# Multivariate polynomial coefficients including zeros

Dears,

I would like to get the coefficients of a multivariate polynomial **including the zero coefficients (in their correct positions).** I have found a similar answer as regards a polynomial f of two variables x,y

```
P.<x,y> = PolynomialRing(ZZ, 2, order='lex')
f=3*x^2*y^2+x*y+3
```

Then using the following code:

```
coeffs = []
for i in range(f.degree(x), -1, -1):
for j in range(f.degree(y), -1, -1):
coeffs.append(f.coefficient({x:i, y:j}))
```

The result is as expected: [3, ,0 , 0, 1, 0, 0, 0, 0, 3]

**Now, I would like to extend this solution for a multivariate polynomial of n variables [xo,x1,...xn-1]**
The polynomial is defined with the following code: (Note: q=next_prime(10000))

```
A1 = [(', '.join('x%i'%i for i in [0.. n-1]))]; ### construct a suitable multivariate ring
V = var(A1[0])
x=vector(list(V))
P1=PolynomialRing(GF(q),V)
```

How can I do that? Any help will be much appreciated.

Regards, Natassa

A tip independent of your actual question: you can construct this polynomial ring in a cleaner way with

If you want the variables bound to symbols so that you can write

`x0^2+x1^2`

etc. then you can useor, if you want the variables as a tuple/list/whatever:

etc.