Polynomial Roots

[Jon]

http://jons-math.bravehost.com/nthdegree.html

In n dimensions you can pick and choose which 3D slice to make a
calculation, but ultimately a point in n-space requires n mutually
orthogonal vectors to construct that point.

I have provided the basis for the n-degree case, but due to the
incorporation of a normal vector that has components from all n dimensions,
it depreciates the required n vectors to only 3.

If the signs on the coefficients of a polynomial are changed, the resulting
roots are different. This observation leaves me skeptical that I have
arrived at a solution, but if the full battery of basis components are
carried out, this doubt is unjustified and the solution more complicated.

Why would anyone want to know the roots to a polynomial or to a power
series?

Because Progress demands it.

[Virgil]

Post by Jon
In n dimensions you can pick and choose which 3D slice to make a
calculation, but ultimately a point in n-space requires n mutually
orthogonal vectors to construct that point.

While it may requires an independent set of n vectors to construct an
arbitrary point in a n-dimensional vector space, nothing requires them
to be orthogonal, they can merely be independent.

And unless your space has a well-defined inner product on it, there may
not even be identifiably orthogonal vectors in it.