Re: FindRoot & Grobner basis
- To: mathgroup@smc.vnet.net
- Subject: [mg11767] Re: FindRoot & Grobner basis
- From: Etienne HUENS <huens@fynu.ucl.ac.be>
- Date: Sat, 28 Mar 1998 00:25:09 -0500
- Organization: University of Louvain - Nuclear Physics Department
- References: <6embiq$njj@smc.vnet.net> <6f155r$fq9$4@dragonfly.wolfram.com>
Michael Chang wrote: > > blablabla ... If one has > any tutorial about Groebner Basis, I'd also be interested in hearing > about it! > You will find interesting stuff in http://www.can.nl/CA_Library/Groebner/ There is a link called "tutorials". Here is a question : I start with an introduction. In[1]:= Expand[ (1 + 2x + y)^3 ] Out[1]= 1 + 6 x + 12 x^2 + 8 x^3 + 3 y + 12 x y + 12 x^2 y + 3 y^2 + 6 x y^2 + y^3 The terms are put in ascending order. So, I can write : x < x^2 < x^3 < y < x y < x^2 y < y^2 < x y^2 < y^3 If I associate to each term a vector with the variable's power, we have: (1,0) < (2,0) < (3,0) < (0,1) < (1,1) < (2,1) < (0,2) < (1,2) < (0,3). If s and t are the vectors associated to two terms of a pol., we have, w.r.t. the order used by Mathematica : s < t <=> the most rigther non-zero component of t-s is positive. It's a kind of "lexical" order. Q1 : What is the name of this order ? Q2 : Is it possible (and how) to ask Mathematica to work with a different order ? It may be intersting when working with grobner basis. I hope to be clear. If not, tell me. Thanks, Etienne Huens