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D.15.9.4 jungnormal
Procedure from library resjung.lib (see resjung_lib).
- Usage:
- jungnormal(ideal J, int i);
J = ideal
i = int
- Assume:
- J = two dimensional ideal
- Return:
- a list l of rings
l[k] is a ring containing two Ideals: QIdeal and BMap.
BMap defines a birational morphism from V(QIdeal)-->V(J), such that
V(QIdeal) has only singularities of Hizebuch-Jung type.
If i!=0 then it's assumed that J is in noether position with respect
to the last two variables.
If i=0 the algorithm computes a coordinate change such that J is in
noether position.
Example:
| LIB "resjung.lib";
ring R=0,(x,y,z),dp;
ideal J=x2+y3z3;
list li=jungnormal(J,1);
==> // ** killing the basering for level 0
li;
==> [1]:
==> // characteristic : 0
==> // number of vars : 4
==> // block 1 : ordering dp
==> // : names T(1)
==> // block 2 : ordering dp
==> // : names x x(2) y(1)
==> // block 3 : ordering C
==> [2]:
==> // characteristic : 0
==> // number of vars : 4
==> // block 1 : ordering dp
==> // : names T(1)
==> // block 2 : ordering dp
==> // : names x x(1) y(0)
==> // block 3 : ordering C
def S=li[1];
setring S;
QIdeal;
==> QIdeal[1]=T(1)*x(2)^3*y(1)+x
==> QIdeal[2]=-T(1)*x+x(2)^3*y(1)^2
==> QIdeal[3]=T(1)^2+y(1)
==> QIdeal[4]=x(2)^6*y(1)^3+x^2
BMap;
==> BMap[1]=x
==> BMap[2]=x(2)*y(1)
==> BMap[3]=x(2)
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