User:Slereah/Arithmetica

Here be a draft for Αριθµητικών :

Αριθµητικών is an esoteric programming language based on the arithmetical notation of the eponymous book by Diophantus.

The notation is the following :

• Small case letters : Greek numerals (up to 999). Every term must have one on the right. The 0 uses the Hellenistic zero, ō
• Μ : Monad, used for constants.
• ς : Αριθµός, the variable for one-variable functions.
• Δ^Υ, Κ^Υ, ... : For one-variable functions, powers of the variable. Δ (δύναµις) to square, Κ (κύβοv) to cube, and combinations of the form (1)(2) for ς to the power of (1)+(2), such as ΔΔ^Υ (δυναµοδύναµις) for 4, and so on.
• Fractions are expressed by a/b = a^b, or a^ον for 1/a. Inverse are expressed with a superscript χ. 1/x is ς^χ, 1/x² is Δ^χΥ and so on.
• Multiple variables are expressed by a^ου. The first variable would be α^ου, the second β^ου and so on.
• (1)(2) for (1) + (2). For instance, ςαΜε means x + 5
• (1)↑(2) for (1) - (2) (The closest symbol is actually GREEK ACROPHONIC HERMIONIAN TEN, but most fonts do not display it).
• (1) µερ (2) to divide (1) by (2).
• (1) επί (2) to multiply (1) by (2).
• εάν (c) τότε (1) αλλιώς (2) for if (c) then (1) else (2)
• (1) ι^σ (2) is (1) = (2), which evaluates to either true or false (looking for translations)
• ἕκθ : Used for function definition. ἕκθ [function name] [function]. Functions are called by [function name] [arg1] [arg2] ... [arg n-1] καί [arg n]

It is a functional language that uses the numbers available at the time, integers and fractions. Negative numbers, such as 1-2 (Μα↑Μβ) will return the error ἀδύνατος (impossible).