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(Free42, DM42, HP42S): Polynomial Solver
03-21-2022, 02:29 PM
Post: #4
RE: (Free42, DM42, HP42S): Polynomial Solver
(03-21-2022 11:37 AM)Namir Wrote:  This is a Shammas Polynomial
Of course, you are free to name a class of functions whatever you want.
But if a common mathematical term like polynomial is used, people will likely assume that Shammas Polynomials are a special kind of polynomial.

And with that, they will assume that these functions have the same properties.

For example that \(f: \mathbb{R} \to \mathbb{R}\)
However, for \(f(x) = x^\tfrac{1}{2}\) this is not the case since the square root for negative numbers is undefined.

Or then that \(f\) is differentiable on \(\mathbb{R}\) which is also not the case for \(f(x) = x^\tfrac{1}{2}\) at \(x = 0\).

Also that polynomials compose, which means that the composition of a polynomial with another polynomial is again a polynomial.
But this is not the case either, e.g. for:
\(
f(x) = (1 + x)^\frac{1}{2}
\)

However, if you call \(x^\tfrac{1}{2}\) a polynomial, it's just plain wrong.
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RE: (Free42, DM42, HP42S): Polynomial Solver - Thomas Klemm - 03-21-2022 02:29 PM



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