@acer Thank you for the explanation. fixup saves me a lot of time when transferring my results from Maple to LaTeX.  

@acer Thank you, but I think I may have missed something. fixup returns the same input expression expr, doesn't it? How was it modified?

@acer Sorry to reopen the thread, but do you happen to know how to fix z*x? I mean…

from

[sigma*y, (-sigma - 1)*y + z*x, (rho - 1 - z)*beta - (x + y)*x]

to

[sigma*y, (-sigma - 1)*y + x*z, (rho - 1 - z)*beta - (x + y)*x]

@acer I could not ask for more.  Thank you.  

@acer I could never have come up with such a clean procedure—it's got Carl written all over it. I can't thank him enough for all the help he's given me. And now, you're part of that too.

Example

lorenz := [-sigma*x + sigma*y, rho*x - x*z - y, -beta*z + x*y];
vars := [x,y,z];

map(w->monomialsGB(w,vars),lorenz);

and output is

[[sigma, -sigma], [y, x], [-1, -1, rho], [z*x, y, x], [-beta, 1], [z, y*x]]

The ordering should be [x,y], [x,y,x*z] and [z,x*y].  

Actually I need both versions. I mean Carl's and yours.   

Many thanks.

@acer Thank you! That’s perfect. I came across only a few cases where repetition occurs, and this will save me the trouble of handling them separately.

Admitting my total lack of skill (even though I've been a Maple user for years) and hoping it's not too much trouble — how could the following procedure be modified to use the ordering established above?

monomialsGB := proc (p::algebraic, vars::list)
local
     M,
     v:= indets(p, suffixed({vars[]})),
     C:= coeffs(expand(p), v, 'M'),
     P:= plex(ListTools:-Reverse([v[]])[]),
     S:= sort(`[]`~([C],[M]), (a,b)-> not Groebner:-TestOrder(a[2], b[2], P));
     (map2(op, 1, S), map2(op, 2, S)):
end proc:

Please include details on how you modified the procedure. I really need to learn the basics of Maple once and for all.

@acer Many thanks.  Yes, there is the possibility of repeated terms.

@acer As usual, you went above and beyond—thank you for that! It's a great way for me to learn more about Maple commands. In the cases I typically work with, the entries usually have the same level of nesting.

@acer Thank you for making it clear.  The inner most entries are number (integers, rationals and possbily reals) and/or symbols (variables), or empty. In cases I am interested in they are a solution of an equation.   

@acer Sorry if I'm missing something obvious—could you clarify what exactly makes it under-specified?

@acer Many thanks.   After the first outer list, entries are either lists or sets.

@acer Thank you!  

@acer Could you explain why ":-coef" is used, please?   Thanks. 

@acer Yes, it is—thanks for pointing out the SubstituteAll function!  

@acer Wow! Thanks so much for the thorough explanation — it really helped me a lot.
I’m always forgetting some of the things you and Carl explained in your previous replies to my questions.
Thanks for your patience, both of you!