Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/AlgebraicHaplo.R

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.

1 |

`A` |
The coefficient of x^3. |

`B` |
The coefficient of x^2. |

`C` |
The coefficient of X. |

`D` |
The constant. |

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.

Returns `cubic`

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

Using cardenian formular, a well known method.

Jan Wolfertz

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

haplotypeit,callhaplotype

1 2 |

```
[1] 1.0+0.0000000i -0.5+0.8660254i -0.5-0.8660254i
[1] 0e+00-2.419647e-09i -1e+00+0.000000e+00i 0e+00+2.419647e-09i
```

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