2021-12-25 02:00:02 +0200 received badge ● Notable Question (source) 2021-09-27 03:04:14 +0200 received badge ● Popular Question (source) 2021-05-13 15:46:15 +0200 received badge ● Popular Question (source) 2020-07-19 20:24:44 +0200 received badge ● Scholar (source) 2020-07-19 20:24:32 +0200 received badge ● Supporter (source) 2020-07-19 18:21:45 +0200 asked a question What are these extra terms in symmetric polynomial calculations? I am trying to calculate the discriminant of the cubic using symmetric polynomials, here is my attempt: P = PolynomialRing(QQ, 'x', 3) x = P.gens() S = SymmetricFunctions(QQ) e = SymmetricFunctions(QQ).e() def nice_symmetric_poly(coeffs, u): v = var(coeffs) return sum(x[1]*product(v[i] for i in x[0]) for x in list(u)) d = (x[0]-x[1])*(x[0]-x[2])*(x[1]-x[2]) u = e.from_polynomial(d^2) nice_symmetric_poly('a b c d e', u)  This gives me u: e[2, 2, 1, 1] - 4*e[2, 2, 2] - 4*e[3, 1, 1, 1] + 18*e[3, 2, 1] - 27*e[3, 3] - 8*e[4, 1, 1] + 24*e[4, 2]  and the nice polynomial version: b^2*c^2 - 4*b^3*d - 4*c^3 + 18*b*c*d - 8*b^2*e - 27*d^2 + 24*c*e  but I was expecting the result from here https://www.johndcook.com/blog/2019/0... Δ = 18bcd – 4b³d + b²c² – 4c³ – 27d².  I don't understand why these "e" terms exist: - 8b^2e + 24ce and why is there anything with a e[4] in it inside u. Thank you for any insight into this problem. 2020-07-18 21:22:37 +0200 asked a question How to calculate discriminant using symmetric polynomials? I want to calculate discriminants using symmetric polynomials. I am working on the quadratic discriminant first. Here is my attempt: P.=PolynomialRing(QQ) S=SymmetricFunctions(P.base_ring()) e = S.elementary() e(S.from_polynomial((x1-x2)^2))  this produces e[1, 1] - 4*e[2]  How can I convert this output to b^2 - 4 * a * c? Thank you 2020-06-15 16:18:45 +0200 received badge ● Student (source) 2020-06-14 05:10:55 +0200 asked a question Why is Galois group computation failing? L = NumberField(x^2 - x - 1, 'theta') G = L.galois_group()  works L = NumberField(x^3 - x - 1, 'theta') G = L.galois_group()  gives me the error TypeError: You must specify the name of the generator.