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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.

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

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

   • Ask Sage question 55842: Set of polynomials under a certain degree

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

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