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## Homework 07 - Solving Polynomial Equations I

Use the template PRO-2012-Polynomial-Division-Assignment.mws to implement the algorithm of polynomial division.

1. Divide polynomial f = x^2*y+x*y^2+y^2-1 by polynomials f1 = x*y-1, f2 = y^2+x+1:
1. Consider the lexicographical ordering with x > y and find the (polynomial) coefficients as well as the remainder for f:(f1,f2) and f:(f2,f1).
2. Consider the lexicographical ordering with y > x and find the (polynomial) coefficients as well as the remainder for f:(f1,f2) and f:(f2,f1).
2. Divide polynomials in the PRO-2012-Polynomial-Division-Assignment.mws corresponding to your number (w.r.t. cz,en).
1. Consider the lexicographical ordering with x > y and find the (polynomial) coefficients as well as the remainder for f:(f1,f2) and f:(f2,f1).
2. Consider the lexicographical ordering with y > x and find the (polynomial) coefficients as well as the remainder for f:(f1,f2) and f:(f2,f1).

Upload via the course ware the zip archive hw07.zip containing

1. hw07.mws Maple worksheet containing the solution to the above problems (algotihms, results, comments).

#### Slides

The examples and pseudo-algorithm of polynomial division can be found here.