- ring of polynomials in variables with operations of addition, subtraction,
multiplication and exponentiation by a nonnegative integer; see
the examples of polynomials ; polynomial coefficients can be numbers from
a number domain
- power series, other kinds of series
- rational functions (extension of
polynomials by the operation of division) with operations of
addition, subtraction, multiplication, division and exponentiation
by an integer; see the examples of rational functions
- extension of rational functions by radicals (rational exponents),
with operations of addition, subtraction, multiplication,
division and exponentiation by a rational number
- algebraic functions implicitly defined by polynomials with integer coefficients
which depend on algebraic functions and variables from , e.g.,
the algebraic function defined by the polynomial
- elementary transcendental functions ,
extension of rational functions by elementary transcendental
functions; if we have only one variable and an
expression contains , we can denote
and work with a rational function of
-- the extension is given only by rules
like , etc.
- transcendental functions: e.g., ;
extension of rational functions by transcendental functions
- matrix rings
- differential fields
- finite groups
- a user can use algebraic expressions from an arbitrary domain for
the most part; the program will decide which domain the
expression belongs in and use an appropriate algorithm

Richard Liska