Resolution
Global GMS
ES Strata
Build. Blocks
Comb. Appl.
HCA Proving
Arrangements
Branches
Classify
Coding
Deformations
Equidim Part
Existence
Finite Groups
Flatness
Genus
Hilbert Series
Membership
Nonnormal Locus
Normalization
Primdec
Puiseux
Plane Curves
Saturation
Solving
Space Curves
Spectrum
SINGULAR Example: Flattening Stratification
We compute the flattening stratification of M, given by the presentation

LIB "matrix.lib";
ring A=0,(x(0..4)),dp;
matrix M[2][4] = x(0),x(1),x(2),x(3),x(1),x(2),x(3),x(4);
flatteningStrat(M);

==>
  [1]:
     _[1]=x(3)^2-x(2)*x(4)
     _[2]=x(2)*x(3)-x(1)*x(4)
     _[3]=x(1)*x(3)-x(0)*x(4)
     _[4]=x(2)^2-x(0)*x(4)
     _[5]=x(1)*x(2)-x(0)*x(3)
     _[6]=x(1)^2-x(0)*x(2)
  [2]:
     _[1]=x(4)
     _[2]=x(3)
     _[3]=x(2)
     _[4]=x(1)
     _[5]=x(0)
    
From the output we can read the flattening stratification of M:





where

Application to Singularities.

KL, 06/03 http://www.singular.uni-kl.de