sub-module membership test

asked 2019-08-07 17:21:32 -0600

arpit gravatar image

updated 2019-08-07 17:24:03 -0600

I have a submodule of the module $\mathbb{Z}_2[x,y,z]^3$, which can be specified by its 6 generators that are the columns below \begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & y+z & 0\newline 0 & 1+x& 1+y & x+y & 0 & z^2 \end{array}

How can I implement the sub-module membership test in sage? For example, I want to check whether \begin{array}{c} x+z \newline x+y\newline y+z \end{array} belongs to the above submodule or not?

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Comments

You consider it as a module over which ring?

vdelecroix gravatar imagevdelecroix ( 2019-08-09 13:21:04 -0600 )edit

over the polynomial ring $\mathbb{Z}_2[x,y,z]$

arpit gravatar imagearpit ( 2019-08-09 22:49:27 -0600 )edit