Singular Manual: plainInvariants

D.6.6.10 plainInvariants

Procedure from library curvepar.lib (see curvepar_lib).

Usage:: plainInvariants(i); i ideal
Assume:: i is the defining ideal of a (reducible) plane curve singularity.
Return:: list L of charts. L[j] is the invariants of the jth branch and the last entry of L is a list containing the intersection matrix,contact matrix,resolution graph of the curve.
L[j][1]: intvec (characteristic exponents of the jth branch) L[j][2]: intvec (generators of the semigroup of the jth branch) L[j][3]: intvec (first components of the puiseux pairs of the jth branch) L[j][4]: intvec (second components of the puiseux pairs of the jth branch) L[j][5]: int (degree of conductor of the jth branch) L[j][6]: intvec (multiplicity sequence of the jth branch. L[last][1]: intmat (intersection matrix of the branches) L[last][2]: intmat (contact matrix of the branches)
L[last][3]: intmat (resolution graph of the curve)

Example:

LIB "curvepar.lib";
ring r=0,(x,y),ds;
ideal i=x14-x4y7-y11;
plainInvariants(i);
==> [1]:
==>    [1]:
==>       7,10
==>    [2]:
==>       7,10
==>    [3]:
==>       10
==>    [4]:
==>       7
==>    [5]:
==>       54
==>    [6]:
==>       7,3,3,1,1,1
==> [2]:
==>    [1]:
==>       1
==>    [2]:
==>       1
==>    [3]:
==>       0
==>    [4]:
==>       0
==>    [5]:
==>       0
==>    [6]:
==>       1
==> [3]:
==>    [1]:
==>       1
==>    [2]:
==>       1
==>    [3]:
==>       0
==>    [4]:
==>       0
==>    [5]:
==>       0
==>    [6]:
==>       1
==> [4]:
==>    [1]:
==>       1
==>    [2]:
==>       1
==>    [3]:
==>       0
==>    [4]:
==>       0
==>    [5]:
==>       0
==>    [6]:
==>       1
==> [5]:
==>    [1]:
==>       1
==>    [2]:
==>       1
==>    [3]:
==>       0
==>    [4]:
==>       0
==>    [5]:
==>       0
==>    [6]:
==>       1
==> [6]:
==>    [1]:
==>       0,7,7,7,7,
==>       0,0,1,1,1,
==>       0,0,0,1,1,
==>       0,0,0,0,1,
==>       0,0,0,0,0 
==>    [2]:
==>       0,1,1,1,1,
==>       1,0,1,1,1,
==>       1,1,0,1,1,
==>       1,1,1,0,1,
==>       1,1,1,1,0 
==>    [3]:
==>       1,0,0,1,0,0,0,1,1,1,1,
==>       0,2,1,0,0,0,0,0,0,0,0,
==>       0,1,3,0,0,1,0,0,0,0,0,
==>       1,0,0,4,1,0,0,0,0,0,0,
==>       0,0,0,1,5,1,0,0,0,0,0,
==>       0,0,1,0,1,6,1,0,0,0,0,
==>       0,0,0,0,0,1,-1,0,0,0,0,
==>       1,0,0,0,0,0,0,-2,0,0,0,
==>       1,0,0,0,0,0,0,0,-3,0,0,
==>       1,0,0,0,0,0,0,0,0,-4,0,
==>       1,0,0,0,0,0,0,0,0,0,-5

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