previous experiences with difforder, I had temporarily fooled myself into believing that (f')^n would have differential order n, when, in fact, it is only of order one, as you correctly assert.

Concerning what I am trying to accomplish: I would like to construct a procedure that can determine whether a scalarly (in the matrix sense) quantity can be written completely (or perhaps partially, separating off as many terms/addends as possible) as a total divergence of some current, returning that current (in conjunction with the remainder, in the partial case). To serve that procedure reasonable expressions, I would like to exclude functions of derivatives of functions.

PS: Perhaps such a procedure already exists in Maple, but if that is the case, then I have been unable to locate it.

@Kitonum: Thanks for clearing that up for me. A function may of course take on extremum values at the boundary, if any, of its domain, the boundary in this case consisting of a pair of points. What clearly threw me of track here is that even though solve returns a = b - 5, as also acer finds above, it does not say/warn that this solution holds only for b in 2..8.

@vv: I agree, the solution is correct for b in 2..8 only. But why does solve do such a thing? Why does it not solve piecewisely, or at least throw some warning?, I ask myself. Instead of throwing a warning, it surely threw me of track.

Update: After Kitonum's post above, it is now clear to me that solve should not, as I call for above, solve piecewisely, as there is no such solution. But I still think that it should inform one that the solution holds only for b in 2..8, rather than presenting the solution as {a = b - 5,b = b}, i.e., with b arbitrary, as I found previously.

@Kitonum: We can obviously not both be correct. I wonder whether I am making some silly mistake.

Update: My method is clearly faulty, see update to my post. I do not really understand why solve behaves as it does.

@trace: I am confused. You say that you do not know M(t,x) and J(t,x), while at the same time providing their explicit forms in the attached worksheet. Is what you are looking for rather a confirmation, by Maple, that the provided functions do perform the actual transformation?

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