Polynomial real roots

Tools to compute the real roots of quadratic, cubic, and quartic polynomials. More...

Functions/Subroutines
pure subroutine, public	mod_polynomial_real_roots::solve_quadratic (a, b, x, n_roots)
	Solve quadratic equation in monic form.
pure subroutine, public	mod_polynomial_real_roots::solve_cubic (a, b, c, x, n_roots)
	Solve cubic equation in monic form.
pure subroutine, public	mod_polynomial_real_roots::solve_quartic (a, b, c, d, x, n_roots)
	Solve quartic equation in monic form.

Detailed Description

The equations must be represented in the monic form, that is the leading coefficient of the polynomial is equal to 1:

\[ x^n + a_{n-1} x^{n-1} + \cdots + a_0 = 0 \]

The coefficients must be real numbers.

Function/Subroutine Documentation

solve_cubic()

pure subroutine, public mod_polynomial_real_roots::solve_cubic	(	double precision, intent(in)	a,
		double precision, intent(in)	b,
		double precision, intent(in)	c,
		double precision, dimension(3), intent(out)	x,
		integer, intent(out)	n_roots )

The cubic equation to solve must be in the form:

\[ x^3 + ax^2 + bx + c = 0 \]

Parameters

[in]	a,b,c	Coefficients of the third order polynomial in monic form.
[out]	x	The three real roots.
[out]	n_roots	Number of real roots.

solve_quadratic()

pure subroutine, public mod_polynomial_real_roots::solve_quadratic	(	double precision, intent(in)	a,
		double precision, intent(in)	b,
		double precision, dimension(2), intent(out)	x,
		integer, intent(out)	n_roots )

The quadratic equation to solve must be in the form:

\[ x^2 + ax + b = 0 \]

Parameters

[in]	a,b	Coefficients of the second order polynomial in monic form.
[out]	x	Real roots of the polynomial.
[out]	n_roots	Number of real roots.

solve_quartic()

pure subroutine, public mod_polynomial_real_roots::solve_quartic	(	double precision, intent(in)	a,
		double precision, intent(in)	b,
		double precision, intent(in)	c,
		double precision, intent(in)	d,
		double precision, dimension(4), intent(out)	x,
		integer, intent(out)	n_roots )

The quartic equation to solve must be in the form:

\[ x^4 + ax^3 + bx^2 + cx + d = 0 \]

Parameters

[in]	a,b,c,d	Coefficients of the fourth order polynomial in monic form.
[out]	x	The four real roots.
[out]	n_roots	Number of roots