I am having hard time controlling my Latex:-Settings now. The issue is that I do not know what each setting accepts as values, and what each value does.  The way I've been doing it is by collecting what useful ones posted in this forum, and what it does and save it in my cheat sheet. 

But now I see I need to change something, but not sure to what.

Is there a way to find what all the settings are, and description  of what each does and accepts as values? For example, 

            powersoftrigonometricfunctions

Accepts mixed and computernotation  But where are these described in terms of what they do? does it accept anything else?  Notice that ?leavespaceafterfunctionname does not show anything.

If I do 

restart;
Latex:-Settings()

it gives

[cacheresults = true, invisibletimes = " ", leavespaceafterfunctionname = false, 
powersoftrigonometricfunctions = mixed, spaceaftersqrt = true, usecolor = true, 
useimaginaryunit = I, useinputlineprompt = true, userestrictedtypesetting = false, 
usespecialfunctionrules = true, usetypesettingcurrentsettings = false]

But do not know how to obtain full description and possible value of each to see what they mean and do.

I think having Latex:-Settings() is a great idea, as it allows maximum flexibility for user to configure how they want the Latex output to be, but as more options are added, this type of information become more important to know and to keep track of.

I am using 2020.2 and Physics version 893

I was trying to find if the type of module wide variable is considered local or global.

I have an exported variable in module. Maple then said it was local . OK

restart;
foo:=module()
   export n::integer;
   export boo:=proc()::integer;
     return n;
   end proc;       
end module;
                   

n:=foo:-boo():
type(n,`local`);

               # true

But when I did this

restart;
foo:=module()
   export n::integer;
end module;

n:=foo:-n;
type(n,`local`)

         #false

Now Maple says it no longer local.

What is the difference? The module wide variable is exported in both cases. So one can access it directly like in the second example above, or via call to a proc inside the module, which returns it.

Why in one case it is local and in the second case it is not?

Ok, I found the issue. It seems when doing return  n; in the first example above, it created and returned a local n to the proc itself (where n was not declared in the example). (even though maplemint did not complain. Strange).

I have assumed when doing return n Maple will know this is the module wide variable n since that is the closest one around.  i.e. the proc is inside the module. And n sits inside the module. So return n should referenced this variable. But it did not, because when I changed the code to this

restart;
foo:=module()
   export n::integer;
   export boo:=proc()::integer;
     return foo:-n;
   end proc;       
end module;

n:=foo:-boo():
type(n,`local`);

     #false

Now it returned false. The same as the second example.

But it also returned false when asking if it is global

n:=foo:-boo():
type(n,`global`);

    #false

So the module wide variable n in this example is not local and is not global.

Is there another type to use to check if the variable/symbol returned is a module wide type?

Maple 2020.2

I assume the goal is to have the Latex output close to the screen output in Maple. In these examples this is the case.

Example 1

restart;
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]):
LinearAlgebra:-NullSpace(A)

But the Latex generated for the above, using the Latex() command is

\{ \left[\begin{array}{c}0 \\2 \\-1 \\1 \end{array}\right] \} 

Which when compiled

\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\[
\{ \left[\begin{array}{c}0 \\2 \\-1 \\1 \end{array}\right] \} 
\]
\end{document}

gives

The latex should instead be 

\left\{ \left[\begin{array}{c}0 \\2 \\-1 \\1 \end{array}\right] \right\} 

Which compiles to

Example 2

restart;
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]):
LinearAlgebra:-RowSpace(A)

The Latex of the above is 

[\left[\begin{array}{cccc}1 & 0 & 0 & 0 \end{array}\right], 
\left[\begin{array}{cccc}0 & 1 & 0 & -2 \end{array}\right], 
\left[\begin{array}{cccc}0 & 0 & 1 & 1 \end{array}\right]]

Which when compiled gives

\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\[
[\left[\begin{array}{cccc}1 & 0 & 0 & 0 \end{array}\right], 
\left[\begin{array}{cccc}0 & 1 & 0 & -2 \end{array}\right], 
\left[\begin{array}{cccc}0 & 0 & 1 & 1 \end{array}\right]]
\]  
\end{document}

gives

A better Latex would be

\left[\left[\begin{array}{cccc}1 & 0 & 0 & 0 \end{array}\right], 
\left[\begin{array}{cccc}0 & 1 & 0 & -2 \end{array}\right], 
\left[\begin{array}{cccc}0 & 0 & 1 & 1 \end{array}\right]\right]

Which compiles to

Now the size of the [[ is the same on both ends.

example 3

restart;
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]):
LinearAlgebra:-ColumnSpace(A)

The Latex given for the above is

[\left[\begin{array}{c}1 \\0 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\1 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\0 \\1 \end{array}\right]]

Which when compiled

\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\[
[\left[\begin{array}{c}1 \\0 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\1 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\0 \\1 \end{array}\right]]
\]  
\end{document}

gives

A better Latex is

\left[\left[\begin{array}{c}1 \\0 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\1 \\0 \end{array}\right], 
\left[\begin{array}{c}0 \\0 \\1 \end{array}\right]\right]

Which compiles to 

Maple 2020.2 with Physics  891 

Here is the problem. I am trying to use sort() to make solution to ode show up with constant of integrations _C1 at the front of the term, instead of how Maple shows it, which is after the term, which does not look good.

As recommened in  Why-Maple-Refuses-To-Change-Location

sort() works well. Except for this: I am also using alias for the constant of integrations, to get nicer Latex output, as recommended in earlier post (which I can't find now). 

But once I use alias, now sort no longer produce the result I want. Here is an example

restart;
sol:=dsolve(diff(y(x),x) = x+y(x),y(x));
sort(sol)

Here sort works. It moved the term with constant of integration to the front, and _C1 at front, which is what I want as it looks more clear.

But when I do 

restart;
alias(seq(c[k]=_C||k,k=0..10)):
sol:=dsolve(diff(y(x),x) = x+y(x),y(x));
sort(sol)

This is because, I am assuming, the order of _C1 is higher than c[1] and sort is using the alias of _C1 to sort on and not _C1 itself.

The only reason I am using alias, is to get nicer Latex output when converting the solution to Latex vs. when using _C1

Is there a way to tell sort to treat c[1] as _C1, and c[2] as _C2, etc...  in terms of lexicographical ordering?

I see an order option for the command sort() in help, but so far did not know how to use it for the above purpose. This only affects _C1,_C2,_C3,_C4,.. and nothing else and I only use sort() on the output of the solution of ode. May be I need to write an order function and in there tell it c[1] has same order as _C1? But _C1 has c[1] as alias? so I do not think this will not work.

Basically I want to use the alias, but also use sort() on the result as if these constants of integrations where _C1,_C2, etc..

in my code, I set the alias at the global level, before I call any function in my package.

Any ideas how to do this or workaround this?

Maple 2020.2 on windows

This puzzling to me. First will show the code, then explain the problem

restart;
ode:=diff(diff(y(x),x),x)+8*diff(y(x),x)+25*y(x) = 1;
sol:=dsolve(ode);
sol:= y(x)= _C2*exp(-4*x)*sin(3*x)+ _C1*exp(-4*x)*cos(3*x) + 1/25;
sol:= y(x)= _C2*exp(-4*x)*sin(3*x)+ _C1*exp(-4*x)*cos(3*x) + 1/25;
sol:= y(x)= _C2*exp(-4*x)*sin(3*x)+ _C1*exp(-4*x)*cos(3*x) + 1/25;

restart;

sol:= y(x)= _C2*exp(-4*x)*sin(3*x)+ _C1*exp(-4*x)*cos(3*x) + 1/25;

I was trying to changing the constant of integrations, to make them show at front, where it is better. But Maple refused to do so. Here is the output:

Why restart is needed to make Maple keep the output same as input? is it possible to rewrite it without having to do restart?

Download why_restart_needed.mw