6.16.1  Context-dependent functions.

The + operator

The + operator is infixed and ’+’ is its prefixed version. The + operator will add numbers (see Section 6.8.2), concatenate strings (see Section 6.3.12), and convert a number to a string if necessary. Addition makes sense for other objects, and + can flexibly deal with them; the result of using the + operator depends on the nature of its arguments.

Examples.

• Input:
  1+2+3+4
  or:
  ’+’(1,2,3,4)
  or:
  (1,2)+(3,4)
  or:
  (1,2,3)+4)
  Output:

  10

  (See Section 6.39.9.)
• Input:
  1+i+2+3*i
  or:
  ’+’(1,i,2,3*i)
  Output:

  3+4 i

• Input:
  [1,2,3]+[4,1]
  or:
  [1,2,3]+[4,1,0]
  or:
  ’+’([1,2,3],[4,1])
  Output:

  ⎡ ⎣

  5,3,3

  ⎤ ⎦

• Input:
  [1,2]+[3,4]
  or:
  ’+’([1,2],[3,4])
  Output:

  ⎡ ⎣

  4,6

  ⎤ ⎦

• Input:
  [[1,2],[3,4]]+[[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎣

  2 4       6 8

  ⎤ ⎥ ⎦

• Input:
  [1,2,3]+4
  or:
  ’+’([1,2,3],4)
  Output:

  ▯ 1,2,7▯

  (This is a polynomial; see Section 6.27.1.)
• Input:
  [1,2,3]+(4,1)
  or:
  ’+’([1,2,3],4,1)
  Output:

  ▯ 1,2,8 ▯

• Input:
  "Hel"+"lo"
  or:
  ’+’("Hel","lo")
  Output:
  "Hello"

The -,* and / operators

The -, * and / operators (and their prefixed versions ’-’, ’*’ and ’/’), like the + operator, are flexible and operate on compound objects (such as lists and sequences), but don’t concatenate strings.

Examples of - and ’-’.

• Input:
  (1,2)-(3,4)
  Output:

  −4

• Input:
  (1,2,3)-4
  Output:

  2

• Input:
  [1,2,3]-[4,1]
  or:
  [1,2,3]-[4,1,0]
  or:
  ’-’([1,2,3],[4,1])
  Output:

  ⎡ ⎣

  −3,1,3

  ⎤ ⎦

• Input:
  [1,2]-[3,4]
  or:
  ’-’([1,2],[3,4])
  Output:

  ⎡ ⎣

  −2,−2

  ⎤ ⎦

• Input:
  [[3,4],[1,2]]-[[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎣

  2 2       −2 −2

  ⎤ ⎥ ⎦

• Input:
  [1,2,3]-4
  or:
  ’-’([1,2,3],4)
  Output:

  ▯ 1,2,−1▯

• Input:
  [1,2,3]-(4,1)
  Output:

  ▯ 1,2,−2 ▯

Examples of * and ’*’.

• Input:
  (1,2)*(3,4)
  or:
  (1,2,3)*4
  or:
  1*2*3*4
  or:
  ’*’(1,2,3,4)
  Output:

  24

• Input:
  1*i*2*3*i
  or:
  ’*’(1,i,2,3*i)
  Output:

  −6

• Input:
  [10,2,3]*[4,1]
  or:
  [10,2,3]*[4,1,0]
  or:
  ’*’([10,2,3],[4,1])
  Output:

  42

  These compute the scalar product.
• Input:
  [1,2]*[3,4]
  or:
  ’*’([1,2],[3,4])
  Output:

  11

  These compute the scalar product.
• Input:
  [[1,2],[3,4]]* [[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎣

  7 10       15 22

  ⎤ ⎥ ⎦

• Input:
  [1,2,3]*4
  or:
  ’*’([1,2,3],4)
  Output:

  ⎡ ⎣

  4,8,12

  ⎤ ⎦

• Input:
  [1,2,3]*(4,2)
  or:
  ’*’([1,2,3],4,2)
  or:
  [1,2,3]*8
  Output:

  ⎡ ⎣

  8,16,24

  ⎤ ⎦

• Input:
  (1,2)+i*(2,3)
  or:
  1+2+i*2*3
  Output:

  3+6 i

Examples of / and ’/’.

• Input:
  [10,2,3]/[4,1]
  Output:

  ⎡ ⎢ ⎢ ⎣

  5 2

  ,2

  ⎤ ⎥ ⎥ ⎦

• Input:
  [1,2]/[3,4]
  or:
  ’/’([1,2],[3,4])
  Output:

  ⎡ ⎢ ⎢ ⎣

  1 3

  ,

  1 2

  ⎤ ⎥ ⎥ ⎦

• Input:
  1/[[1,2],[3,4]]
  or:
  ’/’(1,[[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎢ ⎢ ⎢ ⎣

  −2 1      3 2 − 1 2

  ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

• Input:
  [[1,2],[3,4]]*1/ [[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎣

  1 0       0 1

  ⎤ ⎥ ⎦

• Input:
  [[1,2],[3,4]]/ [[1,2],[3,4]]
  Output:

  ⎡ ⎢ ⎣

  1 1       1 1

  ⎤ ⎥ ⎦

  (This is term-by-term division.)