Discussion:
roots to power series
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spiny urchin
2015-07-03 19:52:41 UTC
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I have added several more gif images at the end of my web page,

http://www.stonetabernacle.com/7th-degree-root.html

for anyone interested. This treats the 7th, 25th, 1000th and nth degree
polynomials, their solutions and how to arrive at them.
Justin Thyme
2015-07-04 08:39:42 UTC
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Post by spiny urchin
I have added several more gif images at the end of my web page,
http://www.stonetabernacle.com/7th-degree-root.html
for anyone interested. This treats the 7th, 25th, 1000th and nth degree
polynomials, their solutions and how to arrive at them.
Could you demonstrate with a concrete example, say x^7 - 28x^6 + 322x^5
- 1960x^4 + 6769x^3 - 13132x^2 + 13068x - 5040 = 0? The solutions are
known, let's see what your method gets.

A minor point: polynomials and power series are not the same.
--
Shall we only threaten and be angry for an hour?
When the storm is ended shall we find
How softly but how swiftly they have sidled back to power
By the favour and contrivance of their kind?

From /Mesopotamia/ by Rudyard Kipling
IV
2015-07-04 10:58:03 UTC
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Post by spiny urchin
http://www.stonetabernacle.com/7th-degree-root.html
for anyone interested. This treats the 7th, 25th, 1000th and nth degree
polynomials, their solutions and how to arrive at them.
I assume:
Each fractional equation can be transformed into a polynomial equation by
repeated isolation of a single fractional term at one side of the equation
and mutiplying the equation by the denominator of the isolated fractional
term.
Each root equation can be transformed into a polynomial equation by repeated
isolation of a single root term at one side of the equation and mutiplying
the equation by the denominator of the exponent of the isolated root term.

The coefficients of the resulting polynomial equation can in general be
symbolically written in terms of Bell polynomials with the help of the
multinomial coefficients. The Bell polynomials are partion polynomials. That
means, they describe the numbers and types of integer partitions and set
partitions.
IV
2015-07-04 11:31:09 UTC
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Post by IV
root equation
...
and mutiplying the equation by the denominator of the exponent of
the isolated root term.
Correction:
and raising the equation to a power that is the denominator of the exponent
of the isolated root term.

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