Polynomials: Relationship between roots and coefficients

[@hyperduality2838]

Roots are dual to coefficients -- symmetric polynomials.
Subgroups (quantum, discrete) are dual to subfields (classical, continuous) -- the Galois Correspondence.
The size of a Galois group measures how symmetric a polynomial is.
Highly symmetric polynomials have large Galois groups!
Injective is dual to surjective synthesizes bijective or isomorphism.
Symmetry is dual to conservation (invariance) -- the duality of Noether's theorem.
"Always two there are" -- Yoda.

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