Naming polynomial ring variables (indeterminants)

 

Every polynomial and every matrix in Macaulay must be defined over a polynomial ring. The indeterminates of a ring are either single letters or are single letters indexed by one or more integers. More specifically, these indeterminates have the following form.

1. a single letter: a-z, A-Z, where upper and lower case are distinct or
2. a single letter, indexed by a set of integers or integer expressions, separated by commas and enclosed by square brackets.

For example, if ``i'' is a user defined integer variable, then the following are legal ring indeterminates:

    a
    A
    F[1,2,3]
    z[-1,2*i]

The ring command informs Macaulay which variables you wish to use. These names do not conflict with any user defined variable names (i.e. one can have a matrix named ``a'', as well as an indeterminate in the base ring of this matrix, named ``a''. The only time a conflict is possible is with polynomial expressions. See Sections 3.6 and 4.3 for more details.

We often call ring indeterminates either ``variables'' or ``ring variables''. These should not be confused with user defined variables which are rings.