MuPAD codes which implement limit-computable functions that cannot be bounded by any computable function
Let E<sub>n</sub> = {x<sub>k</sub> = 1, x<sub>i</sub> + x<sub>j</sub> = x<sub>k</sub>, x<sub>i</sub> · x<sub>j</sub> = x<sub>k</sub> : i, j, k ∈ {1, ..., n}}. For a positive integer n, let f (n) denote the smallest non-negative integer b such that for each system S ⊆ E<sub>n</sub> with a solution in non-negative integers x<sub>1</sub>, ..., x<sub>n</sub> there exists a solution of S in non-negative integers not greater than b. We prove that if a function Γ : ℕ \ {0} → ℕ is computable, then f dominates Γ i.e. there exists a positive integer m such that Γ(n) <; f (n) for any n ≥ m. For positive integers n, m, let g(n,m) denote the smallest non-negative integer b such that for each system S ⊆ E<sub>n</sub> with a solution in {0, ..., m - 1}<sup>n</sup> there exists a solution of S in {0, ..., b}<sup>n</sup>. Then, equations and equation We present an infinite loop in MuPAD which takes as input a positive integer n and returns g(n,m) on the m-th iteration.