@Markiyan Hirnyk 

What unbased words?

 p =    

p<0 implies argument(sqrt(p))  = Pi/2  ==>   ex = - (positive)*sqrt(p)  has the argument -Pi/2.

For omega=10^6, the graph of u(t) e.g. looks like this for t in [0.5,1]:

@adel-00 

It is nothing wrong with your system. It is linear and has a unique "nice" solution from a mathematical point of view.

It is the oscillatory nature of the solution. Have you read my simple example (previous answer)? The same situation happens here.
You can obtain a series solution but because Omega is so large, the Order of the series must also be large and then the roundoff errors will be huge. But even if an exact solution would be possible, it is not clear to me how are you going to use it -- unless you need it only in a small neighborhood (-eps,eps) or [0,eps).

@John Fredsted 

Instead of using "proc valued procs", why don't you use procs with 2 arguments an then curry (or rcurry) if needed.

h:=(x,y) -> 2*x+3*y;

curry(h,a);

curry(h,a)(b);

@Preben Alsholm 

But this way, unapply will be executed each time g is invoked, isn't it?

What special features of Maple are you talking about?

@fereydoon_shekofte

@litun 

consts is simply a list of your float constants.
You should work symbolically. In the last step, when you need a numerical value for an expression expr
use eval(expr, consts).

Later,

otherconsts:=[...];
eval(expr, otherconsts);

Expressions with floats are hard to simplify. For example, the addition is not associative.
Therefore it is much better to use rationals and symbolics and plug in the floats as late as possible.

@litun 

@litun 

It is better to use floats after simplify.
Symbolic expressions with floats must be manipulated carefully.

test-1x.mw

In earlier versions, Maple had the terms "monomial" and "term" twisted. But now they are used as I said.

BTW, please note that the Monomial Order would not be a true order in the set of monomials if a monomial would contain coefficients. But if you prefer the twisted terminology, it's OK.

Note also that if we want the terms of G,

op ~(G)

is enough.

@Markiyan Hirnyk 

Usually, in Groebner package these are terms, not monomials, see e.g. ?LeadingTerm.

@Markiyan Hirnyk 

@acer 

This is no doubt the most natural solution, and appears clearly in the help file.
Unfortunately it seems to me that the search mechanism in the help system and its organization are now worse than they used to be. I even found parameters not described in the help page but they appear in a tutorial!

Thank you for the answer. I was looking for a quick method to test/modify/debug one procedure without having do execute all of them. Not a big deal, the execution group can be split of course.

@tomleslie

@Markiyan Hirnyk 

In worksheet mode, which I almost always use, it is OK.

@H-R 

It's not enough to assume that u is real; you must work in a domain where all radicals have nonnegative arguments and unambiguous signums for their subexpressions (factors).

Otherwise, you could be right, but:

1. This kind of things happen in any CAS.
2. There are workarounds.
3. Using complex numbers has many advantages and should not scare.
4. I would not switch to Mathematica just for that. It's your choice though.