Let us consider L be the following list of 6 lists of polynomials which all of their polynomials are linear combination of B=[x^2,x*y,z^2,1]. 

L:=[[a*x^2+b*x*y-1, -(a*b-b)*x*y/a-z^2+(a-1)/a, -a*c*z^2/(b*(a-1))+(b+c)/b], [a*x^2+b*x*y-1, -(a*b-b)*x*y/a-z^2+(a-1)/a, 1],

[a*x^2+b*x*y-1, -z^2+(a-1)/a, c*x*y+1], [b*x*y-1, -x^2-z^2, (b+c)/b], [-1, -x^2-z^2, c*x*y], [-1, -x^2-z^2]].

Now, I need the matrix coefficients of any member of L (please note that any matrix has 4 columns according to the list B) . Is there any command for this?

Thank you in advanced.

Let us consider S := [x^2 = A1, x*y = A2, z^2 = A3] as a list. Is there any command to obtain  SS = [A1=x^2 , A2=x*y , A3=z^2] from S?

Hi dears,

I hope that my request (question) is appropriate for Mapleprimes.

I know Gröbner bases and Buchberger's algorithm and I want to understand  the F4-algorithm. However, I know that  the corresponding paper can be found:

https://www.sciencedirect.com/science/article/pii/S0022404999000055 

Could you please state the sketch and main parts of the algorithm s.t. I can understand it?
Is there any primary Maple implementation of F4-algorithm?

Thanks in advance.

Hi Dears,

I installed Maple 15 and 18 on my PC. But, when I want to use the PolyhedralSets package the following error is appeared. Is this package only on Maple 2015?

With the bests.

Hi Dears,

Let us consider the following polyhedral cone which is defined by 8 inequalities (also, x,y,z ≥0): 

1. y-z ≥0

2. 3y-2z ≥0

3. 2y-2z ≥0

4. x-2y+z ≥0

5. x-y ≥0

6. 2x-y ≥0

7. x-z ≥0

8. x+y-z ≥0. 

How can we deduce that the inequalities 3 and 4 may be define this polyhedral cone and the others are redundant?

How can remove the redundant inequalities for defining this polyhedral cone?

Is there any Maple command or function that recive these 8 inequalities and return inequalities 3 and 4? In fact, inequalities 3 and 4 are facets of this polyhedral cone. 

Thank you in advanced. 

Sincerely yours