@Markiyan Hirnyk 

But t is >0; you had no objections about this. Now you come back? Infinite loop?
As I see you want to test my patience.

@Markiyan Hirnyk 

I have mentioned that this follows from ex^2=-1.

is( (- sqrt(p)* t )^2  < 0  )  assuming p>=0, t>0;

    false

is( (- sqrt(p)* t )^2  < 0  )  assuming p<0, t>0;

    true

@Markiyan Hirnyk 

argument( - sqrt(p)* t ) assuming p<0, t>0;

@Markiyan Hirnyk 

If you indicate which assertion is not obvious, I will try to turn my empty words into full ones.

@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