- #1

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Professor claims there is an algorithm we were supposed to know for this question on the midterm. I missed it. Any ideas?

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- Thread starter math_grl
- Start date

- #1

- 49

- 0

Professor claims there is an algorithm we were supposed to know for this question on the midterm. I missed it. Any ideas?

- #2

- 336

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g can be expressed as required using Newton's formula ; f is not even symmetric.

- #3

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[tex]g = (\sigma_1^2 - 2\sigma_2)\sigma_1 - \sigma_1 \sigma_2 + 3\sigma_3 = \sigma_1^2 - 3\sigma_1 \sigma_2 + 3\sigma_3[/tex]

where the [tex]\sigma_i[/tex]'s are the elementary symmetric polynomials?

just trying to verify that I did it right?

and f is not of the form [tex]\sum^n_{i=1} x_i^k[/tex] for some [tex]k \in \mathbb{N}[/tex] so we can't use newton's formula....but I was wondering one would know precisely that it's not possible to express it in terms of the e.s.p.'s?

- #4

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and f is not of the form [tex]\sum^n_{i=1} x_i^k[/tex] for some [tex]k \in \mathbb{N}[/tex] so we can't use newton's formula....but I was wondering one would know precisely that it's not possible to express it in terms of the e.s.p.'s?

Suppose that f = P(s1,s2,...) is expressible in terms of the e.s.p.'s. P won't change on switching y & z ; f will. A contradiction.

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