#ompy.cubic

[ompy]

Cubic equations

This article summarizes the theory behind the concepts represented in the module ompy.cubic, explained in post /documentation-ii.

[ompy]

Documentation II

Full documentation can be found on https://ompy.tumblr.com/documentation

cubic

Analysis for cubic equations (for now, to be developed).

cbrt(radicand)       Calculates the real cubic root -principal value- of rational representations of real numbers.

      Parameters: radicand: int, float; required.       Number to take the root of.

      Returns: float; cubic root.

      Examples:

>>> import ompy.cubic as cb >>> cb.cbrt(216) 6.0 >>> cb.cbrt(-27.0) -3.0 >>> cb.cbrt(10) 2.154434690032

to_depressed(a, b, c, d)       Transforms a general cubic equation to a depressed cubic equation. It takes general equation coefficients 'a', 'b', 'c', 'd' and returns depressed equation coeffcients 'p', 'q'.

      Parameters: a: int, float; required (it cannot be 0).

                          b: int, float; required.

                          c: int, float; required.

                          d: int, float; required.

      Returns: tuple. 

                          [0]: coefficient 'p'.

                          [1]: coefficient 'q'.

      Examples:

>>> import ompy.cubic as cb >>> cb.to_depressed(1, -3, -3, 1) (-6.0, -4.0) >>> cb.to_depressed(1, 1, 1, 1) (0.6666666666666667, 0.7407407407407407) >>> cb.to_depressed(1, 0, 2, 3) (2.0, 3.0) >>> cb.to_depressed(2, 0, 0, 0) (0.0, 0.0)

cbdelta(p, q)       Calculates the cubic discriminant (delta) for a depressed cubic equation

      Parameters: p: int, float; required. Coefficient 'p' from depressed equation.

                          q: int, float; required. Coefficient 'q' from depressed equation.

      Returns: float. Cubic delta number.

      Examples:

>>> import ompy.cubic as cb >>> cb.cbdelta(3, 4) 20.0 >>> cb.cbdelta(-3, -2) 0.0 >>> cb.delta(5.55555, -4.44444) -5.6495085912265

depressed_roots(p, q)       For depressed cubic equations returns a tuple with its roots.

      Parameters: p: int, float; required.       Coefficient 'p' from depressed equation.

                          q: int, float; required.       Coefficient 'q' from depressed equation.

      Returns: tuple; equation roots.

             [0] : str; first root, represents a real number.              [1] : str; second root, represents a real or complex number.              [2] : str; third root, represents a real or complex number.\

      Examples:

>>> import ompy.cubic as cb >>> cb.depressed_roots(-3, -2) ('2.0', '-1.0', '-1.0') >>> cb.depressed_roots(1, 0) ('0.0', '-0.0 + 1.0i', '-0.0 - 1.0i') >>> cb.depressed_roots(0, 1) ('-1.0', '0.5 + 0.86602540378i', '0.5 - 0.86602540378i') >>> cb.depressed_roots(1.11111, 2.22222) ('-1.02650941551', '0.513254707755 + 1.37891304479i', '0.513254707755 - 1.37891304479i')

roots(a, b, c, d)       Calculates cubic general equations roots.

      Parameters: a: int, float; required (it cannot be 0).       Equation coefficient 'a'.

                          b: int, float; required.       Equation coefficient 'b'.

                          c: int, float; required.       Equation coefficient 'c'.

                          d: int, float; required.       Equation coefficient 'd'.

      Returns: tuple; equation roots.

             [0] : str; first root, represents a real number.              [1] : str; second root, represents a real or complex number.              [2] : str; third root, represents a real or complex number.

      Examples:

>>> import ompy.cubic as cb >>> cb.roots(1, -15, 75, -125) ('5.0', '5.0', '5.0') >>> cb.roots(2, -3, -11, 6) ('3.0', '-2.0', '0.5') >>> cb.roots(1, 2, 3, 4) ('-1.6506291914', '-0.1746854043 + 1.5468688872i', '-0.1746854043 - 1.5468688872i') >>> cb.roots(3, 0, 0, 0) (0.0, 0.0, 0.0)