sub-module membership test
I have a submodule of the module Z2[x,y,z]3, which can be specified by its 6 generators that are the columns below 0001+x+y+xy1+y+z+yz1+x+z+xz1+z1+x00y+z001+x1+yx+y0z2
How can I implement the sub-module membership test in sage? For example, I want to check whether x+zx+yy+z belongs to the above submodule or not?
You consider it as a module over which ring?
over the polynomial ring Z2[x,y,z]