Computation of a resolution that seems incorrect:, ideal C=z^3+x^2*y^2*z+x^4+y^4;

[lorenzin@…]

This is the script that I tried to run

LIB"resolve.lib"; LIB"reszeta.lib"; ring R=0,(x,y,z),dp; ideal C=z^3+x2*y^2*z+x4+y^{4; list CC=resolve(C); list CCC=intersectionDiv(CC); CCC;}

I am not convinced that the output is correct.

SINGULAR /

A Computer Algebra System for Polynomial Computations / version 3-1-6

0<

by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Dec 2012

FB Mathematik der Universitaet, D-67653 Kaiserslautern \

LIB"resolve.lib";

loaded /usr/share/Singular/LIB/resolve.lib (13499,2010-10-15) loaded /usr/share/Singular/LIB/sing.lib (14840,2012-04-20) loaded /usr/share/Singular/LIB/random.lib (14661,2012-03-05) loaded /usr/share/Singular/LIB/matrix.lib (13658,2010-11-16) loaded /usr/share/Singular/LIB/nctools.lib (14246,2011-05-26) loaded /usr/share/Singular/LIB/poly.lib (14852,2012-04-30) loaded /usr/share/Singular/LIB/ring.lib (15322,2012-10-12) loaded /usr/share/Singular/LIB/general.lib (14191,2011-05-04) loaded /usr/share/Singular/LIB/inout.lib (13499,2010-10-15) loaded /usr/share/Singular/LIB/linalg.lib (13733,2010-12-06) loaded /usr/share/Singular/LIB/presolve.lib (14203,2011-05-05) loaded /usr/share/Singular/LIB/primdec.lib (14732,2012-03-30) loaded /usr/share/Singular/LIB/absfact.lib (14191,2011-05-04) loaded /usr/share/Singular/LIB/triang.lib (13499,2010-10-15) loaded /usr/share/Singular/LIB/elim.lib (14661,2012-03-05)

LIB"reszeta.lib";

loaded /usr/share/Singular/LIB/reszeta.lib (14203,2011-05-05) loaded /usr/share/Singular/LIB/normal.lib (15094,2012-07-10) loaded /usr/share/Singular/LIB/algebra.lib (14661,2012-03-05) loaded /usr/share/Singular/LIB/reesclos.lib (14005,2011-03-17) loaded /usr/share/Singular/LIB/hnoether.lib (14196,2011-05-04) loaded /usr/share/Singular/LIB/primitiv.lib (13499,2010-10-15) loaded /usr/share/Singular/LIB/solve.lib (13733,2010-12-06)

ring R=0,(x,y,z),dp; ideal C=z^3+x2*y^2*z+x4+y^{4; list CC=resolve(C); list CCC=intersectionDiv(CC); CCC;}

[1]:

-5,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

[2]:

0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

[3]:

[1]:

[1]:

6,1,1

[2]:

9,1,1

[2]:

[1]:

4,2,1

[3]:

[1]:

4,2,2

[2]:

6,2,1

[4]:

[1]:

5,2,1

[5]:

[1]:

7,2,1

[6]:

[1]:

7,2,2

[2]:

9,2,1

[7]:

[1]:

8,2,1

[4]:

1,4,4,4,4,4,4

[anne]

Dear Dino Lorenzini,

Thank you for posting the 4 examples. The last one was particularly helpful in tracking down the bug, because of the small size of the tree of charts.

Here it turns out that the resolution is computed correctly, but then the identification of the execptional divisors in the different charts goes wrong for the exceptional curve arising in the second blow-up (It is irreducible over the rationals, but has 4 different components over the complex numbers; all of these appearing in 6 different final charts). This messes up the intersection matrix completely. I am working on a bug-fix for this.

Best regards, Anne Frühbis-Krüger

[hannes]

The commit bbd7c81bbd8e197270854c2e529e9a7d6479dc49 may help:

--- a/Singular/LIB/reszeta.lib
+++ b/Singular/LIB/reszeta.lib
@@ -4264,9 +4264,8 @@ EXAMPLE:  example collectDiv;   shows an example
              setring S;         // back to the ring which we want to consider
              if(savedCent==1)
              {
-               vector otherComp;
-               otherComp[M[int(leadcoef(path[1,ncols(path)])),size(BO[4])-1]]
-                        =1;
+               vector otherComp=
+               gen(M[int(leadcoef(path[1,ncols(path)])),size(BO[4])-1]);
              }