After this post, apparently, the concern was just the opposite.

After this post, apparently, the concern was just the opposite.

with this Java GUI, I would prefer to use my favorite editor and a facility to inject code into the session, than a builtin Java programming editor/IDE.

with this Java GUI, I would prefer to use my favorite editor and a facility to inject code into the session, than a builtin Java programming editor/IDE.

input regions, but not in 2D input regions. Ie toggling the button on does not seem to have any effect. This is documented in ?worksheet,documenting,tabkey

input regions, but not in 2D input regions. Ie toggling the button on does not seem to have any effect. This is documented in ?worksheet,documenting,tabkey

in Word 2000 and Abiword 2.4.4: Insert > Page Numbers. Also OpenOffice Writer 2.4:Insert - Fields - Page Numbers.

show analytically that the 'CauchyPrincipalValue' is right. We can get the leading behavior for epsilon ->0 this way:

s:=omega > epsilon,epsilon > 0:

K:=int(sqrt(x)*omega/(x*(omega-x)), x = 0 .. omega-epsilon)+
int(sqrt(x)*omega/(x*(omega-x)), x = omega+epsilon .. infinity) 
assuming s;

subs(omega+epsilon=u^2,omega=Omega^2,K);

simplify(%) assuming u>Omega, Omega>0;

subs(u=convert(series(sqrt(omega+epsilon),epsilon=0,3),polynom),
Omega=sqrt(omega),%);

subsindets(%,specfunc(algebraic,arctanh),
x->convert(series(x,epsilon,3),polynom));

evalc(%) assuming s;

                   -epsilon/sqrt(omega)

Ie, the limit is 0 when epsilon ->0.

A workaround is needed here because of some weaknesses in the simplification.

with 'RealRange'. Eg nonumeric arguments are not allowed:

RealRange(a,a) assuming a::real;

Error, (in assuming) when calling 'RealRange'. 
Received: 'invalid arguments'

Indeed, this is documented. But I do not see any good reason for this implementation. Apparently, the only aproximation to that is via 'ComplexRange', something like:

ComplexRange(a,a) assuming a::real;

In fact, I do not expect this to work, but in this line, I find this error message more informative than the help page:

is(1.5 in ComplexRange(a,b)) assuming a<1 and b>2;

Error, (in assuming) when calling 'property/ConvertSetOf'. 
Received: 'second operand to `in' must be a set, a SetOf(property),
or a property, but got ComplexRange(a,b)'

PS OK, to add something else to this mixture, this works:

verify(1.5,a..b, 'interval') assuming a<1 and b>2;
                                 true

is that there is not better thing to represent sets like real intervals  (similarly  for  sets  in the  complex plane, etc). In general, the support for (abstract) sets is weak. Facilities for union, intersection, etc, of real intervals as sets should be provided.

And it should be possible to specify a set of discrete  (non explicit) values and make a sum over them (eg sum over fractions of the form odd integer/2 ) or a set as a union of real intervals and make an integral over them.

I do not think that these facilities would be very hard to implement. So, I do not understand why these so basic mathematical tools are not provided.

I doubt that it could work.

Such functions could be expressed in terms of a sum of Heaviside terms, one for each discontinuity point, xi say, with jump Ci. Hence it satisfies an ODE in the sense of distributions, with inhomogeneity as a sum of terms Ci* Dirac(x-xi).

To produce such ODE, or something equivalent, somehow  'dpolyform' should locate these xi, and find their Ci.

PS Apparently, 'discont' works here to locate the xi:

discont(f(x),x);

{0, -exp(1/2*Pi*(1+2*_Z4)), -exp(1/2*Pi*(1+2*_Z8)), 
exp(1/2*Pi*(1+2*_Z1)), exp(1/2*Pi*(1+2*_Z5))}

of using LaTeX for input. Sadly, Maplesoft is focused on a kind of mathml, Maple-mathml say. I do not have much hope of a change in the near future. As I see it, either you use this Maple-mathml as here:

plot(sin(x),x=0..Pi,title=sin(`σ`));

ie _backquote_ampersand_sigma;_backquote_ (in the Standard GUI only), or you postprocess the exported plot with some LaTeX capable tool.

that

is(ComplexRange(1,2+I) in ComplexRange(0,2+2*I));

do not work as 'in' represents element membership. Being sets, I would expect that a set inclusion relationship had to work, as eg:

{1} subset {1,2};

                                 true

is({1} subset {1,2});

                                 true
verify({1},{1,2},`subset`);

                                 true

but with 'subset' it does not:

ComplexRange(1,2+I) subset ComplexRange(0,2+2*I);

       ComplexRange(1, 2 + I)  subset  ComplexRange(0, 2 + 2 I)

is(ComplexRange(1,2+I) subset ComplexRange(0,2+2*I));

Error, (in is) invalid input: is/internal uses a 2nd argument, prop, which is missing

verify(ComplexRange(1,2+I),ComplexRange(0,2+2*I),`subset` );

                                false

as:

is(RealRange,type);
                                 true

is(ComplexRange,type);

                                false

And ?RealRange states:

RealRange is a Maple program - it analyzes the input parameters; ComplexRange is not a program

Though, also states:

A ComplexRange is an object more general than a RealRange in that it contains it as a particular case.

I do not catch here what the author of this phrase means. I find these statements confusing, if not contradictory. It states what ComplexRange is not but not what it is. And whatever it is, it states that it contains RealRange, which is a program, as a particular case.

So, I read these sentences and I wonder what is this more general thing that it is not a program but contains a program.

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

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