We say that two elements a and b of an algebra B are algebraically independent if P [member of] C[[z.

2] are two algebraically independent functions, then the algebra generated by them is isomorphic to C[[z.

n]) if, adding any number of other indeterminates (elements transcendental and algebraically independent over K([X.

n+r] are transcendental and algebraically independent over K([X.

16] are

algebraically independent over F and hence the polynomial Q is uniquely determined.

Let O be an open set in K, and let P [member of] O be a polytope with vertex set V which we suppose to be in general position, for instance the coordinates of the vertices are

algebraically independent.

Another approach is to assign algebraically independent values to the nonzeros (i.

T] (the latter graph is equivalent to the directed graph of F with the edge directions reversed); this equivalence again assumes that the numerical values of the nonzeros in F are algebraically independent.

Y,y] is

algebraically independent of the cycles [Z.

r] : r [member of] H} is

algebraically independent.

1 Any maximal weakly separated subset [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] corresponds to k(n - k) +1

algebraically independent Plucker coordinates [[DELTA].

W] is again a polynomial algebra, and it can be generated by n

algebraically independent homogeneous polynomials [f.