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Different forms of operation, RPN, INFIX; POSTFIX, PREFIX, EXOFIX, etc. - compsystems - 12-09-2018 09:19 PM
Hello, you agree with the following definitions.
INFIX, operator in the middle.
PREFIX, operator at the beginning.
POSTFIX, operator at the end.
EXOFIX, operator on the outside.
PHP Code:
a union b (union as infix operator), a ∪ b (∪ as symbolic infix operator), ∪ a,b (∪ as prefix operator), ∪(a,b) (∪ as prefix functional operator), (a, b)∪ (∪ as postfix functional operator), a, b ∪ (∪ as postfix operator)
a intersection b (intersection as infix operator), a ∩ b (∩ as symbolic infix operator), ∩(a,b) (∩ as prefix functional operator), (a, b)∩ (∩ as postfix functional operator)
not a (not as prefix operator), ¬a (¬ as symbolic prefix operator), ¬(a) (¬ as prefix functional operator), a¬ (¬ as postfix operator)
ceil(a) (ceil as functional operator, ⌈a⌉ (ceil as exofix operator)
floor(a) (floor as functional operator), ⌊a⌋ as (floor as exofix operator)
abs(a) (floor as functional operator), |a| (abs as exofix operator)
root(a) (root as functional operator) √(a) (√ as symbolic functional operator)
integral() (integral as functional operator), ∫() (∫ as symbolic functional operator)
sum() (sum as functional operator), Σ() (Σ as symbolic functional operator)
product() (product as functional operator), Π() (Π as symbolic functional operator)
a <= b (<= as digraph infix operator), a ≤ b (≤ as real infix operator)
a >= b (>= as digraph infix operator), a ≥ b (≥ as real infix operator)
a != b (!= as digraph infix operator), a ≠ b (≠ as real infix operator)
factorial(a) (functional operator), a! (postfix operator)
a^3 (^ explicit infix operator) to a³ (implicit infix operator)
a^2 (^ explicit infix operator) to a² (implicit infix operator)
Example
(3+4) * (5-6) returns -7 // infix operation (standard notation)
*(+(3,4),-(5,6)) // symbolic functional prefix operation
Product(Sum(3,4),Subtraction(5,6)) // functional prefix operation
Product Sum 3,4, Subtraction 5,6 // prefix operation
3, 4 Sum, 5, 6 Subtraction, Product // postfix operation
( (3,4)Sum, (5,6)Subtraction )Product // functional postfix operation
( (3, 4)+ (5, 6)- )* // symbolic functional postfix operation
3,4 +, 5, 6 - * // symbolic postfix operation
3 4 + 5 6 - * // RPN