Date: Sat, 23 May 2009 10:38:48 -0500
From: "Daniel R. Grayson" <dan@math.uiuc.edu>
To: mike.stillman@mac.com
CC: dan@math.uiuc.edu
Subject: [aboocher@gmail.com: Eliminate Command in M2]
Reply-to: dan@math.uiuc.edu


It seems that our eliminate command is slower than it has to be.  In the
example below it uses the monomial ordering

	R=QQ[x,y,a,b,c,d,e,f,g,h,i,j,k,l,MonomialOrder=>{GRevLex => 2, GRevLex => 12}]

but

	R=QQ[x,y,a,b,c,d,e,f,g,h,i,j,k,l,MonomialOrder=>Eliminate 2]

is faster.  Is that generally to be expected?  Shall I change it?

------- Start of forwarded message -------
To: dan@math.uiuc.edu
From: Adam Boocher <aboocher@gmail.com>
Subject: Eliminate Command in M2
Date: Fri, 22 May 2009 19:38:30 -0700

Hi again,

I noticed that the eliminate command was behaving strangely a few  
months ago.  I wrote to Prof. Stillman about it, but David suggested  
I write to you as well.  For this example, (at least on my machine) I  
can compute an entire Grobner basis in a few seconds (and thus  
compute the elimination ideal that way) but the eliminate({x,y},I)  
command hangs.

Here's the example I was trying to do:

R=QQ[x,y,a,b,c,d,e,f,g,h,i,j,k,l,MonomialOrder=>Eliminate 2]
p=a*x^2+b*x*y+c*y^2+d*x+e*y+f
q=g*x^2+h*x*y+i*y^2+j*x+k*y+l
M=matrix{{diff(x,p),diff(y,p)},{diff(x,q),diff(y,q)}}
D=determinant M
I=ideal(p,q,D)
- --it will compute the Grobner basis in a few seconds
time G = gb I;				        -- used 3.49 seconds
time S = gens G;				-- used 18.06 seconds
- --but the eliminate command hangs
eliminate({x,y},I)

- -Adam 

