The basic format for representing mathematical formulae is the algebraic form : an expression is internally encoded as a list with prefix operators:
x + 1 ⇒ (PLUS X 1)
x + y + 1 ⇒ (PLUS X Y 1)
x + y * z + 1 ⇒ (PLUS X (TIMES Y Z) 1)
x∧(y + 1) ⇒ (EXPT X (PLUS Y 1))
Algebraic forms are used for many purposes, for data input, for transferring data between various system components and for output. To get a feel as to how algebraic forms look like, you can make REDUCE display them for you, e.g. by the following sequence:
The first statement assigns an algebraic expression to a variable as usual in algebraic mode, and the second statement forces REDUCE to print the algebraic form corresponding to this expression in symbolic mode.