feat: the Chebyshev polynomials C and S

[trivial1711]

We define the rescaled Chebyshev polynomials $C_n$ and $S_n$ (also known as the Vieta–Lucas and Vieta–Fibonacci polynomials, respectively). They are related to the Chebyshev polynomials $T_n$ and $U_n$ by the formulas $C_n(2x) = 2T_n(x)$ and $S_n(2x) = U_n(x)$. Most theorems about $T_n$ and $U_n$ have analogues involving $C_n$ and $S_n$.

We prove that $C_n$ and $S_n$ are special cases of the Dickson polynomials (though unlike general Dickson polynomials, they are defined for every integer $n$, not just natural numbers).

These polynomials are necessary to state a formula for $(r_1 r_2)^m v$, where $v \in V$ is an element of a module, $r_1, r_2 \in GL(V)$ are reflections, and $m$ is an integer. The formula will be used to define and construct reflection representations of a Coxeter group over an arbitrary commutative ring, not necessarily having an invertible 2. See #13291.

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• [x] depends on: #13133