On of the most important tasks performed by a computer algebra system is the reduction of an algebraic expression to a canonical form. A reduction process is canonical if it guarantees that two expressions are transformed to the same form if and only if they are algebraically identical. Unfortunately canonical forms are not known for all algebraic objects, e.g. for surds. The canonical form of REDUCE is the standard quotient (“SQ”) which is a quotient of two standard forms (“SF”). An SF is a polynomial in internal representation and an SQ is a quotient of two polynomials, a rational function. At the same time SQ and SF are the forms used internally for most arithmetic.
In this section the structures of SF and SQ are described, followed by a list of operations on these. For programming and debugging in symbolic mode it is often necessary to decipher an expression of this type. However, the knowledge about this part of the internal REDUCE structure should never be used to access SF of SQ directly by LISP primitives. Instead use only “official” primitives supplied by REDUCE.