- Introduction
- Newton Polygons
- Creation of Newton Polygons
- Vertices and Faces of Polygons
- Tests for Points and Faces
- IsFace(N, F) : NwtnPgon,Tup -> BoolElt
- IsVertex(N, p) : NwtnPgon,Tup -> BoolElt
- IsInterior(N,p) : NwtnPgon,Tup -> BoolElt
- IsBoundary(N, p) : NwtnPgon,Tup -> BoolElt
- IsPoint(N,p) : NwtnPgon,Tup -> BoolElt
- Polynomials Associated with Newton Polygons
- Finding Valuations of Roots of Polynomials from Newton Polygons
- Using Newton Polygons to Find Roots of Polynomials over Series Rings
- SetVerbose("Newton", v) : MonStgElt, RngIntElt ->
- Operations not associated with Duval's Algorithm
- PuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum[RngSerPuisElt]
- ExpandToPrecision(f, c, n) : RngUPolElt, RngSerElt, RngIntElt -> RngSerElt
- ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt
- Example Newton_poly-ops-ex (H55E6)
- IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
- IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
- Example Newton_pol-is (H55E7)
- PuiseuxExponents(p) : RngSerElt -> SeqEnum
- PuiseuxExponentsCommon(p, q) : RngSerElt, RngSerElt -> SeqEnum
- Example Newton_exps (H55E8)
- Operations associated with Duval's algorithm
- Roots of Polynomials
- Bibliography
V2.28, 13 July 2023