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

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

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 )

Solve cubic equation in monic form.

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 )

Solve quadratic equation in monic form.

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 )

Solve quartic equation in monic form.

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