# cubic: Function that can resolve the cubic equation numerical stable... In AlgebraicHaploPackage: Haplotype Two Snips Out of a Paired Group of Patients

## Description

A*x^3+B*x^2+C*x+D=0. All coefficients had to be numeric or integers. This function calculates from 4 coefficient all possible and senfully solutions. D=0 returns no values at all. This would be a impossibel case. It returns upto 3 potential complex solutions. Less solutions are copied to get the tripple solution format.

## Usage

 `1` ```cubic(A, B, C, D) ```

## Arguments

 `A` The coefficient of x^3. `B` The coefficient of x^2. `C` The coefficient of X. `D` The constant.

## Details

This function is called by haplotypeit. The results are returned as vector of the three possible solutions: output[1],output[2],output[3]. Further data for checks of the roots. p,q and the discriminat. 10 and 11 are only usable for symmetry checks.

## Value

Returns `cubic`(A,B,C,D)[c(1:3)] roots of the at most cubic equation.

## Note

Using cardenian formular, a well known method.

Jan Wolfertz

## References

Cardans formular as in e.g. The Mathematical Gazette (1993); 77 (Nov, No 480), 354-359 (jstor) http://www.nickalls.org/dick/papers/maths/cubic1993.pdf or any other book for algebraic solutions. See also : http://de.wikipedia.org/wiki/Cardanische_Formeln and http://en.wikipedia.org/wiki/Cubic_equation

 ```1 2``` ```cubic(1,0,0,-1)[c(1:3)] cubic(1,1,0,0)[c(1:3)] ```