ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 22 Apr 2021 17:52:13 +0200Obtaining the immanent associated to a partitionhttps://ask.sagemath.org/question/56771/obtaining-the-immanent-associated-to-a-partition/For a partition $\lambda$ let $y_{\lambda}$ be the corresponding irreducible representation of the symmetric group $S_n$.
Let $p_{\lambda}=\sum\limits_{\pi \in S_n}^{}{y_\lambda( \pi) x_{1 \pi(1)} ... x_{n \pi(n)}}$ be the immanent corresponding to $\lambda$. (For the sign representation we will just get the determinant for example).
This is a polynomial in the $n^2$ variables $x_{i,j}$ over $\mathbb{Z}$.
My question is how can I obtain the immanent given a parition $\lambda$ using Sage?
My first problem is already that we need the polynomial ring in the $n^2$ variables $x_{i,j}$ and I am not sure how to define this in Sage depending on $n$.klaaaThu, 22 Apr 2021 17:52:13 +0200https://ask.sagemath.org/question/56771/how to check if a polynom is a squarehttps://ask.sagemath.org/question/50825/how-to-check-if-a-polynom-is-a-square/ I'ld like to put a condition in a programm that looks like:
"if Q is a square, then ..."
Q being a polynom (in GF(p)).
How can I do that ?DasiatysFri, 17 Apr 2020 23:32:38 +0200https://ask.sagemath.org/question/50825/Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.https://ask.sagemath.org/question/47267/define-the-polynomial-ring-bbb-qcxfind-the-c-values-where-x2-x-c-1-has-a-double-root/ **Sage question:**
Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.
Sage code I have found.
K.<c>=QQ['c']
R.<x>=K[]
f=x^2+x+c+1
f
How do I find the code for the $c$ values where $x^2 + x + c + 1$ has a double root. Also, can you give some examples so that I can construct some programming code in sage?
ArnabThu, 25 Jul 2019 15:00:01 +0200https://ask.sagemath.org/question/47267/is_polynomial with symbolic coefficients: bug ?https://ask.sagemath.org/question/10621/is_polynomial-with-symbolic-coefficients-bug/sage: s, a, b= var('s a b')
sage: (1/s^2 + s).is_polynomial(s)
False
sage: (a/s^2 + b*s).is_polynomial(s)
True
Should the second call of is_polynomial not return False as in the first case ?
Is this a bug ?
Who and howto report ?alessandroThu, 17 Oct 2013 16:50:31 +0200https://ask.sagemath.org/question/10621/