A distributed polynomial is a polynomial with a special internal
representation different from the ordinary one.
An ordinary polynomial (having
type 2) is internally represented
in a format, called recursive representation.
In fact, it is represented as an uni-variate polynomial with respect to
a fixed variable, called main variable of that polynomial,
where the other variables appear in the coefficients which may again
polynomials in such variables other than the previous main variable.
A polynomial in the coefficients is again represented as
an uni-variate polynomial in a certain fixed variable,
the main variable. Thus, by this recursive structure of polynomial
representation, it is called the `recursive representation.'
On the other hand, we call a representation the distributed representation of a polynomial, if a polynomial is represented, according to its original meaning, as a sum of monomials, where a monomial is the product of power product of variables and a coefficient. We call a polynomial, represented in such an internal format, a distributed polynomial. (This naming may sounds something strange.)
For computation of Groebner basis, efficient operation is expected if polynomials are represented in a distributed representation, because major operations for Groebner basis are performed with respect to monomials. From this view point, we provide the object type distributed polynomial with its object identification number 9, and objects having such a type are available by Asir language. Here, we provide several definitions for the later description.
<<0,1,2,3,4>>and also can be input in such a form. This example shows a term in 5 variables. If we assume the 5 variables as
e, the term represents
b*c^2*d^3*e^4in the ordinary expression.
2*<<0,1,2,3,4>>and also can be input in such a form.
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