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  • An '''elementary symmetric sum''' is a type of [[summation]]. The <math>k</math>-th '''elementary symmetric sum''' of a [[set]] of <math>n</math> numbers is the sum of all products of
    2 KB (275 words) - 11:51, 26 July 2023
  • ** [[Elementary symmetric polynomial]] ** [[Newton's Sums]]
    2 KB (198 words) - 15:06, 7 December 2024
  • '''Newton sums''' give us a clever and efficient way of finding the sums of [[root]]s of a [[polynomial]] raised to a power. They can also be used Newton's sums tell us that,
    4 KB (704 words) - 07:28, 24 November 2024
  • ..._3\zeta_1,\ e_3 = \zeta_1\zeta_2\zeta_3</math> (the [[elementary symmetric sums]]). Then, we can rewrite the above equations as Let <math>s_n = \zeta_1^n + \zeta_2^n + \zeta_3^n</math> (the [[power sums]]). Then from <math>(1)</math>, we have the [[recursion]] <math>s_{n+3} = s
    2 KB (221 words) - 01:49, 19 March 2015
  • The '''symmetric sum''' <math>\sum_{\rm sym} f(x_1, x_2, x_3, \dots, x_n)</math> of a funct More generally, a '''symmetric sum''' of <math>n</math> variables is a sum that is unchanged by any [[perm
    1 KB (255 words) - 11:52, 8 October 2023
  • We recall the factorization (see [[elementary symmetric sum]]s)
    881 bytes (134 words) - 13:36, 5 July 2013
  • So now we have three equations for the elementary symmetric sums of <math>x,y,z</math>: [[Newton's Sums]]
    5 KB (888 words) - 07:18, 22 April 2024
  • ...ynomials]] <math>abc, ab+bc+ca, a+b+c</math>. In general, prove [[Newton's sums]].
    19 KB (3,412 words) - 13:57, 21 September 2022
  • We can use Newton Sums to solve this problem. ...sum (<math>x^n + y^n</math>). Using this, we can make the following Newton sums:
    13 KB (2,264 words) - 23:27, 19 September 2024
  • ...ond equation <math>ab+bc+ca=183</math>. Then with the elementary symmetric sums with three variables, their solutions are the solutions to the cubic <math>
    734 bytes (118 words) - 22:28, 8 April 2024