Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers

There have been two approaches to linear forms in the logarithms of algebraic numbers: the first is the Gelfond-Baker method (with improvements using commutative algebra), the second is the Schneider-Laurent method. Both approaches use auxiliary functions which, in the latter, are called interpolation determinants. Consider the special case that Λ = ∑n j=1 bjlog αj 6= 0 with αj = aj,1/aj,2 (j = 1, ..., n) and all aj,1, aj,2, bj integers. The former method yields