“Reverse” Vieta's Formulas
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In one of my investigations, I needed to figure out sums of powers of roots of polynomial equations. These are not very hard to figure out. For monic polynomials, the first three sums are:
Sum of roots: -a_{n-1}
Sum of squares: a_{n-1}²-2a_{n-2}
Sum of cubes: -a_{n-1}³+3a_{n-1}a_{n-2}-3a_{n-3}
Would anyone have a reference where all of these formulas can be found? Do you know of any applications that these formulas have?
polynomials roots symmetric-polynomials
asked Dec 4 '18 at 1:17
LemmaLemma
63529
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add a comment |
$begingroup$
In one of my investigations, I needed to figure out sums of powers of roots of polynomial equations. These are not very hard to figure out. For monic polynomials, the first three sums are:
Sum of roots: -a_{n-1}
Sum of squares: a_{n-1}²-2a_{n-2}
Sum of cubes: -a_{n-1}³+3a_{n-1}a_{n-2}-3a_{n-3}
Would anyone have a reference where all of these formulas can be found? Do you know of any applications that these formulas have?
polynomials roots symmetric-polynomials
asked Dec 4 '18 at 1:17
LemmaLemma
63529
$endgroup$
1
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
1
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24
add a comment |
$begingroup$
In one of my investigations, I needed to figure out sums of powers of roots of polynomial equations. These are not very hard to figure out. For monic polynomials, the first three sums are:
Sum of roots: -a_{n-1}
Sum of squares: a_{n-1}²-2a_{n-2}
Sum of cubes: -a_{n-1}³+3a_{n-1}a_{n-2}-3a_{n-3}
Would anyone have a reference where all of these formulas can be found? Do you know of any applications that these formulas have?
polynomials roots symmetric-polynomials
asked Dec 4 '18 at 1:17
LemmaLemma
63529
$endgroup$
In one of my investigations, I needed to figure out sums of powers of roots of polynomial equations. These are not very hard to figure out. For monic polynomials, the first three sums are:
Sum of roots: -a_{n-1}
Sum of squares: a_{n-1}²-2a_{n-2}
Sum of cubes: -a_{n-1}³+3a_{n-1}a_{n-2}-3a_{n-3}
Would anyone have a reference where all of these formulas can be found? Do you know of any applications that these formulas have?
polynomials roots symmetric-polynomials
polynomials roots symmetric-polynomials
asked Dec 4 '18 at 1:17
LemmaLemma
63529
asked Dec 4 '18 at 1:17
LemmaLemma
63529
asked Dec 4 '18 at 1:17
LemmaLemma
63529
asked Dec 4 '18 at 1:17
LemmaLemma
63529
asked Dec 4 '18 at 1:17
LemmaLemma
63529
63529
1
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
1
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24
add a comment |
1
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
1
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24
1
1
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
1
1
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24
add a comment |
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1
$begingroup$
en.wikipedia.org/wiki/…
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 1:24
1
$begingroup$
I think you'll find what you need in this
$endgroup$
– EvanHehehe
Dec 4 '18 at 1:24