The preliminary mini-project

Date of postage.

Thursday 12 of February.

Due format.

A porgram in AXIOM, ALDOR or MAPLE. The language must be the same as for the project.

Date for submission.

Thursday 11 of March.

Description.

You have the write a function that takes as input two polynomials f₁, f₂ in $\mbox{${\mathbb Q}$}$[x, y] and returns their common roots in a similar form as TRIADE (that is, a list of triangular sets). Assume that x < y holds. This means that we want to compute univariate conditions in x rather than in y. Then, you can call an existing function for computing the resultant of f₁, f₂ w.r.t. x. Let r be the square-free part of this resultant and let $\mathbb {A}$ be the product of fields $\mbox{${\mathbb Q}$}$[x]/$\langle$r$\rangle$. The next and last step is the computation of the gcd of f₁, f₂ regarded as univariate polynomials in $\mbox{${\mathbb A}$}$[y]. You must implement this step yourself, without callling any gcd function from TRIADE.