I am not able to use Maple's map() to do the following. Given 2 lists of things (of equal length), map a function that take 2 arguments, from these 2 lists, in order.  Here is an example to illustrate. In Mathematica

a = {1, 2, 3}; b = {7, 8, 9};
MapThread[f, {a, b}]

           {f[1, 7], f[2, 8], f[3, 9]}

In Maple, I tried map and map2, map[n] etc.. not able to get the result I want. I want to use map, and not ~

A:=[1,2,3];
B:=[7,8,9];
map((x,y)->f(x,y),A,B)

          [f(1, [7, 8, 9]), f(2, [7, 8, 9]), f(3, [7, 8, 9])]

map[2]((x,y)->f(x,y),A,B)

           [f([1, 2, 3], 7), f([1, 2, 3], 8), f([1, 2, 3], 9)]

and other things.

How to get same result as MapThread, using map?

I did not know about these before. Was looking at 

https://fr.maplesoft.com/support/help/Maple/view.aspx?path=repository/management

And wanted to display the actual values of $MAPLE,$TOOLBOX, $VERSION,$HOME gives about. 

But everything I tried does not work. 

anames('environment');
getenv("$MAPLE");
print("$MAPLE/toolbox/$VERSION/$TOOLBOX/lib")

Where are these things defined and how to display them from inside Maple to see where they point to?

Maple 2020.1 on windows 10

dAlembert ode has the form

https://fr.maplesoft.com/support/help/Maple/view.aspx?path=odeadvisor/dAlembert

Which also agrees with textbooks and Wikipedia

https://en.wikipedia.org/wiki/D%27Alembert%27s_equation

So the ODE should have   x  in there (the independent variable).  

Then why  in the following, when I give Maple ode of form   y=f(p)+g(p)  it says it is d'Alembert? notice that there is no x in there

restart;
ode:=y(x)=ln(cos(diff(y(x),x)))+diff(y(x),x)*tan(diff(y(x),x))

DEtools:-odeadvisor(ode)

I am not saying Maple is wrong, as I am not sure, but I am just trying to understand what is going on. All references I've seen so far say x should be there.  Otherwise, how did Maple determine it is dAlembert if not using the orginal form to check against?

The strange thing is calling dsolve on the ode, with no option gives different answer if calling dsolve telling it is is dAlembert:

dsolve(ode,[dAlembert]);

but

dsolve(ode)

Why it did not give the same result? 

I noticed the following. I have 2 worksheets. A.mw and B.mw.  From A.mw, it does something as follows

libname := currentdir(), libname
foo();

Where foo() is entry inside my say TMP.mla in currentdir(). This works fine with no problems and foo() executes and complete OK.

Now I make changes to the code foo.mpl, and need to update TMP.mla. currently I use LibraryTools. But i'd like to delete TMP.mla each time and create new one so I am sure there is no problem. So from B.mw I run this code

libname:= currentdir(),libname;
FileTools:-Remove("TMP.mla");
LibraryTools:-Create("TMP.mla");
read "foo.mpl";
LibraryTools:-Save('foo',"TMP.mla");

This all works well, except it fails at the Remove line, since "TMP.mla" could not be removed, since it was open before when running the A workseet, and it seems to be still open and Maple could not delete the file.

So each time this happens, I close all worksheets, close Maple, open Maple again, and now I can run the above code OK to update the mla.

Is there a better way to do all of this?

I worry if I do not delete the mla each time, I could end up with old code there I do not want, if I rename things in my code. That is why I like to start with fresh mla file each time.  But I always have to restart Maple now to update the mla.

from help, it says 

The expression assuming property calling sequence evaluates the expression under the assumption property on all names in expression.

Then why 

restart;
expr := Sum((-1)^n - 1, n = 1 .. infinity):
simplify(op(1,expr)) assuming n::even;

does not simplify expr to zero, while

restart;
expr := Sum((-1)^n - 1, n = 1 .. infinity):
assume(n::even):
simplify(op(1,expr))

does simplify expr to zero.

I would have expected both to give zero.