these tests have been installed, except:

	for res we have never provided a Hilbert function hint and I don't know how to do it
	IM2_GB_set_hilbert_function seems to be only for gb's, not for res's

	how do I tell whether a matrix is homogeneous with respect to just the first component of the degree?

=============================================================================

In-Reply-To: <200606281441.k5SEf4Y01872@u00.math.uiuc.edu>
From: Michael Stillman <mike@math.cornell.edu>
Subject: Re: good morning!
Date: Wed, 28 Jun 2006 11:05:05 -0400
To: dan@math.uiuc.edu

>
> It's correct (!), as the ^0 is a slick way of transforming the  
> string into a
> net.  The test is to take the value of the string and check for  
> equality with
> the original thing:
>

That's right, I remember that one!


If you get time, could you add the following tests to the front end?   
(for res, this might mean using a different algorithm instead, as in  
res.m2) (These will improve behavior for multigraded rings, and  
towers of rings).

Needed for using Hilbert functions to aid in Groebner basis computation:
   Ring is poly ring over a field (or skew commutative, or quotient  
ring of such, or both)
   Ring is singly graded, every variable is positive
   Ring is homogeneous in this grading
   Matrix is homogeneous in this grading

Needed to compute resolutions, (algorithms 0,1,2,3):
    Ring is poly ring over a field (or skew commutative, or quotient  
ring of such, or both)
   Ring is graded, first degree of every variable is positive
   Ring is homogeneous in this grading (actually, only need graded  
with respect to the first degree)
   Matrix is homogeneous in this grading (same note as previous line)
Additional requirements for resolution algorithm 3 (which uses  
hilbert function):
     Ring is singly graded

I might try to relax the singly graded constraint on these.  But the  
positivity for every variable will still be required...
