Ask Your Question
1

Elements of the Stanley-Reisner ring

asked 2018-07-25 16:00:44 -0500

vukov gravatar image

I have a simplicial complex, and I'm trying to manipulate the Stanley-Reisner ring of that simplicial complex. This is just a quotient of a polynomial ring. The generators of the quotient ring are called (according to R.gens()) x0bar, x1bar, x2bar, x3bar. However, when I try to refer to elements of the ring in this way (for example, to create an ideal containing certain elements), I get an error. For example:

sage: X = SimplicialComplex([[1,2,3], [0,2,3], [0,1,3]])
sage: R = X.stanley_reisner_ring()
sage: R(x0bar)

This gives me the following error:

NameError                                 Traceback (most recent call last)
<ipython-input-3-b65205a640d6> in <module>()
----> 1 R(x0bar)

NameError: name 'x0bar' is not defined
edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
2

answered 2018-07-25 17:23:16 -0500

You can define e.g.

xbar = R.gens()

Then xbar[0] will be the first generator, namely x0bar, etc.

You can also do

R.inject_variables()

which defines the variable x0bar to be the corresponding generator (etc.), if you insist.

The first approach seems cleaner to me. The second one could be convenient in an interactive session.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2018-07-25 16:00:44 -0500

Seen: 37 times

Last updated: Jul 25