# 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 suggestion to use a function

`max_degree`

for polynomial rings atHowever, it seems there is no

`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!

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