ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 27 Jan 2019 16:09:04 +0100codimension of an ideal or free submodulehttps://ask.sagemath.org/question/45174/codimension-of-an-ideal-or-free-submodule/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 possibleFri, 25 Jan 2019 07:16:59 +0100https://ask.sagemath.org/question/45174/codimension-of-an-ideal-or-free-submodule/Answer by FrédéricC for <p>Is there an option to calculate the codimension of an ideal Sage? For example, I have the following ideal </p>
<p>$I=(1+xy, x+y)$</p>
<p>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</p>
https://ask.sagemath.org/question/45174/codimension-of-an-ideal-or-free-submodule/?answer=45202#post-id-45202Like 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()
2
Sun, 27 Jan 2019 16:09:04 +0100https://ask.sagemath.org/question/45174/codimension-of-an-ideal-or-free-submodule/?answer=45202#post-id-45202