Struct Pol

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pub struct Pol<T> { /* private fields */ }

Expand description

polynomial, coefficients are listed from lowest to highest power

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impl<T> Pol<T>

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pub fn new(coef: Vec<Complex<T>>) -> Self

construct polynomial from vector of coefficients

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pub fn eval(&self, z: Complex<T>) -> Complex<T>
where T: Clone + Num,

evaluate the polynomial at point z

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pub fn diff(&self) -> Pol<T>
where T: From<u32>, Complex<T>: Clone + Mul<T, Output = Complex<T>>,

the general derivative of the polynomial, symbolic

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pub fn integrate(&self, c: Complex<T>) -> Pol<T>
where T: From<u32>, Complex<T>: Clone + Div<T, Output = Complex<T>>,

the general antiderivative of the polynomial, symbolic, with constant term c

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pub fn roots(&self, n: usize, m: usize, r_coef: T, eps: T) -> Vec<Complex<T>>
where T: Clone + Num + Neg + Float + Send + Sync + From<u32> + From<f64>, Complex<T>: Mul<Complex<T>, Output = Complex<T>> + Div<Complex<T>, Output = Complex<T>> + Mul<T, Output = Complex<T>> + Div<T, Output = Complex<T>> + From<T>,

attempt to find all the complex roots of the polynomial with radii n * its degree, maximum iterations of newton’s method m, coefficient of rounding for eliminating identical solutions r_coef, and eps, passed to sampling and newton’s method, and used for rounding a degree k polynomial will have k roots (although they may be the same) and is not trivially solved differentiating this a times will yield a polynomial with k - a roots if k - a = 1 or 2, this can be trivially solved for its zeros the zeros of the derivative of a polynomial lie inside the convex hull of its zeros by the Gauss-Lucas theorem therefore, we begin newton’s method at the points of the derivative’s zeros radiating out to attempt to land initial points in the basins of convergence of every root