IndexedVariable -- the class of all indexed variables

Description

Indexed variables provide the possibility of producing polynomial rings R[x_0, x_1, ..., x_(n-1)] in n variables, where n is not known in advance. If x is an symbol, and i is an integer, then x_i produces an indexed variable. After this has been done, an assignment x_i=v will assign another value to it. A new sequence of indexed variables of length n assigned to the symbol x can be produced with x_1 .. x_n and that sequence can be used in constructing a polynomial ring.

i1 : ZZ/101[t_0 .. t_4]

      ZZ
o1 = --- [t , t , t , t , t ]
     101   0   1   2   3   4

o1 : PolynomialRing

i2 : (t_0 -  2*t_1)^3

      3     2          2     3
o2 = t  - 6t t  + 12t t  - 8t
      0     0 1      0 1     1

      ZZ
o2 : --- [t , t , t , t , t ]
     101   0   1   2   3   4

Methods that use an indexed variable :

IndexedVariable .. IndexedVariable, see .. -- a binary operator, uses include ranges; sequence of consecutive items
IndexedVariable <- Thing, see <- -- assignment with left side evaluated
IndexedVariable ? IndexedVariable, see ? -- comparison operator
Symbol ? IndexedVariable, see ? -- comparison operator
baseName(IndexedVariable), see baseName -- the base name of a generator
IndexedVariable _ Ring -- get a ring variable by name
Ring _ IndexedVariable -- missing documentation
value(IndexedVariable) -- retrieve the value of an indexed variable

For the programmer

The object IndexedVariable is a type, with ancestor classes BasicList < Thing.