Discussion:
polynomial
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spiny urchin
2015-06-25 20:23:06 UTC
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For starters I attempted to solve the 7th degree polynomial. With
satisfactory results I attempted to solve the 1000th degree and finally the
nth degree polynomial roots. I included a 7th degree example and a start on
the traditional method for solving all of these instances.

In the correct answer to the 7th, dimensional analysis requires these
degrees of coefficients:

7th/7th 6th/6th 5th/5th 4th/4th 3rd/3rd 2nd/2nd 1st/1st

For instance, 1st/1st = a_0/a_7 2nd/2nd = a_1*a_2/a_7^2 and so on.

I used the Quadradic Formula but could have used the Cubic. In the
Quadradic I grouped parts of the full, equated to zero and normalized the
results in nested radicals.
Justin Thyme
2015-06-25 20:27:45 UTC
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Post by spiny urchin
For starters I attempted to solve the 7th degree polynomial. With
satisfactory results
Meaning what by "solve"? Could you demonstrate with a concrete example?
Post by spiny urchin
I attempted to solve the 1000th degree and finally
the nth degree polynomial roots. I included a 7th degree example and a
start on the traditional method for solving all of these instances.
In the correct answer to the 7th, dimensional analysis requires these
7th/7th 6th/6th 5th/5th 4th/4th 3rd/3rd 2nd/2nd 1st/1st
For instance, 1st/1st = a_0/a_7 2nd/2nd = a_1*a_2/a_7^2 and so on.
I used the Quadradic Formula but could have used the Cubic. In the
Quadradic I grouped parts of the full, equated to zero and normalized
the results in nested radicals.
--
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
Justin Thyme
2015-06-25 22:48:09 UTC
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Post by Justin Thyme
Post by spiny urchin
For starters I attempted to solve the 7th degree polynomial. With
satisfactory results
Meaning what by "solve"? Could you demonstrate with a concrete example?
Say x^7 - 28x^6 + 322x^5 - 1960x^4 + 6769x^3 - 13132x^2 + 13068x - 5040
= 0. That looks awful but it's solns are x = 1, 2, 3, 4, 5, 6, 7.
Let's see what your method gets.
Post by Justin Thyme
Post by spiny urchin
I attempted to solve the 1000th degree and finally
the nth degree polynomial roots. I included a 7th degree example and a
start on the traditional method for solving all of these instances.
In the correct answer to the 7th, dimensional analysis requires these
7th/7th 6th/6th 5th/5th 4th/4th 3rd/3rd 2nd/2nd 1st/1st
For instance, 1st/1st = a_0/a_7 2nd/2nd = a_1*a_2/a_7^2 and so on.
I used the Quadradic Formula but could have used the Cubic. In the
Quadradic I grouped parts of the full, equated to zero and normalized
the results in nested radicals.
--
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
Sam Wormley
2015-06-25 23:32:01 UTC
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Post by Justin Thyme
Say x^7 - 28x^6 + 322x^5 - 1960x^4 + 6769x^3 - 13132x^2 + 13068x - 5040
= 0. That looks awful but it's solns are x = 1, 2, 3, 4, 5, 6, 7.
Nice
Post by Justin Thyme
http://www.wolframalpha.com/input/?i=x%5E7+-+28x%5E6+%2B+322x%5E5+-+1960x%5E4+%2B+6769x%5E3+-+13132x%5E2+%2B+13068x+-+5040+%3D+0
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Ross A. Finlayson
2015-07-03 13:13:11 UTC
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Oh, you mean just
solving for integer roots!

Maybe then
solving for real roots, try
solving for rational roots.

Then of course Ruffini-Abel
and etcetera (not all
parametric roots are elementary functions).

Then those solve among the
spaces of those functions,
here for the integer, linear
routine (intractable).

Sam Wormley
2015-06-25 21:03:48 UTC
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Post by spiny urchin
I used the Quadradic Formula but could have used the Cubic. In the
Quadradic I grouped parts of the full, equated to zero and normalized
the results in nested radicals.
http://www.wolframalpha.com/input/?i=a_1x+%2B+a_2x%5E2+%2B+a_3x%5E3++%2B+a_4X%5E4+%2B+a_5x%5E5+%2B+a_6x%5E6+%2B+a_7x%5E7+%3D+0
--
sci.physics is an unmoderated newsgroup dedicated to the discussion
of physics, news from the physics community, and physics-related
social issues.
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