# Understanding SAGE code

Hey, I want to implement a functionality I found in sage math code into my matlab code, to do so I need to understand what is happening which I really dont, could someone ellaborate and explain the steps? X is apparently creating a GF2 which gives the output x that is in F2 while F is a definition of the X^4+X^3+1? And F_mul somehow ends up with this 0x7f7467c66450 And that I cannot really understand

```
X = GF(2).polynomial_ring().gen()
F = GF(2**4, name="a", modulus=X**4+X**3+1)
def F_mult(x, y):
return (F.fetch_int(x) * F.fetch_int(y)).integer_representation()
```

Thanks a bunch!

Where do you get

`0x7f7467c66450`

from? It is too large to correspond to an element of the field`F`

.`X`

is the generator of a polynomial ring with coefficients in the field F_2. The field F (of size 2^4) is defined using the particular polynomial`X^4 + X^3 + 1`

as its modulus; look at`GF?`

to read the help string for`GF`

. Once you've defined`F`

, look at`F.fetch_int?`

to read the help string for that.