Variables
Variables are defined to be a type of field element, though they do not (though could be extended to) support operations like addition. Variables represent strings such as ``x1'', ``y'' etc. over which polynomials and straight-line programs are defined. Variables are assumed to be ordered, i.e. each variable has a rank. For example, the user might define the variable set to be ``x1'', ``x2'' and ``x3'' which are ranked 1, 2 and 3 respectively (i.e. x1 > x2 > x3 ). The user does not need to explicitly tell APU what variables he intends to use. Every variable that is encountered, such as when reading in polynomials with the read_poly() routine, is automatically inserted into the list of variables if it is not already present.
Note : The behaviour of variables is typically hidden from the user and unless one is interested in direct manipulations involving them it is not necessary to understand how they work in APU.