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===== Homework 06 - Solving Polynomial Equations I =====

=== Task ===

Use the template [[http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Labs/PRO-2012-Polynomial-Division-Assignment.mws|PRO-2012-Polynomial-Division-Assignment.mws]] to implement the algorithm of polynomial division. 

  - Divide polynomial f = x^2*y+x*y^2+y^2-1 by polynomials f1 = x*y-1, f2 = y^2+x+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).
    - 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).
  - Divide polynomials in the [[http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Labs/PRO-2012-Polynomial-Division-Assignment.mws|PRO-2012-Polynomial-Division-Assignment.mws]] corresponding to your number (w.r.t. [[https://www.fel.cvut.cz/cz/education/rozvrhy-ng.B201/public/html/paralelky/P46/78/par4678206.1.html|cz]],[[https://www.fel.cvut.cz/cz/education/rozvrhy-ng.B201/public/html/paralelky/P46/82/par4682106.1.html|en]]).
    - 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).
    - 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 ===

Upload via the [[https://cw.felk.cvut.cz/upload/|course ware]] the zip archive ''hw06.zip'' containing 
  - hw06.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 in [[https://cw.fel.cvut.cz/b201/_media/courses/pro/02_slides_solving_equation.pdf|lecture slides from week 9 and 10 ]].