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Coefficients of symmetric polynomials Hi everyone, I want to get the coefficients of symmetric polynomials, and then m

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[3]
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.

Sorry for the ambiguity in the question, and I would edit it to make it precise. Your answer is exactly what I wanted, t

Coefficients of symmetric polynomials Hi everyone, I want to get the coefficients of symmetric polynomials, and then m

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

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 suggestion to use a function max_degree for polynomial rings at

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

   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!

P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x[0]^4); f The above cod

'P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x[0]^4); f' The above c

P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = [g.add_bigoh(3) for g in P.gens()]; f=P(x[0]^4); f The above cod

P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x[0]^4); f

P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x[0]^4); f The ab

P = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = [g.add_bigoh(3) for g in P.gens()] f=P(x[0]^4); f The above code

Thank you for your answer! I tried the following code: Q = PowerSeriesRing(QQ, 3, 'x', default_prec = 3); x = Q.gens();

Thank you for your answer! I tried the following code: Q = PowerSeriesRing(QQ, 3, 'x', default_prec = 3) x = Q.gens() f

Thank you very much for fixing my link and your comment!

Multivariate polynomial ring with total degree no larger than n Hello everyone, I need to compute the product: f(x_1)f(