2019-09-09 05:13:23 -0500 | commented answer | Determinants of Matrices with Symmetric Functions Many thanks! Interestingly it seems as though for n = 4 your solution takes an age to finish computing whereas my original solution returns an answer within around 90 minutes (on my not-very-good computer). I'm not sure how much I can really trust my answer though. |

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2019-09-08 10:21:17 -0500 | asked a question | Determinants of Matrices with Symmetric Functions I'm interested in calculating the determinant of the matrix $ A = (a_{i+j})$ for $0\leq i,j\leq n$ in which $a_{k} = \frac{h_k}{e_k}$ where $h_k, e_k$ are the homogeneous (elementary, resp.) symmetric functions of degree $k$. I would like to express the numerator of $\det(A)$ in terms of monomial symmetric functions. I have written some code that I think does the job, but it seems an incredibly hacky way of doing it in my opinion. Since I am quite new to sage I was wondering whether someone might be able to take a look at what I've done and suggest a more sage-like way to tackle this problem? My code is below. I define a set of functions: Then I open sage in the command line and type the following: which returns which I believe is what I'm after. |

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