Polynomials (lib601.poly)

Polynomials with addition, subtraction, multiplication, and roots.

class lib601.poly.Polynomial(c)

Represent polynomials, and supports addition, subtraction, multiplication, and root finding.

Parameters:c – a list of numbers, starting with lowest order coefficient.
Variables:order – Integer representing the order of the polynomial
add(other)
Parameters:other – the instance of Polynomial which we want to add to self
Returns:a new instance of Polynomial, which is the sum of self and other

Does not affect either input.

coeff(i)
Returns:the coefficient associated with the \(x^{\mathtt{i}}\) term of the polynomial
mul(other)
Parameters:other – the instance of Polynomial which we want to multiply by self
Returns:a new instance of Polynomial, which is the product of self and other

Does not affect either input.

roots(start=(0.4+0.9j), epsilon=1e-12, max_iterations=1000)

Computes the roots of the Polynomial using the Durand-Kerner method.

Parameters:
  • start – (optional) seed value, defaults to \(.4+.9j\). Initial guesses for the \(k\) roots are \({\mathtt start}^0, {\mathtt start}^1, \ldots, {\mathtt start}^k\)
  • epsilon – (optional) threshold, defaults to 1e-12. The algorithm terminates (returning the roots) when one iteration changes none of the roots by more than epsilon.
  • max_iterations – (optional) the maximum number of iterations to run, defaults to 1000. If this number of iterations is reached and the algorithm has not converged, it will terminate and return None.
Returns:

A list containing the roots of the polynomial
sub(other)
Parameters:other – the instance of Polynomial which we want to subtract from self
Returns:a new instance of Polynomial, which is the difference of self and other

Does not affect either input.

val(v)
Parameters:v – number
Returns:the value of the polynomial when \(x\) has the value specified by the argument v.