@Kitonum 

I agree in principle, that is the sort of thing I normally do. The Sigmas are also being problematic.

Another evariant of this  I have had a problem with recently

A₁:= 2b+c                                     

               maple returns                                  A₁:=2b+c

Trere could be 10 of these A₁..A₁₀

Sometimes I need to list the equations later and it would be very usefuel to see, expecially when the equations are long

For i to 10 do

Display A_{i ;}

end do

A₁  2b+c

A₂   3c-4d

A₃   ...... etc

@roman_pearce 

Wow. Thank you very much. That totally solved the problem.

@Kitonum 

Thank you. That is useful to know.

@roman_pearce 

Can't figure out the mapping. I removed 2 elements from f and made f1 and a new list C1. I neet to compare list C1 to C and insert 2 0's at the appropiate points.

Download mapping.mw

@Kitonum 

Hi thanks for reply. I'll explain in more detail why I am sorting as a list. For example.

 V1 = [x,yx,xyz,xy^2, x^2yz,xz^2] is a list of variables. This has and associated list of coefficients

 C1=[1+a,a^2-3,a^3-a^2,15,2+a,-12]     Both these lists have 6 elements      

V2= [x,yx,xyz, x^2yz,xz^2]             

C2=[a,2,1-3a,a^2-5,7a,a^2]  5 elements in V2 & C2. V2 is missing "xy^2", i.e. the 4th element in V1

I have 19 lists of variables and coefficients. Max list length is 19 some lists only 16 or 17 elements. The coefficients lists form the rows of 19x 19 matrix. The determinant is used to get a univariate polynomial in "a".

The missing elements in the variable lists cause elements of the coefficient lists to be placed in wrong columns.

I see 2 possible sorting stratagies

a) add a 0 to C2  in 4th position increasing its length by 1.

b) sort C1,V1 based on the sequence of variables in V2 and placing the "xy^2" at the end of the list

New  V1 = [x,yx,xyz, x^2yz,xz^2,xy^2] and C1=[1+a,a^2-3,a^3-a^2,2+a,-12,15]  

I do not know how the impliment either of the approaches.

I posted this last night when trying to sort the problem. The above describes the core of the problem

http://www.mapleprimes.com/questions/211562--Groebner--Produces-Inconsistent-Result

I think I have figured out the source of the problem. The sorting produces a list of variables ss_n and a list of coefficients sm_n. The max length of the useful variable list is 19 with a corresponding list of 19 coefficients. Some lists are shorter say  have 16 or 17 elements in them.

for example ss_29 is missing u2^3u0,u2^3u1 & u2^4

u2^3u0 & u2^3u1 are 6th 7th elements in a full list. This caused the remainder of the elements to be placed in the wrong columns. As u2^2 is at the end of the list that doesn't cause a problem.

Possible solution

Add 0's where needed in the short coefficient lists to compensate. How would I do that?

How to chech that all lists are following the same sequence?  Different runs produce different sequence of elements in the lists.

Is there a better way of sorting the equations to produce the desired result?

Download List_Problem.mw

@Torre Thank You. Have Experimented with your Suggestion. Closeset I got was with Q diagonal matrix [1,1,0]. Produdes correct number of zeroes but row and columns e4 and e5 would need to be reversed. Looks like I need a 4x4 matrix as shown at end. Could not make a table with the "Structure Equations. Would appreciate any further suggestions.

Download Clifford.mw

@Markiyan Hirnyk 

Hello do you know where this book can be purchased from and is it written in English?

@vv Thank you. worled well!

@Markiyan Hirnyk What I mean't was e.g (form one of the answers supplied) 

I wish to see what the Basis equations contain in terms of the produsts of the variables.

@nutnutman Firstly "vv 575" substitution method is really excellent. I decided to try a bit more complex too. Higher order derivatives and mixed derivatives. I looked at the link you provided, I didn't have a clue either. Have not used the substitution method here but it could be applied.

Download diff_sum_2.mw

@vv Never thought of "subs" and being able to add them that way.

@Carl Love That is a point I wasn't sure about myself.

@nutnutman 

What I posted was just an idea. Don't really know what you are doing. Post a work sheet (as I did) with a more complex example. That might encourage others to look at the problem. Nobody wants to retype complex formulas.

I am using Maple 18. Documentation says Solidworks 2013 required. I am on SW 2015. Connection won't open. Have you access to SW 2013?