# intersection of two free submodules

I have two modules found as follows

```
F=GF(2);R.<x,y,z> = PolynomialRing(F)
f1 = 1+z;g1=1+y;h1=0;
I1 = Ideal([f1,g1,h1])
M1 = I1.syzygy_module(); M1
```

[ 0 0 1]

[y + 1 z + 1 0]

```
F=GF(2);R.<x,y,z> = PolynomialRing(F)
f2 = 0;g2=1+y;h2=1+x;
I2 = Ideal([f2,g2,h2])
M2 = I2.syzygy_module(); M2
```

[ 1 0 0]

[ 0 x + 1 y + 1]

Is it possible to find the intersection of two such submodules $M_1$ and $M_2$ in sage? Another possibility would be to find the syzygy of the module generated by vectors (f1,g1,h1) and (f2,g2,h2).