### Multivariate polynomial ring with total degree no larger than n

Hello everyone,

I need to compute the product: f(x_1)f(x_2)...f(x_n), where f is a polynomial of degree n, and I do not need the part with total degree larger than n. To reduce the computation complexity, I think it would be helpful to construct an n-variable multivariate polynomial ring, with terms total degree no larger than n. I found the following two possible ways to do this, however, I could not make either of them work for my settings.

Create a multivariate polynomial ring then quotient out every monomial with total degree larger than n. However I do not know how to express this ideal.

```
Q = PolynomialRing(QQ, n, 'x')
x = Q.gens()
```

I found a link on this site concerning "set-of-polynomial-under-a-certain-degree" (I cannot post it since I am a new user) which suggests a function `max_degree`

for polynomial rings. However, it seems there is no such a `max_total_degree`

function for the multivariate case.

I am new to python, sage, and this community, so thank you in advance for your helpful suggestions and comments!