2023-05-11 01:50:13 +0200 received badge ● Popular Question (source) 2022-03-15 01:31:33 +0200 received badge ● Editor (source) 2022-03-15 01:31:33 +0200 edited question Coefficients of symmetric polynomials Coefficients of symmetric polynomials Hi everyone, I want to get the coefficients of symmetric polynomials, and then m 2022-03-15 01:24:30 +0200 marked best answer Coefficients of symmetric polynomials Hi everyone, I want to get the coefficients of symmetric polynomials, and then make them a vector. I tried the following code: Sym = SymmetricFunctions(QQ) e = Sym.elementary() g = e[2, 1] - 3*e g.coefficients()  The output is [1, -3], but my desired result is [0, 1, -3], where the zero is the coefficient of e[1, 1, 1]. I found this question get the coefficients from the polynomial, but it seems .coefficients(sparse=False) and .list() only work for the univariate polynomial ring. Thank you in advance for your answer and comments! Edit: I would like to make some clarification about the desired result. What I want is a vector of dimension p(n) where p is the partition function. And each of its components is the coefficient of g under the basis e(part), where part ranges over all the partitions of n. 2022-03-15 01:24:27 +0200 commented answer Coefficients of symmetric polynomials Sorry for the ambiguity in the question, and I would edit it to make it precise. Your answer is exactly what I wanted, t 2022-03-14 17:07:30 +0200 asked a question Coefficients of symmetric polynomials Coefficients of symmetric polynomials Hi everyone, I want to get the coefficients of symmetric polynomials, and then m 2022-03-14 16:50:37 +0200 received badge ● Supporter (source) 2022-03-14 16:50:24 +0200 commented answer Multivariate polynomial ring with total degree no larger than n Thank you very much for your answer! It works fine now. By the way, do you know how to fix this problem under your setti 2022-03-14 16:45:02 +0200 marked best answer 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 at However, 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! 2022-03-14 16:45:02 +0200 received badge ● Scholar (source) 2022-03-13 08:21:33 +0200 commented answer Multivariate polynomial ring with total degree no larger than n P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x^4); f The above cod 2022-03-13 08:21:15 +0200 commented answer Multivariate polynomial ring with total degree no larger than n 'P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x^4); f' The above c 2022-03-13 08:21:08 +0200 commented answer Multivariate polynomial ring with total degree no larger than n P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x^4); f The above cod 2022-03-13 08:20:43 +0200 commented answer Multivariate polynomial ring with total degree no larger than n P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x^4); f 2022-03-13 08:20:27 +0200 commented answer Multivariate polynomial ring with total degree no larger than n P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x^4); f The ab 2022-03-13 08:20:20 +0200 commented answer Multivariate polynomial ring with total degree no larger than n P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x^4); f The above code 2022-03-13 02:11:51 +0200 commented answer Multivariate polynomial ring with total degree no larger than n Thank you for your answer! I tried the following code: Q = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = Q.gens(); 2022-03-13 02:00:57 +0200 commented answer Multivariate polynomial ring with total degree no larger than n Thank you for your answer! I tried the following code: Q = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = Q.gens() f 2022-03-13 01:52:44 +0200 commented question Multivariate polynomial ring with total degree no larger than n Thank you very much for fixing my link and your comment! 2022-03-12 18:09:18 +0200 received badge ● Student (source) 2022-03-12 18:01:24 +0200 asked a question Multivariate polynomial ring with total degree no larger than n Multivariate polynomial ring with total degree no larger than n Hello everyone, I need to compute the product: f(x_1)f(