@Kitonum many thanks.  Since the polynomials can have more than three variables in other examples, I tried to extend the tests within if to 

member(true,zip((w,v)->depends(w,v),fff,[x,y,z]));

 

but that this gives a different result (third coordinate) when compared to the three dependences in our code.  What have I done wrong?

@acer many thanks.  I start to understand what is going on.  I will convert the old help files slowly specially after finding out that a good description and the command Describe will give a reasonsble alternative for the help, at least while I figure out how to rebuild all my functions.

@acer Many thanks.  I have modified your script for my needs (only path) and got an empty help page at the end. When I try for the second time, I got:

Error, (in HelpTools:-HelpCallUI) cannot add duplicate topic 'myprefix,sampling'

s.txt and myhelp.help are sitting on my maplev2 dir and seem ok.   I have tried to search for sampling on the help system but it is not there.  

As for the other methods, I have no idea where to start.  

@acer I am running 14, 18 and 2016 versions.  Thanks.

@Carl Love Thank you ever so much.

@Carl Love Thanks again for the explanation and for the procedure that works just fine.  Again thank you for your patience and help.   As you know I have lots of monomails like the ones above. Is there a way to print them line by line in a nice output?

@emendes To be honest, I could not understand the part where sort was used.  I have tried sort with plex but it always return an error.

@Carl Love Yes, that is right.  

I just want to thank you all for the help.

@Carl Love Many thanks.   If the plex order were to be added, would it be more complicated?  Thank you ever so much.  I have learned a lot these past few days. 

@emendes It would be nice if monomials could return the monomials but also the coefficients so that I do not need to worry about the order. I have tried coeffs with collect but the order is different from monomails.

@Carl Love Many thanks for your help and patience.  I managed to modify the original "monomials" to accomodate collect before I saw you reply (finally it seems that I am getting somewhere!).  

Please find attached the example where "The procedure does not work if collect has been used".

Please tell me what I did wrong.   Thanks again.

Example_Monomials_not_working.mw

@emendes The procedure does not work if colllect has been used, so I wonder how it can be modified to use the order imposed by collect(p,vars,'distributed')?  Many thanks

@Carl Love About 500000 polynomials.  That is my aim but I don't think it is feasible.  The Grobner is calculated over each one of them.   That was the reason I have asked a question on how to limit the amount of time spent on calculating the GBs (the ones that exceed the time are left behind).  The GBs are calculated for each one of the polynomials not for the whole set (If that were the case, you could certainly call me crazy).  The 20 thousand in the example I have sent are the result of the GBs.   Finally I care about the order and I need to know many repetitions there are in the set.   GB can choke up easily with the polynomials I am using.  

@tomleslie Many thanks for your reply.  To be honest the list I was aiming for has 2^20 polynomials.   Using powerset to build it does not seem to be the problem.  The problem shows up when I have to reduce it by removing some elements using a for.  aux:=aux,result does not seem a good choice.  I am going to modify the code to use table.  Then I will reduce it further by finding the repeated elements after finding the Grobner basis (here is the main problem- there is no guarantee that a solution will be found - last time I try 30 GB wasn't enough).   Any suggestions?