Vector space dimension of a graded algebra over a field

[just starting]

Hi all, 

I'm completely new to Macaulay2 and there's something I'm sure is simple to do I can't find in the documentation. Namely, I start with a polynomial ring over the rationals and mod out by a big enough ideal that I'm sure the result has finite dimension as a rational vector space. How can I extract the dimensions of the graded components? For example, is there an command that converts a Q-algebra to a vector space over Q?


Thanks!

[Frank Moore]

The command you are looking for is 'basis':

R = QQ[x]/ideal{x^2+1}

basis R

If R is graded, then one can get the homogeneous component in a given degree using basis(ZZ,Ring):

S = QQ[a,b]

basis(4,S)

Frank

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Dr. W. Frank Moore
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Department of Mathematics, Wake Forest University

email: moo...@wfu.edu

[just starting]

Frank,

Thank you!