This is your worksheet reviewed.

Download Fourier_transform_(reviewed).mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

As per the Title, you can set the invisibletimes (the spacing or symbol used to represent a product); its default value is " " (to reproduce, please update to v.883 of the Maplesoft Physics Updates). In your example:

Note, however, that this affects every product, not just after \sqrt{}.

Regarding yours and @itsme comments, I basically think the same: the latex typesetting system is already excellent. Trying to tweak it is something to be done with extra care and only in exceptional situations. For example, \sin (x) is not typeset with a space before (x), but in an automatic mode, we go with \sin \left(x \right), which is typeset with a space after sin, so I see no harm in translating this as \sin\! \left(x \right). And as @itsme says, providing an option to undo this tweak (you can input Latex:-Settings(leavespaceafterfunctionname = true) and won't see that \! anymore).

Altogether, I will think about the specific case of \sqrt{xxx}. There is a point in that, in the worksheet, I see a space before the a that I don't see in the tex-compiled translation. On the other hand, it is also true that for latex typesetting, that space shouldn't be there.

And I want to take the opportunity, following @itsme, to thank you for all the feedback you are giving. It is a very fruitful exchange for all Maple users. As it is the case of all the DE, Physics and Mathematical Functions, code; this kind of feedback and exchange (through the Maplesoft Physics Updates) is the best possible approach I imagine to develop software.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

If you quote your input, it is echoed on the screen with an equation label that you can refer to all around. If besides, you place the cursor on the input line and press the combo Ctrl + Delete (or Command + Delete on a Mac), that input line disappears, but the output and its equation label remain. It is an easy way to produce equation labels for math correctly displayed, and that is not executed. Using the "Context Bar" (see the View menu), you can also change this output by centring Y/N or make parts of it italic or bold, underline, change colours etc. 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

Nicely spotted; there was a typo in a list of math functions for which latex has a special command. The fix is distributed as usual, within the Maplesoft Physics Updates, v.780 or newer.

Additionally, I don't like the lack of space between 4 and the exponential, due to using \mathrm. In v.781 and newer, that is resolved, so that the tex-translation is now this one:

and upon latex compilation -> PDF, we get this look

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi

This was asked before. If, after having used Latex, you change the way things are Typeset on the screen, say by direct calls to the Typesetting package, remember to clear Latex's caches so that the new look is taken into account. In brief, to have things working the way you want, in v.879 and before, after Typesetting:-Settings(prime=x,typesetprime=true), enter Latex:-Forget(). Alternatively, just use Latex(...., forget); and that will make Latex not remember previous results.

In v.780, you can also use the new Latex:-Settings(cacheresults = false), the default value is cacheresults = true; setting cacheresults to false makes Latex not to cache results, so you don't need to enter Forget after changing the way things are typeset on the screen, nor to pass the keyword forget to ignore previous results.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi

I understand there was a glitch in the MapleCloud server, versions 875 and 877 didn't get stored. The problem got resolved. Current is v.878.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

This is development, things are moving ahead. At this point you have Latex:-Settings. Use that instead of assigning the variables yourself. This is your worksheet using Settings:

Among other things, using Settings you don't need to use Latex:-Forget after changing any setting.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi
Indeed, this is an issue introduced recently when adding the new Latex:-Settings(powersoftrigonometricfunctions = textbooknotation), see this Mapleprimes reply. It is adjusted in the Maplesoft Physics Updates v.870 and newer.

To the side: with v.869, you can still work OK if you input Latex:-Settings(powersoftrigonometricfunctions = computernotation), which is the standard notation used by Maple to display trig and arctrig functions. I am experimenting with having textbooknotation as default, say that is option 1. There is option 2: textbook notation only for trig (so cos(x)^2 is tex-translated as cos^2(x), but arccos(x) remains arccos, not cos^(-1)). Then option 3 is to have computernotation by default. Some people already expressed that for students this textbooknotation is a bit confusing. I remember that too from the time I was teaching at university.

So most probably textbooknotation will be optional, not the default as you see in this moment.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

It is the first time I see someone complaining about \rm ....(wow!). Learning. If some packages don't handle \rm, we need a replacement. By the way, \rm is being used within the whole Latex in only one place, to represent the e of 'exponential'. Where else is that you saw it popping up? And for a single letter, \mathrm or \textrm work as well. Any indication that  one is better than the other one?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

As everybody guessed, there was a place in the code where an expansion of exp(x + y) was not happening, that place was PDEtools:-Library:-IsNotSeparable, a quick shortcut to avoid wasting time with unsolvable problems. Without that expansion, for some arbitrary F(x + y),  deq1 := diff(u(x, y), x) - diff(u(x, y), y$2) = F(x + y); is of course not separable.

This issue is resolved and the adjustment distributed for everybody within the Maplesoft Physics Updates v.865 and higher; thanks for posting the example.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

One condition, with denominator different from zero, for the existence of a solution using the S-function method was missing. A fix for this is distributed within the Maplesoft Physics Updates v.864 or newer.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

Good point, although there is always the issue of who is the prime variable.. I'll add something for this in the next version of the Maplesoft Physics Updates. And what do you expect for PDE boundary conditions? Jet notation as you see in the help page for PDEtools:-ToJet?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

See Workaround for the problem of installing MapleCloud packages in the Windows platform; probably that is your case.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

For reasons A and B that I skip here, in cases like this one, I coded to try a particular solution using symmetries, a computationally not-expensive and conceptually simple approach, however not well known by most people. See ?dsolve,details. In Maple, this approach is coded within DEtools[particularsols] for nonlinear equations. I don't have the books with me right now, but it may be explained in the symmetry books by George Bluman or the one by Peter Olver.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Textbook notation shows "sin^2 x", not "sin^2 (x)" as Mathematica does. I understand the lack of parenthesis in textbook notation is the reason for showing the exponent right after the function's name.

In the DLMF, arguably the main reference for mathematical functions, basically all functions of one argument are displayed without parenthesis. For all of them, one could expect the exponent right after the function's name. On the other hand, in Mathematica, only Log and trig (not arctrig) functions are displayed that way.

This topic you bring is thus more about a convention for displaying powers of trig functions only - shall they be displayed differently than other functions Y/N?

The answer is debatable. I think the relevant things to keep in mind are:

1. standard notation
2. consistency
3. non-ambiguous notation
4. keep an eye on possible confusion with input notation

That said, consider these images:

These three expressions are mathematically different, the third one actually is a wrong representation of sin(x)^2, but of course valid input that makes sense in some (operator) contexts. So we want a representation for the three of them. In Maple, the second one in the input is actually equal to sin(x)^2.Textbook notation, however, represents the second one in the input, as the third one in the output - mixing these two, against item 3. If we go with what you suggest, we would also have no notation for the first expression in the input unless you suggest that sin^(2) <> sin^2, which for me would be against items 1. and 3. Complicated.

Next two images tell the same, just focusing closer:

These two are different expressions, that also look different in the input and the output. Your suggestion would make the two sides of the inequality look the same. Likewise, consider:

Here again, two different objects are displayed differently in the output - that is good, but your suggestion would make them look the same when translated to LaTeX.

So I see merit in what you say, the habit of writing "sin x" and, therefore, "sin^2 x" (not sin^2 (x)) is a compelling argument towards tex-translating sin(x)^2 to \sin^2 x. However, the computer still handles (sin@@2)(x) and also the (operator form) "sin^2 * x" and we need a representation for those too.

Taking all into account, what do you suggest?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft