Yes, I am asking because a search for definitions and explanations had led me to restricted resources to which I do not have access.

I have yet difficulties to understand this:

It means convex but only on paths which are aligned with an axis rather than between arbitrary points, ie on straight lines parallel to an axis.

as "convex" is used as a property of "curved" lines not stright lines. Could you post or give a  link to a picture of something that is axis convex and something that is not? Is there any relation with the pictures in this article? (whose nomenclature I find at least unusual: "A function f is said to be concave if − f is convex.")

appears to have some "geometric" knowledge, but I have not inspected its code in detail to know whether it just does repeated 1-dimensional integrals or something else.

Perhaps at this point it is useful to put the example in Maple form so as to talk on more concrete terms:

X:=<x,y>;U:=<u,v>;#the coordinate matrices

A:=<<alpha|beta>,<gamma|delta>>;#the transformation matrix

X=A.U;#ie the transformation "equation"

B:=<<a1|b1>,<a2|b2>,<a3|b3>,<a4|b4>>;

C:=<c1,c2,c3,c4>;#the matrices of boundary coefficients

BX:=B.X=C;#ie the "equations" for the boundaries in (x,y)

BU:=B.A.U=C;#the "equations" for the boundaries in (u,v)

B1:=eval(B,[a1=1,b1=0,a2=1,b2=0,a3=0,b3=1,a4=0,b4=1]);

C1:=eval(C,[c1=0,c2=1,c3=0,c4=1]);

BX1:=B1.X=C1;#the boundaries of the unit square in (x,y)

BU1:=B1.A.U=C1;#its transformed boundaries

zip(`=`,convert((simplify@(lhs-rhs))(BX1),list),0);

                 [x = 0, x - 1 = 0, y = 0, y - 1 = 0]

zip(`=`,convert((simplify@(lhs-rhs))(BU1),list),0);

  [alpha u + beta v = 0, alpha u + beta v - 1 = 0,
  gamma u + delta v = 0, gamma u + delta v - 1 = 0]

What does it mean?

in a dot version...

on the country where you live.

It's great to be a student nowadays.

The Reference guide sect. 4.8 deals with this issue.

I have added some additional info on this subject here

However, I do not see a clear relationship between input/output and automatic simplification. Eg, I give the input:

2*(a+b);

and I get the output

	2*a+2*b

not because of input/output format issues. And similarly if I wanted to factor out "2".

I have added some additional info on this subject here

However, I do not see a clear relationship between input/output and automatic simplification. Eg, I give the input:

2*(a+b);

and I get the output

	2*a+2*b

not because of input/output format issues. And similarly if I wanted to factor out "2".

the domain 0..1 X 0..1that you propose  will transform (generically) into a quadrilateral with no side aligned to the (u,v) axes. So, I do not see how to avoid dealing with this issue.

like writing a result into a specific form may be harder with Maple (or any other CAS) than making "large" calculations like series expansions.

I know some persons that use a CAS only to make a plot or calculate an integral. Apparently, their minds do not seem to match those of the developers, as projected onto how their product works. And some other persons hardly make any calculation without the computer.

In my point of view, it is better to know the strong and weak points of the system and use it for what it is most efficient.

Note also that crosschecking is always useful.

like writing a result into a specific form may be harder with Maple (or any other CAS) than making "large" calculations like series expansions.

I know some persons that use a CAS only to make a plot or calculate an integral. Apparently, their minds do not seem to match those of the developers, as projected onto how their product works. And some other persons hardly make any calculation without the computer.

In my point of view, it is better to know the strong and weak points of the system and use it for what it is most efficient.

Note also that crosschecking is always useful.

Yes, though Maple has very advanced mathematical features, there are some "corners" of the system that remain locked to rather low level manipulation of data structures from its origins in the early 80's.

I think that improvements on isolating the user from those details can and should be made. But probably their scope will be limited by this heritage.

Yes, though Maple has very advanced mathematical features, there are some "corners" of the system that remain locked to rather low level manipulation of data structures from its origins in the early 80's.

I think that improvements on isolating the user from those details can and should be made. But probably their scope will be limited by this heritage.

It is not stated in ?solve,identity but, apparently, the list of variables can be omitted. Here:

solve(identity(func_num = func, x));
  {c = 3.660000000, a = 1.330000000, b = 2.440000000}