Creation of Newton Polygons
NewtonPolygon(f) : RngMPolElt -> NwtnPgon
NewtonPolygon(f) : RngUPolElt -> NwtnPgon
NewtonPolygon(f, p) : RngUPolElt, RngOrdIdl -> NwtnPgon
NewtonPolygon(f, p) : RngUPolElt, PlcFunElt -> NwtnPgon
NewtonPolygon(C) : Crv -> NwtnPgon
NewtonPolygon(V) : SeqEnum -> NwtnPgon
DefiningPoints(N) : NwtnPgon -> SeqEnum
Example Newton_create-ex (H46E1)
Vertices and Faces of Polygons
Faces(N) : NwtnPgon -> SeqEnum
InnerFaces(N) : NwtnPgon -> SeqEnum
LowerFaces(N) : NwtnPgon -> SeqEnum
OuterFaces(N) : NwtnPgon -> SeqEnum
AllFaces(N) : NwtnPgon -> SeqEnum
Example Newton_faces-ex (H46E2)
Vertices(N) : NwtnPgon -> SeqEnum
InnerVertices(N) : NwtnPgon -> SeqEnum
LowerVertices(N) : NwtnPgon -> SeqEnum
OuterVertices(N) : NwtnPgon -> SeqEnum
AllVertices(N) : NwtnPgon -> SeqEnum
Example Newton_vertices-ex (H46E3)
EndVertices(F) : NwtnPgonFace -> SeqEnum
FacesContaining(N,p) : NwtnPgon,Tup -> SeqEnum
Example Newton_sp-vertices-ex (H46E4)
GradientVector(F) : NwtnPgonFace -> Tup
GradientVectors(N) : NwtnPgon -> [ Tup ]
Weight(F) : NwtnPgonFace -> RngIntElt
Slopes(N) : NwtnPgon -> SeqEnum
InnerSlopes(N) : NwtnPgon -> SeqEnum
Example Newton_grad-ex (H46E5)
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
HasPolynomial(N) : NwtnPgon -> BoolElt
Polynomial(N) : NwtnPgon -> RngElt
ParentRing(N) : NwtnPgon -> Rng
IsNewtonPolygonOf(N, f) : NwtnPgon, RngElt -> BoolElt
FaceFunction(F) : NwtnPgonFace -> RngElt
IsDegenerate(F) : NwtnPgonFace -> BoolElt
IsDegenerate(N) : NwtnPgon -> BoolElt
Finding Valuations of Roots of Polynomials from Newton Polygons
ValuationsOfRoots(f) : RngUPolElt -> [ < RngIntElt, RngIntElt > ]
ValuationsOfRoots(f, p) : RngUPolElt, RngIntElt -> [ < RngIntElt, RngIntElt > ]
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 (H46E6)
IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
Example Newton_pol-is (H46E7)
PuiseuxExponents(p) : RngSerElt -> SeqEnum
PuiseuxExponentsCommon(p, q) : RngSerElt, RngSerElt -> SeqEnum
Example Newton_exps (H46E8)
Operations associated with Duval's algorithm
DuvalPuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum
ParametrizationToPuiseux(T) : Tup -> SeqEnum
PuiseuxToParametrization(S) : RngSerElt -> Tup
Example Newton_duval-ex (H46E9)
Roots of Polynomials
Roots(f) : RngUPolElt -> [<RngSerElt, RngIntElt>]
HasRoot(f) : RngUPolElt -> BoolElt, RngSerElt
Example Newton_roots-ex (H46E10)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013