Copyright | (c) Maciej Bendkowski 2017-2018 |
---|---|

License | BSD3 |

Maintainer | maciej.bendkowski@tcs.uj.edu.pl |

Stability | experimental |

Safe Haskell | None |

Language | Haskell2010 |

The following module implements subroutines for combinatorial systems based on the excellent paper of Carine Pivoteau, Bruno Salvy, and Michèle Soria:

Algorithms for combinatorial structures: Well-founded systems and Newton iterations. Journal of Combinatorial Theory, Series A 119 (2012) p. 1711–1773.

- isEmptyAtZero :: (Eq a, Num a) => System a -> Bool
- zeroCoordinates :: System a -> Bool
- wellFoundedAtZero :: (Eq a, Num a) => System a -> Bool

# Documentation

isEmptyAtZero :: (Eq a, Num a) => System a -> Bool Source #

Evaluates the given system Y = H(Z, Y) at coordinates Z = 0 and Y = 0 and checks if the outcome system is empty, i.e. H(0, 0) = 0 or not.

zeroCoordinates :: System a -> Bool Source #

Detects whether the given system, satisfying H(0,0) = 0 and having a nilpotent Jacobian matrix, admits zero coordinates in its solution. See also the 0-coord subroutine of Pivoteau et al.