UnirationalComponentOf6GonalGenus11Curves :: equisingularDefCurveNodes

equisingularDefCurveNodes

Synopsis

Usage:
A=equisingularDefCurveNodes(G,I,H)
Inputs:

G, an ideal, the ideal of a plane curve with only double points as singularities
I, an ideal, ideal of its canonical model
H, a matrix, a row matrix whose entries define equisingular deformations of the plane curve

Outputs:

A, a matrix, a matrix whose columns correspond to the first order deformation of the canonical curve, induced from the equisingular deformations of the plane model

Description

Computes a matrix whose columns define the first order embedded deformations of the canonical curve, induced by the equisingular deformations of the plane curve, which are given by columns of the matrix H.

i1 : p=nextPrime 100;--a prime number

i2 : time (G,Ican)=random6gonalGenus11Curve10Pencil(p); -- used 1.11916 seconds

-- used 1.39199 seconds

i3 : H=equisingularDefOfPlaneCurve(G);--basis of equsingular deformation

ZZ 1 ZZ 34

o3 : Matrix (---[x , x , x ]) <--- (---[x , x , x ])

101 0 1 2 101 0 1 2

i4 : time A=equisingularDefCurveNodes(G,Ican,H_{1});

-- used 31.793 seconds

ZZ 36 ZZ 1

o4 : Matrix (---[r , r , r , r , r , r , r , r , r , r , r ]) <--- (---[r , r , r , r , r , r , r , r , r , r , r ])

101 0 1 2 3 4 5 6 7 8 9 10 101 0 1 2 3 4 5 6 7 8 9 10

Ways to use equisingularDefCurveNodes :

equisingularDefCurveNodes(Ideal,Ideal,Matrix)