
D.5.8.1 blowUp
Procedure from library resolve.lib (see resolve_lib).
 Usage:
 blowUp(J,C[,W][,E]);
W,J,C = ideals,
E = list
 Assume:
 J = ideal containing W ( W = 0 if not specified)
C = ideal containing J
E = list of smooth hypersurfaces (e.g. exceptional divisors)
 Note:
 W the ideal of the ambient space, C the ideal of the center of
the blowup and J the ideal of the variety
Important difference to blowUp2:
 the ambient space V(W) is blown up and V(J) transformed in it
 V(C) is assumed to be nonsingular
 Compute:
 the blowing up of W in C, the exceptional locus, the strict
transform of J and the blowup map
 Return:
 list, say l, of size at most size(C),
l[i] is the affine ring corresponding to the ith chart
each l[i] contains the ideals
 aS, ideal of the blownup ambient space
 sT, ideal of the strict transform
 eD, ideal of the exceptional divisor
 bM, ideal corresponding to the blowup map
l[i] also contains a list BO, which can best be viewed with showBO(BO)
detailed information on the data type BO can be viewed via the
command showDataTypes();
Example:
 LIB "resolve.lib";
ring R=0,(x,y),dp;
ideal J=x2y3;
ideal C=x,y;
list blow=blowUp(J,C);
def Q=blow[1];
setring Q;
aS;
==> aS[1]=0
sT;
==> sT[1]=y(1)^2x(2)
eD;
==> eD[1]=x(2)
bM;
==> bM[1]=x(2)*y(1)
==> bM[2]=x(2)

