The following are the built-in functions and operators especially useful for writing and debugging Derive programs:


Use the MAP and MAP_LIST functions to map functions over the elements of vectors and sets.  If u is an expression involving the variable x and c is a set or a vector, MAP_LIST(u, x, c) evaluates u(x) for x equal to each element of c and returns the results as a set or vector (depending on the type of c).  MAP_LIST(u,k,m,n,s) evaluates u(k) for k=m to n in steps of size s.  s defaults to 1.  The function MAP evaluates u identical to MAP_LIST, but it just returns the truth-value "true".


Use the ASSIGN function to assign values to variables generated by programs.  The := assignment operator (see the Author > Variable Value command2SGW02B) and the ASSIGN function are both used to assign values to variables.  The left operand of the := assignment operator must be a variable, since it is not simplified.  Whereas, the first argument of the ASSIGN function can be any expression, so long as it simplifies to a variable.  Therefore, use ASSIGN when it is necessary to generate a variable and then assign it a value.  For example, simplifying the expression

ASSIGN(APPEND("a", 1), 25)

generates the string variable "a1" and assigns it the value 25.


Use the following variable update operators to make user-defined functions more efficient and easier to read:

•        x :+ u  increments the variable x by the value of the expression u.

•        x :- u  decrements the variable x by the value of the expression u.

•        x :* u  multiplies the variable x by the value of the expression u.

•        x :/ u  divides the variable x by the value of the expression u.

For example, the statement x :+ 1 is faster than the equivalent statement x := x+1.  Similarly, the statement x :* 2 is faster than the equivalent statement x := 2·x.


Use the WRITE function in user-defined functions to show intermediate results of a transient nature.  WRITE(u) format the expression u as a single line of text, and displays the result on the Algebra window status line.  Any expression previously displayed on the status line is over-written.  WRITE is useful for displaying counters in program loops to help determine where programming errors have occurred.


Use the DISPLAY function in user-defined functions to display intermediate results in a text box.  DISPLAY(u,n) creates a new text box containing the expression u formatted in 2 dimensions using up to n lines of text.  n defaults to 1.  DISPLAY makes it possible for user-defined functions to show the steps involved in a calculation.


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