division of integers. Alternatively, addition of reciprocal $\operatorname{inv}(x) \equiv 1/x$ and successor $\operatorname{suc}(x) \equiv x+1$ functions allow for construction of continued fractions, see Appendix B in Supplemental Material.

Set of (named) mathematical constant certainly must include $e$, $\pi$, and $i = \sqrt{-1}$ due to , as long as we consider complex numbers. Besides this, some mathematicians consider other constants [@const] as ”important”, like first square roots ($\sqrt{2}, \sqrt{3}, \sqrt{5}$), golden ratio $\phi = (1+\sqrt{5})/2$ [@RIES], $\ln{2}$, $e^{1/e}$ and so on. Noteworthy, all of them are itself in $\exp-\log$ class, i.e., we can generate them from integers and elementary functions. They do not define any new numbers. Their inclusion only alter language definition and therefore Kolmogorov complexity. Other situation is with inclusion of mathematical constants of unknown status/memberships (unknown to be rational or transcendental), like Euler gamma $\gamma = 0.577216\ldots $ or Glaisher constant $A=1.28243\ldots$. They may, or may not, extend $\exp-\log$ class. This is itself an application for constant recognition.

Commutative operations like addition and multiplication are in general $n$-ary. To simulate calculator behavior we must treat them as repeated binary operations: $$x+y+z = (x+y) + z.$$

Elementary functions are not independent, e.g: $$\sinh{x} = \frac{e^x - e^{-x}}{2}, \tan{x} = 