Scalar Functions

There is a class of primitive functions termed scalar functions This class is identified in Table 9 below. Scalar functions are pervasive, i.e. their properties apply at all levels of nesting.  Scalar functions have the following properties:

Table 9: Scalar Primitive Functions

Symbol Monadic Dyadic
+ Identity Plus (Add)
- Negative Minus (Subtract)
× Direction (Signum) Times (Multiply)
÷ Reciprocal Divide
| Magnitude Residue
Floor Minimum
Ceiling Maximum
* Exponential Power
Natural Logarithm Logarithm
Pi Times Circular
! Factorial Binomial
~ Not $
? Roll $
Type (See Enlist) $
^   And
  Or
  Nand
  Nor
<   Less
  Less Or Equal
=   Equal
  Greater Or Equal
>   Greater
  Not Equal
$ Dyadic form is not scalar

Monadic Scalar Functions

Example

      ÷2 (1 4)
0.5  1 0.25

Dyadic Scalar Functions

Examples

      2 3 4 + 1 2 3
3 5 7
 
      2 (3 4) + 1 (2 3)
3  5 7
 
      (1 2) 3 + 4 (5 6)
 5 6  8 9

      10 × 2 (3 4)
20  30 40
 
      2 4 = 2 (4 6)
1  1 0

      (1 1⍴5) - 1 (2 3)
4  3 2

      1↑''+⍳0
0
       1↑(0⍴⊂' ' (0 0))×''
0  0 0

Note:  The Axis operator applies to all scalar dyadic functions.