Geometry and Basic Conventions
Degree(g,B) : RngIntElt,SeqEnum -> FldRatElt
HilbertSeries(g,B) : RngIntElt,SeqEnum -> FldFunRatUElt
HilbertSeries(F,V) : SeqEnum,SeqEnum -> FldFunRatUElt
An Example of Use of the Database
The Database Itself
K3Database() : -> SeqEnum
SetAFR(~DB) : SeqEnum ->
Searching the Database
K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfaceFromAFR(DB,c,n) : SeqEnum,RngIntElt,RngIntElt -> VSrfK3
K3Surface(DB,i) : SeqEnum,RngIntElt -> VSrfK3
X eq Y : VSrfK3,VSrfK3 -> BoolElt
K3 Surfaces in the Database
Number(X) : VSrfK3 -> RngIntElt
Weights(X) : VSrfK3 -> SeqEnum
Basket(X) : VSrfK3 -> SeqEnum
Indices(X) : VSrfK3 -> SeqEnum
Codimension(X) : VSrfK3 -> RngIntElt
Genus(X) : VSrfK3 -> RngIntElt
HilbertNumerator(X) : VSrfK3 -> RngUPolElt
HilbertSeries(X,W) : VSrfK3,SeqEnum -> FldFunRatUElt
Degree(X) : VSrfK3 -> FldRatElt
HilbertSeries(X) : VSrfK3 -> FldFunRatUElt
HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum
AFRNumber(X) : VSrfK3 -> RngIntElt
HilbertForm(X) : VSrfK3 -> SeqEnum
Projection and Unprojection
Centres(~X,DB) : VSrfK3,SeqEnum ->
Centres(X) : VSrfK3 -> SeqEnum
HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt
Example K3_k3-projection (H91E1)
ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
Unprojections(~X,DB) : VSrfK3,SeqEnum ->
Unprojections(X) : VSrfK3 -> SeqEnum
Example K3_k3-unprojection (H91E2)
UnprojectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
Example K3_k3-unprojection-chain (H91E3)
Gathering the Data
Baskets(n) : RngIntElt -> SeqEnum,SeqEnum,SeqEnum,SeqEnum
Example K3_k3-baskets (H91E4)
Working with the Raw Elements
K3Surface(g,B) : RngIntElt,SeqEnum -> VSrfK3
AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
AddLocalGenerators(X) : VSrfK3 -> VSrfK3
ApparentCodimension(X) : VSrfK3 -> RngIntElt