Suppose we have a finite list of $n$ triples of positive integer numbers, as:
$$ \mathcal{L}=\{(a_{i1},a_{i2},a_{i3}):a_{ij}\in \mathbf{N}\setminus\{0\}, \text{ for } j=1,2,3\}_{i=1,\dots,n}.\ $$
Is there a software, where I can give $\mathcal{L}$ as in-put and which gives as out-put a possible formula, denoted by $F(a_{i2},a_{13})$, such that $a_{i1}=F(a_{i2},a_{13})$ (it could be not existing or it is not unique)? This formula can involve any operations of sum, multiplication, power, division, or also integer parts or binomial coefficients.
Just two examples to be clearer.
Consider the following list of $3$-uple: $(5, 12, 13), (7, 24, 25), (8, 15, 17), (20, 21, 29)$. They are Pythagorean triples and $a_{i1} = \sqrt{a_{i2}^2+a_{i3}^2}$, so $F(a_{i2},a_{13})=\sqrt{a_{i2}^2+a_{i3}^2}$ in such a case.
Consider: $(1,3,1), (2,4,1), (3,5,1)$. Then two possible formulas are $F(a_{i2},a_{13})=\mathrm{floor}(\frac{a_{i2}-2}{a_{i3}})$ or $F(a_{i2},a_{13})=a_{i2}-2a_{i3}$.
If $n>>0$, which means that we have a lot of triples, so the the formula $F(a_{i2},a_{13})$ should be unique, or in any case we can have just few of it (if it exists).