@yunlongwang If you find that Matrices of large size do not print in full (showing just a summary item) then adjust the rtablesize interface property.

Eg, to allow Matrices only up to size 20x20 to display in full, use the command,

interface(rtablesize=20):

That will affect both Matrices and Vectors. The default is rtablesize=10 in the Standard Java GUI.

@Mac Dude No, there are three possible settings: always use a new engine (mserver), never use a new one, and ask each time. The last one should bring with it a popup menu to select from running mserver instances, or a new mserver, each time File->New or the desktop launcher is used. And the OP has told us that the kernel computational part of this is working OK.

Having said, that, I am not sure whether or not the Maple 18 behaviour with respect to embedded components was correct. Why should embedded components be shared amongst worksheets/documents, just because the kernel engine is? It doesn't sound outrageous to me to consider that embedded components are individual to the sheet in which they are... embedded.

Or perhaps it is supposed to work, and it was broken by accident.

I suggest that you ask Maplesoft Tech Support ( support@maplesoft.com ) , @TomM , or submit a bug report.

Since you have supplied fsolve with no restricted range on t then why is one root (amongst infinitely many roots to your equation) more acceptable to you than another?

Why should fsolve prefer Pi/4 over -Pi/4 (or any other valid root)?

Do you feel that fsolve should always find the root closest to the supplied starting point? What about when the starting point is midway between two valid roots?

acer

Can you show us an example, even if it is pared down with your private code removed?

acer

@Carl Love I was able to improve the original's performance using Int and evalf (with a coarse tolerance) in the definition of g2 (along with some simplification steps of the ensuing results from diff). As you've noted elsewhere, sometimes it works better to deal with an exact result, while sometimes the purely numeric approach can do better. It's not clear to me which is  better here, as it seems both cases are moderated by simplification or code optimization.

But I did notice that using the method=ftocms option on the exact int call in the defintion of g2 yielded a symbolic result involving erf rather than Fresnel. It may be that this helps, in this approach of doing that inner integral exactly (including code optimization).

@goli Why wouldn't you bother to include that extra known information when posing your question?

@Yiannis Galidakis 

Note that it's not strictly necessary to pare down list F inside the plotting loop, using select. I did that to reduce the plot data and memory requirements. The key to getting your zooming look is, rather, the use of plottools:-transform. to make sure all frames get the exact same view, after rescaling.

In my previous attachment I changed the code to build PP (or P) using a table, which is converted into a list after the loop finishes. It is quite inefficient to construct large lists by appending.

In the following attachment I also made a related to change to the construction of list F, using seq instead of repeatedly appending to the list F in a loop. That runs faster when processing the L made from farey(100) say.

You should really try not to create lists in a loop, by appending. It makes such code as this much slower than it has to be. It can make time and memory resources be O(n^2) rather than O(n), say, and so make your code scale up much less well.

I also added dynanic (faked) x-tickmarks, to show more clearly that it is zooming in. You can of course remove that bit.

A nice next step might be to dynamically construct F depending upon the loop index k (and thus also upon w). The bookkeeping for that is a bit trickier, though, and may involve changing how you build L as well. The idea is to produce the same total number of values for F for each frame, using each k and w value, but to construct them with a repeatedly changing value range. It would mean that the central portion of the plots would remain filled with lines, as it zooms. That would be cheaper to produce, and leaner, than simply bumping up the value passed to farey() to produce a single, re-used, and very large F.

FareySeq_modif2b.mw

@Winkel That error message is telling you that the save command expects additional arguments.

Look at the help-page for save. That command expects the assigned names you want to save to the file.

Eg,

    save name1, name2,...,namek, fileName;

You have merely,

    save fileName;

and so the error message is "must specify names to save".

So, what are the names (whose values have been computed in your worksheet) that you want to save?

@Yiannis Galidakis Is this more like what you want?

Download FareySeq_modif2.mw

What does the Maple command kernelopts(homedir) return? 

(Presumably your OSX user name is not "Name"...)

acer

@Markiyan Hirnyk Yes, Robert's Answer itself contained `&lang;` and `&rang;` rather than < and >. I've corrected it.

@Carl Love It works for me in Maple 2015.1.

Markiyan's worksheet contains ⟨u,v,w⟩ which is,

`⟨u`,v,`w⟩`

That's the unicode U+27E8 and not the usual left bracket. You can also get it in Maple using the plaintext Maple Notation input,

`⟨`

Or maybe it's U+2329... What's also critical is that Markiyan's sheet has that bracket symbol concatenated with the `u`. Similarly for the `w` and the right bracket.

So the second argument to the Plane command is not a Vector, in his uploaded sheet. It's no wonder he has difficulty in getting the example to work.

@mapleq2013 I think I see what you mean now. I'll try and figure it out. I may not be around for a few days, though.

@mapleq2013 Since I don't see C=(-A3^(-1)).(B+A4) getting close to B when g gets close to zero, and since you state that it ought to, then I would hazard that A3 and A4 are not as you intended.

@mapleq2013 You have g appearing in A1,A2,A3, and A4 but not in your construction of B.

You assign (-A3^(-1)).(B+A4) to Bm but then you don't use Bm in constructing C! You just use B in constructing C.

My guess it that you just made an oversight during your revising, to not utilize Bm the Matrix that depended upon g. Is that possible?

Also, I don't see that C is very close to (-A3^(-1)).(B+A4) when g=0, although I do see a difference in Bm between say g=1/10 and g=1/1000.