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codimension of an ideal or free submodule

asked 2019-01-25 00:16:59 -0500

arpit gravatar image

updated 2019-01-25 00:21:58 -0500

Is there an option to calculate the codimension of an ideal Sage? For example, I have the following ideal

$I=(1+xy, x+y)$

in $\mathbb{Z}_{2}\left[x,y\right]$ which is a polynomial ring over the field $\mathbb{Z}_2$. How do I calculate the codimension for this simple example? I would like to generalize to free submodules if possible

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answered 2019-01-27 09:09:04 -0500

FrédéricC gravatar image

Like that

sage: R=GF(2)['x,y']
sage: x,y=R.gens()
sage: I=R.ideal([1+x*y,x+y])
sage: I.vector_space_dimension()
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Asked: 2019-01-25 00:16:59 -0500

Seen: 55 times

Last updated: Jan 27