Algebraic expression domains

 

• 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