User Functions. The programs COT, PSUM, O .... G, and G .... O are
user functions-they begin with the command .... and one or more
names, which together define one or more local variables, followed by
one expression or program. When the user function is stored in a vari-
able, you can use the name of the variable in algebraics as you would
use a built-in function.
Program Structures. The command .... followed by names and an
expression or program is called a
which is one
type of program structure. There are also program structures for
branching (such as IF ... THEN ... ELSE ... END) and looping (such
as DO ... UNTIL ... END). See chapter 26, uProgram Structures," for
descriptions. Also, chapter 28, uProgramming Examples," contains 20
programs that demonstrate every program structure, along with a va-
riety of programming techniques.
Unnamed Programs. Programs don't need to be stored in variables
to be useful; for examples, see HExpanding and Collecting Com-
pletely," on page 253, and HDisplaying a Binary Integer," on page 257.
Algebraics comprise one or more functions and the functions' argu-
ments; the arguments can be numbers, names, or subexpressions.
Algebraics are written and displayed in algebraic syntax, a form simi-
lar to written mathematical notation. There are two types of
algebraics, expressions and equations.
In part 1 you used expressions in three different ways: as data, as
functions, and as implicit equations.
Expressions As Data. When you calculate with expressions, such as
adding two expressions, squaring an expression, or differentiating an
expression, the result is another expression. In these cases the expres-
sions act as data to be manipulated, independent of any values
assigned to the variables.