# Arithmetic and logical expressions

#0. Precedence
#See Table 3.1 on p. 50of V&R, but some common situtations, highest to lowest:

#   function(..)
#   ^            #exponentiation
#   * /          #multiplication, division#
#   + -          #addition, subtraction
#   > < <= == != #comparison operators
  
#but can always use parentheses to force a precedence
  
  x <- 36
  y <- 7
  sqrt(x)*7-2 <  x+y^2
  (((sqrt(x))*7)-2) < (x+(y^2))  #identical to above but "clear" precedence

#1. element by element operations on two vectors
 x <- 1:10
 y <- 11:20
 x+y
 x-y
 x*y
 x/y
 x^y

#2. recycling: when operating on 2 vectors with unequal length
#   length of output = length of longer vector, recycling the
#   shorter vector's values till match longer vector's length

 x <- 2
 y <- 1:6
 x+y       #2+1, 2+2, 2+3, 2+4, 2+5, 2+6
 
 x <- c(2,9)
 x+y       #2+1, 9+2, 2+3, 9+4, 2+5, 9+6

#3. Integer division and modulo reduction
 7 %/% 3       #answer 2, number of times 3 goes into 7
 7 %%  3       #answer 1, 7 - (7 %/% 3)*3

#4 Logical expressions and functions with logical arguments
 x <- c(1,3,5)
 y <- c(2,2,4)

 x < y
 x <= y
 x != y

 any(x<y)  #if any term in vector x<y is T, return T
 all(x<y)  #if all terms in vector x<y is T, return T
 
 (x==3 | y==2)  # union of vector x==3 with vector y==2
                # T|T or T|F or F|T returns T
                # only F|F returns F

 (x==3 & y==2)  # intersection of vector x==3 with vector y==2 
                # only T&T returns T