Mathematical, matrix, string array, and string operators

   MATHEMATICAL OPERATORS             MATRIX AND STRING ARRAY OPERATORS
    +   addition                       |       matrix vertical concatenation
    -   subtraction or unary minus     ~       matrix horizontal concatenation
    *   multiplication                 $|      string array vert concatenation
    .*  ExE multiplication             $~      string array horiz concatenation
    ^   ExE exponentiation             '       transpose
    !   factorial                      .'      bookkeeping transpose
    ./  ExE division
    /   division or linear equation solution of Ax = b, for example: x = b/A;
    %   modulo division
    .*. Kronecker product             STRING OPERATORS
    *~  horizontal direct product      $+      string concatenation

Symbols used for indexing matrices are: "[", "]", "." and ":". For example,

     x[1 2 5]       returns the 1st, 2nd and 5th elements of x.
     x[2:10]        returns the 2nd through 10th elements of x.
     x[.,2 4 6]     returns all rows of the 2nd, 4th, and 6th columns of x.

Scalar-returning relational operators

           Less than:                      Not equal:
               z = x < y;                      z = x /= y;
               z = x LT y;                     z = x NE y;
               z = x $< y;                     z = x $/= y;

           Greater than:                   Greater than or equal to:
               z = x > y;                      z = x >= y;
               z = x GT y;                     z = x GE y;
               z = x $> y;                     z = x $>= y;

           Equal to:                       Less than or equal to:
               z = x == y;                     z = x <= y;
               z = x EQ y;                     z = x LE y;
               z = x $== y;                    z = x $<= y;

The result is a scalar 1 or 0, based upon a comparison of all elements of x and y. ALL comparisons must be true for a result of 1 (TRUE).
The "$" is used for comparisons between character data and other nonnumeric data, e.g. NANs.

The matrix-returning relational operators

    Less than:          Not equal:
        z = x .< y;          z = x ./= y;
        z = x .LT y;         z = x .NE y;
        z = x .$< y;         z = x .$/= y;

    Greater than:       Greater than or equal to:
        z = x .> y;          z = x .>= y;
        z = x .GT y;         z = x .GE y;
        z = x .$> y;         z = x .$>= y;

    Equal to:           Less than or equal to:
        z = x .== y;         z = x .<= y;
        z = x .EQ y;         z = x .LE y;
        z = x .$== y;        z = x .$<= y;

The above operators all produce a matrix of 0's and 1's, with a 1 where the corresponding comparison is TRUE.
The "$" is used for comparisons between character data and other nonnumeric data, e.g. NANs.
The logical operators perform logical or Boolean operations on numeric values. On input, a nonzero value is considered TRUE and a zero value is considered FALSE. The logical operators return a 1 if TRUE and a 0 if FALSE.
These operators require scalar arguments. These are the ones to use in If and DO statements:

  * Complement              * Disjunction           * Equivalence
    z = NOT x;                z = x OR y;             z = x EQV y;

  * Conjunction             * Exclusive OR
    z = x AND y;              z = x XOR y;

The matrix logical operators perform logical or Boolean operations on numeric values. On input, a nonzero value is considered TRUE and a zero value is considered FALSE. The logical operators return a 1 if TRUE and a 0 if FALSE.

  * Complement              * Disjunction           * Equivalence
    z = .NOT x;               z = x .OR y;            z = x .EQV y;

  * Conjunction             * Exclusive OR
    z = x .AND y;              z = x .XOR y;

If the logical operator is preceded by a dot ".", the result will be a matrix of 1's and 0's based upon an element-by-element logical comparison of x and y. For example, if

                   x = { 0 1 0 1 } and y = { 1 1 0 0 }