Such variables that appear within the input polynomials but
not appearing in the input variable list are automatically treated
as elements in the coefficient field
by top level functions, such as gr().
[64] gr([a*x+b*y-c,d*x+e*y-f],[x,y],2); [(-e*a+d*b)*x-f*b+e*c,(-e*a+d*b)*y+f*a-d*c]
In this example, variables a, b, c, and d
are treated as elements in the coefficient field.
In this case, a Groebner basis is computed
on a bi-variate polynomial ring
F[x,y]
over rational function field
F = Q(a,b,c,d).
Notice that coefficients are considered as a member in a field.
As a consequence, polynomial factors common to the coefficients
are removed so that the result, in general, is different from
the result that would be obtained when the problem is considered
as a computation of Groebner basis over a polynomial ring
with rational function coefficients.
And note that coefficients of a distributed polynomial are limited
to numbers and polynomials because of efficiency.
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