Math 480, Spring 2013/Polynomial Division Algorithm

An implementation of the polynomial division algorithm

An experimental implementation of the polynomial division algorithm can be found at

http://cartan.math.umb.edu/vpf/cgi-bin/calculator

using the functions PolyDivStringLex, PolyDivStringGrLex, PolyDivStringLexRev, PolyDivStringGrLexRev, with respective monomial orders: lexicographic (z>y>x), graded lexicographic, lexicographic-reversed (x>y>z), graded lexicographic-reversed (x>y>z). Please note: graded reverse lex order (as given in the book) is NOT the same as graded lexicographic-reversed.

Please use the calculator with caution: the code is still experimental and does contain errors. You can view the c++ code of the calculator by going to the calculator, clicking the top-right link, and clicking again to access the latest version of each of the source code files of the project.

Here is the example from today's exam, using both the lexicographic order (y >x) and the lexicographic-reversed (x>y).

[http://cartan.math.umb.edu/vpf/cgi-bin/calculator?textInput=PolyDivStringLex%7B%7D%28x%5E7+y%5E2%2Bx%5E3y%5E2-y%2B1%2C+x+y%5E2-x%2C+x-y%5E3+%29+%3B%0D%0APolyDivStringLexRev%7B%7D%28x%5E7+y%5E2%2Bx%5E3y%5E2-y%2B1%2C+x+y%5E2-x%2C+x-y%5E3+%29+%3B

PolyDivStringLex{}(x^7 y^2+x^3y^2-y+1, x y^2-x, x-y^3 ) ;

PolyDivStringLexRev{}(x^7 y^2+x^3y^2-y+1, x y^2-x, x-y^3 ) ;]

If you see any wrong printouts in the calculator (or any other bugs) I would be very grateful if you email me at todor.milev at google's email.