Maple, any other CAS, or non-pure-mathematicians are not worth baldness or infarction!

In regards to physicists things are a bit more varied. Certainly the "Operationalism" is somewhat influential and there are even jacobins that teach and write books like Arnold's interlocutor. And you may discover "physical" differentials and many other niceties like that.

You may even find its effects in the documentation of Maple:

?Dirac

... where in all these formulas epsilon represents a sufficiently small real number. In practical applications, as soon as epsilon becomes negligible compared to the distances involved in the problem, it becomes impossible to distinguish between these alternative representations and the usual definition of Dirac as a distribution. ...

But there are also physicists that "understand" Mathematics and are aware of theorems and so on.

Education is indeed influential, but even more important is the purpose. Mathematics for a physicist is a tool, not an end in itself, and the priority is to make the calculations and get the results. So, not so much because of lack of education but because of practical needs, the "optimist" position is frequently taken that if a property is required to go on with calculations, it holds. Sometimes problems do arise, eg limits that do not commute, etc,  but only exceptionally.

In this context it is generally assumed that functions belong to the "good" class: their derivatives commute and so on. And typically it works. Probably because how these functions arise (compositions of elementary functions, solutions of  differential equations or expressed by integrals).

I guess that this is also the "market" of many of the algorithms implemented in Maple. So, I do not see a priory a contradiction. They work and are right provided you restrict to good functions.

The project Axiom, bets to do things "right", theorem based, literally documented, within a long period of development ("the 30 years horizon"). May be that Tim Daly is right, but that is another market.

My impression is that physicists are a small minority in Maplesoft staff.

Conditional solutions is from Maple 11 (?updates,Maple11,symbolics).

The subpackage RootFinding[Parametric] is new in Maple 12. Marketing could say [quoted from ?updates,Maple12,enhancedpackages]:

The new subpackage RootFinding[Parametric] for analyzing and solving systems of polynomial equations and inequalities depending on parameters has been added to the RootFinding package. It offers the ability to answer questions such as the following: for which parameter values does the system have a solution, or a given number of solutions?

Plots of the regions in 2 parameter space are nice, but work well only for Standard GUI:

CellPlot(m,samplepoints=true);

had no problem with Matlab 13, apparently.

On this side, Maple has improved lately:

solve(a*x>b,{x});

with(RootFinding[Parametric]):
m:=CellDecomposition([x^2+b*x+c=0],[x],[b,c]);

for i to 4 do
NumberOfSolutions(m)[i],CellDescription(m,i);
end do;

  [1, 2], [[-infinity, 0, c, c, 1], [-infinity, 0, b, infinity, 0]]
  [2, 2], [[c, 1, c, infinity, 0], [-infinity, 0, b, b  - 4 c, 1]]
  [3, 0], [[c, 1, c, infinity, 0], [b  - 4 c, 1, b, b  - 4 c, 2]]
  [4, 2], [[c, 1, c, infinity, 0], [b  - 4 c, 2, b, infinity, 0]]

I have just read your post and verified this difference between the time in the heading for my last post and my clock time. On the other hand, the intervals in the column  "Recent comments" seem fine.

by default. Give it a higher value, eg 7:

p:=7:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x,7);

by default. Give it a higher value, eg 7:

p:=7:
f:= sum(1/n^p,n=x+1..infinity): asympt(f,x,7);

seems right. Indeed, you could get the same result much more simply.

seems right. Indeed, you could get the same result much more simply.

is indeed an additional issue.

However, my question was about the meaning of your statement "subsets of measure 0" in the context of the Riemannian integral, as measure is not a concept used of this integral, as I know it.

Yes, the integral in "Maple sense" is a melange. i would be very happy if it were available a "DistributionTool" package that provides a 'diff and 'int' in distributional sense, so that ordinary 'diff and 'int' behave as expected for ordinary functions.

And I have made efforts to get removed that aberration of 1/2 for the integral of Dirac delta from 0 to infinity, which were unsuccesful up to now.

Now that I seem to understand this definition, the issue you pose seems to be start from an axis-convex region for all the n variables (apparently it implies R^n convexity). Transform by a general (but overall smooth) change of coordinates and you may get in the new variables a region that is non axis-convex for at least one coordinate (so it is not R^n convex either).

So, you should first recognize this nonconvexity and then split the region into  convex subregions. It does not seem a trivial issue. I see that there is a branch of geometry called Convex geometry.

Thank you for these examples. It means then convex in the 1D set sense for a whole family of parallel stright lines crossing the region.

is what you mean then?

There are sets that curvilinear coordinate charts do not cover like the origin in spherical coordinates and the axis of symmetry in cylindrical coordinates. You mean to "complete" the chart including them somehow to get a closed integration region?

Apparently, it is only possible by asking Will to do it.

[I have not replied to that "duplicated" post so that Will could delete your post and this one]

for r=0, so, these conditions for bijectivity restrict to r>0, if I understand correctly what you mean.