# Global Identifiability Tools

StructuralIdentifiability.extract_identifiable_functionsFunction
extract_identifiable_functions(io_equations, parameters)

For the io_equation and the list of all parameter variables, returns a set of generators of a field of all functions of parameters

Note: an experimental functionality at the moment, may fail be inefficient

StructuralIdentifiability.check_field_membershipFunction
check_field_membership(generators, rat_funcs, p, [method=:GroebnerBasis])

Checks whether given rational function belogn to a given field of rational functions

Inputs:

• generators - a list of lists of polynomials. Each of the lists, say, [f1, ..., fn], defines generators f2/f1, ..., fn/f1. Let $F$ be the field generated by all of them.
• rat_funcs - list rational functions
• p - a real number between 0 and 1, the probability of correctness

Output:

• a list L[i] of bools of length length(rat_funcs) such that L[i] is true iff the i-th function belongs to $F$. The whole result is correct with probability at least p
StructuralIdentifiability.find_identifiable_functionsFunction
find_identifiable_functions(ode::ODE{<: MPolyElem{fmpq}}, p::Float64=0.99)

Input:

• ode - ODE-system
• p - probability of correctness

Output:

• returns a set of generators of the field of all functions of parameters

Find identifiable functions of parameters for a given ode.