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D.5.1.4 NumLocalDim

Procedure from library numerAlg.lib (see numerAlg_lib).

Usage:
NumLocalDim(ideal J, list w, int e); J ideal,
w list of an approximate value of a point v in the algebraic variety defined by J, e integer

Return:
the local dimension of the algebraic variety defined by J at v

Example:
 
LIB "numerAlg.lib";
int e=14;
ring r=(complex,e,I),(x,y,z),dp;
poly f1=(x2+y2+z2-6)*(x-y)*(x-1);
poly f2=(x2+y2+z2-6)*(x-z)*(y-2);
poly f3=(x2+y2+z2-6)*(x-y)*(x-z)*(z-3);
ideal J=f1,f2,f3;
list p0=0.99999999999999+I*0.00000000000001,2,3+I*0.00000000000001;
list p2=1,0.99999999999998,2;
list p1=5+I,4.999999999999998+I,5+I;
def D=NumLocalDim(J,p0,e);
==>
The Local Dimension:
0
def D=NumLocalDim(J,p1,e);
==>
The Local Dimension:
1
def D=NumLocalDim(J,p2,e);
==>
The Local Dimension:
2