- recursive representation is sparse representation with
exponent ordering used to represent multivariate polynomials
- for recursive representation, an ordering of variables has
to be chosen, e.g., alphabetically
- the variable which is chosen first in the ordering is called the
main variable of the polynomial
- coefficients of the powers of the main variable will be
polynomials in the other variables
- for simplicity, we will consider a polynomial in
variables , with variable ordering so that the main variable is

- such a polynomial is represented by a list of pairs where each coefficient is a
polynomial in and is represented by the list of
pairs
- to distinquish a polynomial in from a
polynomial in , we replace each pair of
(exponent, coefficient) by the triple (variable, exponent,
coefficient)
- the polynomial

is then represented by the list

`((x 3 ((y 2 1) (y 1 8))) (x 2 ((y 1 7) (y 0 3))) (x 1 ((y 1 5))) (x 0 4))`

Richard Liska