Polynomial.Hypersurface

Documentation

type Polygon = [Point2D]

The tropical hypersurface of a polynomial f is the n-1 skeleton of the Newton polyotpe of f with a regular subdivision induced by a vector w in R^n. The hypersurface will be stored as a set of points.

type Normals = [Point2D]

mapTermPoint :: (IsMonomialOrder ord, Ord k, Integral k) => Polynomial k ord n -> Map Point2D (Monomial ord n, k)

This function produces a key-value map of the terms of a polynomial with their corresponding coordinates for the Newton polytope

computeIntersection :: Integral k => (Monomial ord n, k) -> (Monomial ord n, k) -> (Monomial ord n, k) -> Point2D

Finds the vertex of a tropical line which corresponds to the intersection of the polyhedral fan of a triangle. The output is the result of the systems of equations given by: ax + by +c = 0; dx + ey f = 0; gx + hy + i = 0.

findFanNVertex :: Integral k => Map Point2D (Monomial ord n, k) -> Polygon -> (Point2D, Normals)

findPolygonNVertex :: Integral k => Map Point2D (Monomial ord n, k) -> Polygon -> (Polygon, Point2D)

innerNormal :: Point2D -> Point2D -> Point2D -> Point2D

innerNormals :: Point2D -> Point2D -> Point2D -> Normals

verticesNormals :: (IsMonomialOrder ord, Ord k, Integral k) => Polynomial k ord n -> Map Point2D Normals

neighborTriangles :: [Polygon] -> Map Polygon [Polygon] -> Map Polygon [Polygon]

pointsWithTriangles :: (IsMonomialOrder ord, Ord k, Integral k) => Polynomial k ord n -> Map Polygon Point2D

polygonCenter :: Map Polygon Point2D -> Polygon -> Point2D

convertMap :: Map Polygon [Polygon] -> Map Polygon Point2D -> Map Point2D [Point2D]

computeEdges :: Map Point2D [Point2D] -> Map Point2D Normals -> [(Point2D, Point2D)]

isInverse :: Point2D -> Point2D -> Point2D -> Point2D -> Bool

analizeNormals :: (Point2D, Normals) -> (Point2D, Normals) -> ((Point2D, Normals), (Point2D, Point2D))

hypersurface :: (IsMonomialOrder ord, Ord k, Integral k) => Polynomial k ord n -> [(Point2D, Point2D)]