Multivariable Polynomial Division

713 views
Skip to first unread message

Raiden

unread,
May 18, 2011, 3:57:31 PM5/18/11
to Macaulay2
Hi, after a lot of searching, I can't figure out the command that is
used to perform a multivariable polynomial division. For example, I'm
looking for a command that would let me choose a monimal order (e.g.
deglex) and a variable order (e.g. x>y) and then perform a polynomial
division (e.g. [x^3y^2-3x^2y+xy-y]/[2x^2y+x]). I know this is probably
a really dumb thing to ask, but I really can't figure out the command
that does this.

Douglas Leonard

unread,
May 18, 2011, 7:35:37 PM5/18/11
to maca...@googlegroups.com
Have you looked at all the examples in the pages related to / // and %?

>>> Raiden <sjh...@mail.missouri.edu> 05/18/11 3:10 PM >>>

--
You received this message because you are subscribed to the Google
Groups "Macaulay2" group.
To post to this group, send email to maca...@googlegroups.com.
To unsubscribe from this group, send email to
macaulay2+...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/macaulay2?hl=en.


Federico Galetto

unread,
May 20, 2011, 5:22:38 AM5/20/11
to Macaulay2
Hi!

You can specify a monomial order in the declaration of the ring. For
example:

R=QQ[x,y,MonomialOrder=>GRevLex]

GRevLex is actually the default option. Other popular choices include
Lex and GLex (check the help page on monomial orderings for more).

Multivariate polynomial division is performed with //. In your case

(x^3*y^2-3*x^2*y+x*y-y)//(2*x^2*y+x)

The remainder is obtained with %. If you need to divide by more than
one polynomial, then put all your polynomials in a matrix and divide
by that.

Hope this helps,
Federico.
Reply all
Reply to author
Forward
0 new messages