@roubeur 

To go back to the initial variables do:

eval(simp, varsx =~ vars);

The admisible solution xxx was obtained using random numbers. If you re-execute the computation (without restart) xxx will change, so it is normal that you obtained another result (simp).

Note: for some admisible xxx, it could be possible that very few variables must be fixed.
You should experiment.

@acer 

Indeed, in Qgr (in 2d)

Representative(a) . Representative(b)

was parsed as:

Typesetting:-delayDotProduct(Representative(a), Representative(b));

Works without errors in Maple 2017.3.

You should try to present the mathematical problem.
Otherwise, for suggestions or alternate solutions a "reverse engineering" of the Maple code will be necessary.

@Rouben Rostamian  

For an "lndirect documentation" see showstat(log).

@Carl Love 

I was also curious to understand on what basis Maple returns true for is(exp(2),irrational);
This information should (probably) be found in `property/exp` but it's not there.
It would be very disappointing if the answer is obtained using approximations because Digits cannot be set to infinity and the answer is simply a guess in this case.

is(x,irrational) seems indeed to be a pure guess because of:

is(sum(10^(-k^3),k=1..infinity), irrational);
        false

@Rouben Rostamian  

If f is the name of a procedure then  f[u](x)  actually calls  f(x), but in the body of f the index/indices
u can be retrived (and used) via  op(procname).
To check whether f is invoked with an index one may use  type(procname,indexed).

(I am not sure whether this is documented, but I found about it long time ago in a Maple book which I do not remember). 

@Carl Love 

But ?type,property clearly says:

Note: Types are properties, but not all properties are types.

Do you know a type which is not property? (I don't mean "proper").

@Jason Lee 

Download linsyst.mw

@Jason Lee 

What exactly is not clear? I have used your notations.
But I just noticed that you are using Maple T.A. and I am not sure whether this works here.

@Carl Love 

Why dou you think that is is using list(rational) as a type? Of course, any type is a property.

is(list(rational), property);
   true

type(list(rational), property);
    true

Probably your notion of "proper property" is useful.

@_Maxim_ 

Of course is uses simplifications. It should  return FAIL much more frequently (when in doubt)  but it does not probably for "commercial" reasons; it prefers `false`. The assume facility deserves a much more careful implementation.

Surprisingly:
is(exp(1)+Pi,irrational);
    FAIL
So, it seems that is adopts a special strategy for properties which are not types.

Also:

is(Pi,irrational);
                              true
is(Pi^2,irrational);
                              FAIL
is(exp(1),irrational);
                              true
is(exp(1)^2,irrational);
                              FAIL
is(exp(2),irrational);
                              true

is(exp(sqrt(2)),irrational); #does not know Lindemann theorem (from 1882!)
                              FAIL

@st104290 

As you see in the example, sort itself does not alter the terms. Probably you have used some other command.
You may append assuming t>0  to that command.

@Markiyan Hirnyk 

As always you want to have the final word even when you are wrong.
But two pages earlier Fichtenholz states:  "generalized sum" (in the sense of Poisson).
He also says that actually Abel was not interested in the summation of divergent series.

Note.
In 1828 Abel wrote `Divergent series are the invention of the devil, and
it is shameful to base on them any demonstration whatsoever.'

[Abel died in 1829]

@Markiyan Hirnyk 

It is also called "power series method" or Poisson (e.g. in the Mathematical Analysis book by G.M. Fichtenholz).