# Creating a multivariate polynomial with ideal

Hello, new user of sage here. I have a computation not too difficult too make, but I am a bit lost since it is above my math level and before the vastness of sage documentation.

I have to create and do a multiplication with a "multivariate polynomial which is an element of a polynomial quotient ring defined by the polynomial ring over GF(2)[x, y, z] modulo the ideal generated by ⟨ $1+x^5$, $1+y^5$, $1+z^{64}$⟩".

I already wrote this:

```
Ring = PolynomialRing(GF(Integer(2)), ['x', 'y', 'z'])
P = Ring; (x, y, z,) = P._first_ngens(3)
I = P.ideal([Integer(1)+x**Integer(5), Integer(1)+y**Integer(5), Integer(1)+z**Integer(64)])
```

but don't know how to continue or if it is correct.

How should I proceed ? Thank you.

`Integer()`

can be omitted everrywhere.