@Alejandro Jakubi thanks, I did not know about Redlog

@Carl Love  thanks but solve parametric does not eliminate variables, example posted above at your request

Using Carl's example, in Mathematica,

Resolve[ ForAll [x, 0 < x && x < 1, x^2 + y^2 - 1 > 0]]

outputs:

y <= -1 || y >= 1  (y less than -1 or y greater than 1)

Notice the variable x was eliminated. Is there a way to do this in Maple?

@roman_pearce : Dear Roman, by any chance do you know a good reference on using many cores with Maple? Sometimes I see Groebner basis scripts are using only 4 cores when there are 6 or 8 available. I'm not sure if I should try to make Maple use the other cores or not.

@Markiyan Hirnyk Thanks! I did not know about the  'known' option. It is quite useful !

@J4James  Use simplify(expr, GAMMA) where expr is the solution in terms of the erf

@Markiyan Hirnyk As you suggested I use printevel:=15 and it seems to give the intermediary computations I needed but I have to create a simpler example to test it. The systems I use get quite large very fast so the printed output is huge. Thanks again.

@Markiyan Hirnyk with print level it seems to work, thanks

@Markiyan Hirnyk  I used infolevel 5 but not the other two, now I will see what they do. Thanks!

@ecterrab thanks for your invaluable help. casesplit is great because it gives the whole picture but say I'm only interested in finding info on some non-trivial local solution. To speed-up things one can use singsol=false but could one set arbitrary=[ivar] if one is willing to assume coefficents of the linear, homegeneous PDE are rational functions defined at some point far from any singularity? I tried but:

casesplit(dsys, arbitrary = [a, b, x, y, w, y, z, v]);
Error, (in DifferentialAlgebra:-DifferentialRing) duplicated independent or dependent variables

where dsys is below (I suspect it has only constant solutions)

I'm not familiar with solving PDEs numerically but perhaps here the problem is not the method but that we are having xtau and ytau very close to zero so M becomes unbounded...

@ecterrab Thanks: I'm dealing with the ugly systems like you saw in my emails. My idea was that I may get better luck if I was able to play with the monomial orders. Is there a way of choosing a particular ordering of variables for the triangularization that PDEtools:-casesplit performs? In my experience with polynomial systems (not differential ones) the ordering can make a huge difference.

@Carl Love  None rejected as I didn't use any. There is the command Ore_algebra[Ore_to_diff] that "converts a differential operator or a list of differential operators of the skew algebra A into a differential equation or a list of differential equations in the function f." and what I'm looking for can be described as somehow doing the opposite when I have a PDE system in several functions and polynomial coefficients:  which differential operators should I declare when using Ore_algebra[diff_algebra] so I can write the PDE system using the operator notation so then later I can use Groebner[Basis] in the system expressed in the Weyl algebra notation. I don't think that there is a command that does the "opposite" of Ore_to_diff but was hoping someone could show (by hand) a simple example how I can do "diff to Ore". I re-wrote my original question, hopefully it is clear now.

@Carl Love   Since I have a ranking of derivatives and I am trying to write the system in terms of the higher derivatives whenever possible your observation helps a lot. I just have to re-label variables so that my order coincides with the one used by Maple. Thanks!

(a-P*MM)*l=0,

(b-Q*MM)*m=0,

 (f-TT*O)*r=0,

You still have P, Q and O in your new system but in other equations you have PP, QQ, and OO...

It should be one or the other right?

I edited the system and run solve with the parametric and real options, solve(sys,vars,'parametric','real');

See solve/parametric in the help section. But even using 4 processors and 3G of memory I get an error:

GC Thread signalAbort 0x2aaad5341940 Execution stopped: Stack limit reached.
maple: fatal error, lost connection to kernel

My guess is the system is too big for Maple to handle. I suggest selecting some numerical values for some parameters and trying it with a smaller system.

Good luck.