you do not need 'map', but use directly x::RealRange(2,6). Ie:

convert(x::RealRange(2,6),relation);
                         And(2 <= x, x <= 6)

In Maple 12:

numer(P3(x,1))/simplify(denom(P3(x,1))) assuming x>0;

-1/2/x^(1/2)*(x+8*x^2+2)/(2*x^2*(x+2)^(1/2)+(x+2)^(1/2)+2*x^(5/2)+2*x^(3/2))/(x+2)^(1/2);

int(%,x=0..infinity);
		-8/5*2^(1/2)

arises in Maple 10.06 and 11.02.

arises in Maple 10.06 and 11.02.

The first part could go as follows:

RealRange(2,5) union RealRange(3,6);
subs(`union`=Or,%);
map(u->x::u,%);
map(convert,%,relation);
simplify(piecewise(%,1,0)):
convert(%,list);

               RealRange(2, 5)  union  RealRange(3, 6)

                 Or(RealRange(2, 5), RealRange(3, 6))

              Or(x::RealRange(2, 5), x::RealRange(3, 6))

             Or(And(2 <= x, x <= 5), And(3 <= x, x <= 6))

                   [x < 2, 0, x <= 6, 1, 6 < x, 0]

The first part could go as follows:

RealRange(2,5) union RealRange(3,6);
subs(`union`=Or,%);
map(u->x::u,%);
map(convert,%,relation);
simplify(piecewise(%,1,0)):
convert(%,list);

               RealRange(2, 5)  union  RealRange(3, 6)

                 Or(RealRange(2, 5), RealRange(3, 6))

              Or(x::RealRange(2, 5), x::RealRange(3, 6))

             Or(And(2 <= x, x <= 5), And(3 <= x, x <= 6))

                   [x < 2, 0, x <= 6, 1, 6 < x, 0]

At least without an additional trick.

Perhaps, an updated comparative review between CAS on special functions could be interesting in the Wiki, at least for reference. In a first stage, present some interesting cases or identities and people with different systems make the tests and put the results.

At least without an additional trick.

Perhaps, an updated comparative review between CAS on special functions could be interesting in the Wiki, at least for reference. In a first stage, present some interesting cases or identities and people with different systems make the tests and put the results.

When I make 'Trace' of the Mathematica integral I get a list of, basically, algebraic expressions. I guess that some pattern matching is involved here. If that is all, no MeijerG function is involved.

When I make 'Trace' of the Mathematica integral I get a list of, basically, algebraic expressions. I guess that some pattern matching is involved here. If that is all, no MeijerG function is involved.

gives -2*sqrt(2) as the old versions of Maple. But this result does not show that this version of Mathematica goes to calculate this integral using the MeijerG function (I think that the old versions of Maple did not). I do not know how to trace what Mathematica does here.

gives -2*sqrt(2) as the old versions of Maple. But this result does not show that this version of Mathematica goes to calculate this integral using the MeijerG function (I think that the old versions of Maple did not). I do not know how to trace what Mathematica does here.

The support for sets in Maple is very limited and fragmented. Do not expect too much. As far as I understand it, 'in' should not be used in this case, as it represents element membership. I think that you mean here the 'subset' relationship. But it does not seem to be much useful here, eg:

R2 subset R2;
                                 true

R1 subset R2;

`subset`(RealRange(1,5),`union`(RealRange(1,3),RealRange(2,5)))

 If you see ?union, all the examples there are for "explicit" sets, ie things like {a,b,c}, which are of type 'set'.

Note also that another kind of sets are those made with the 'SetOf' constructor, but they are not of type 'set', eg:

type(SetOf(real),set);
                                false

is(5.6 in SetOf(real));
                                 true

The support for sets in Maple is very limited and fragmented. Do not expect too much. As far as I understand it, 'in' should not be used in this case, as it represents element membership. I think that you mean here the 'subset' relationship. But it does not seem to be much useful here, eg:

R2 subset R2;
                                 true

R1 subset R2;

`subset`(RealRange(1,5),`union`(RealRange(1,3),RealRange(2,5)))

 If you see ?union, all the examples there are for "explicit" sets, ie things like {a,b,c}, which are of type 'set'.

Note also that another kind of sets are those made with the 'SetOf' constructor, but they are not of type 'set', eg:

type(SetOf(real),set);
                                false

is(5.6 in SetOf(real));
                                 true

because of problems in the theory/algorithms  or in the implementation?