Question

I am writing a little home-made calculator for integers and it includes two binary operators, ‘pow’ and ‘root’. The ‘pow’ operator evaluates (left operand) ^ (right operand), and the ‘root’ operator finds the largest number n such that n ^ (left operand) <= (right operand).

Assuming this isn’t an absurd thing to do, what should the precedence of these operators be? Currently I have them at equal precedence so strings such as

3 root 1500 pow 7

evaluate left to right. Is this right? Should I put this question on mathoverflow?

Answer 1

pow and root are essentially the same operation, expressed differently (similar to binary + and -). I.e., sqrt(a) is the same as pow(a, 0.5), just like a + b is the same as a - (-b). So I’d say they should have equal precedence, and hence be evaluated left-to-right.