Oliver Labs
RICAM (Linz, Austria)

www.OliverLabs.net
mail@OliverLabs.net

www.ricam.oeaw.ac.at
Oliver.Labs@oeaw.ac.at


This Singular code verifies that the 99-nodal septic 
in our article has indeed 99 nodes.


This version: November 2005, RICAM (Linz, Austria).
Original version: August 2004, University of Mainz (Mainz, Germany).
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//   characteristic : 0
//   1 parameter    : alpha 
//   minpoly        : (7*alpha^3+7*alpha+1)
//   number of vars : 4
//        block   1 : ordering dp
//                  : names    x y w z 
//        block   2 : ordering C

The following computation verifies that the total tjurina number of S_alpha is 99
and that all singularities are ordinary double points using the hessian criterion.

Check the total tjurina number of the projective surface:
std...
dim: 0
total tjurina: 99
time in seconds until now: 5

Check that all singularities are ordinary double points:
std non-nodes...
dim: 0 mult: 810
If the dimension is zero, the projective dimension of nonnodes is -1.
We can use this to verify that there are no non-nodes:
Are there only nodes? TRUE
time in seconds used: 30