Newton Polygons

• Construction of a newton polygon: Compact, infinite or including the origin
• Construction of newton polygons from different types of data: $f \in k[x,y]$, $f \in k\left<\!\left<x\right>\!\right>[y]$, a finite set of points; a finite set of faces (weighted dual vectors)
• Finding faces and vertices
• If polygon is derived from a polynomial f, finding restrictions of f to faces
• Locating a given point relative to a newton polygon
• Determining whether a given line supports a face
• Determining whether two polygons are the same