Chebyshev.h

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#pragma once
 
#include "../UnivariatePolynomial.h"
#include <carl-arith/core/Variable.h>
 
namespace carl {
 
/**
 * Implements a generator for Chebyshev polynomials.
 */
template<typename Number>
struct Chebyshev {
    Variable mVar;
    explicit Chebyshev(Variable v): mVar(v) {}
 
    UnivariatePolynomial<Number> operator()(std::size_t n) const {
        UnivariatePolynomial<Number> t0(mVar, Number(1), 0);
        if (n == 0) return t0;
        UnivariatePolynomial<Number> t1(mVar, Number(1), 1);
        if (n == 1) return t1;
        UnivariatePolynomial<Number> twox(mVar, Number(2), 1);
        while (n >= 2) {
            UnivariatePolynomial<Number> tn = twox * t1 - t0;
            if (n == 2) return tn;
            t0 = t1;
            t1 = tn;
            --n;
        }
        assert(false);
        return t0;
    }
};
 
}