graded Module over QQ

[René Birkner]

Hi,

I have given a list of multidegrees {a,b,c},{d,e,f},{g,h,i},...
I want to create a free module over QQ, such that my generators have
the corresponding multidegree.
I.e.:
QQ^{{a,b,c},{d,e,f},{g,h,i},... }
which does not work, since QQ has no multidegree. how can I equipp QQ
with such multidegrees?

Thanks
René

[Mike Stillman]

The easiest way to do so is to make a polynomial ring over QQ with no
variables, but with a DegreeRank:

i42 : R = QQ[DegreeRank=>2]

o42 = R

o42 : PolynomialRing

i43 : R^{{2,3}}

1
o43 = R

o43 : R-module, free, degrees {{-2, -3}}

-- Mike

[René Birkner]

Perfect, that's what I was looking for!

Thanks Mike