isRegularMap -- whether a map to projective space is regular

Synopsis

Usage:

b = isRegularMap(f)
Inputs:
- f, a ring map, a ring map corresponding to a rational map of projective varieties
Optional inputs:
- Verbosity => an integer, default value 0, if 0 then silence the function, if 1 then generate informative output which can be used to adjust strategies, if > 1 then generate a detailed description of the execution
Outputs:
- b, a Boolean value,

This function runs baseLocusOfMap(f) and checks whether the ideal defining the base locus is the whole ring.

i1 : P5 = QQ[a..f];

i2 : P2 = QQ[x,y,z];

i3 : M = matrix{{a,b,c},{d,e,f}};

              2       3
o3 : Matrix P5  <-- P5

i4 : blowUpSubvar = P5/(minors(2, M) + ideal(b - d));

i5 : f = map(blowUpSubvar, P2, {a, b, c});

o5 : RingMap blowUpSubvar <-- P2

i6 : isRegularMap(f)

o6 = true