isRegularMap -- Checks whether a map to projective space is regular

Synopsis

• Usage:

  b = isRegularMap(M)

  b = isRegularMap(L)

  b = isRegularMap(f)

• Inputs:
  • M, a matrix, Row matrix whose entries correspond to the coordinates of your map to projective space
  • L, a list, A list whose entries correspond to the coordinates of your map to projective space
  • f, a ring map, A ring map corresponding to a map of projective varieties.
• Outputs:
  • b, a Boolean value,

Description

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

i2 : M = matrix{{a,b,c},{d,e,f}};

              2        3
o2 : Matrix P5  <--- P5

i3 : segreProduct = P5/minors(2, M);

i4 : blowUpSubvar = segreProduct/ideal(b - d);

i5 : f = {a, b, c};

i6 : isRegularMap({a,b,c})

o6 = true