Is there any Maple command to detect whether the degree of a polynomial w.r.t. all variables is less or equal 1?

For example, if $f=ax+by-1$ when $x$ and $y$ are variables then the output is true and if $g=a*x^2+b*y-c$ then it returns false. 

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.