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### 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.

1. 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()

2. 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. 2 None

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

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

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

2. 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 suggestion to use a function max_degree for polynomial rings. rings at

However, it seems there is no such a max_total_degree function for the multivariate case.