AlgebraicDependencies.jl

A Julia package for computing algebraic dependencies among exponential sequences. Let r_1,...,r_s be algebraic numbers. We can compute a basis for the ideal I containing all algebraic dependencies among r_1^n,...,r_s^n, i.e. for every p in I we have p(r_1^n,...,r_s^n) = 0 for all natural numbers n.

julia> @deps 2 1/2
1-element Array{Expr,1}:
 :(v1 * v2 - 1)

julia> @deps (1-sqrt(5))/2 (1+sqrt(5))/2
1-element Array{Expr,1}:
 :(v1 ^ 2 * v2 ^ 2 - 1)

References

M. Kauers, B. Zimmermann. Computing the algebraic relations of C-finite sequences and multisequences. J. Symb. Comput. 43 (2008): 787-803.