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

## Synopsis

• Usage:
b = isRegularMap(M)
b = isRegularMap(L)
b = isRegularMap(f)
• Inputs:
• M, , 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 corresponding to a map of projective varieties.
• Outputs:
• b, ,

## Description

This function just runs baseLocusOfMap(M) and checks if the ideal defining the base locus is the whole ring.

 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

## Ways to use isRegularMap :

• "isRegularMap(List)"
• "isRegularMap(Matrix)"
• "isRegularMap(RingMap)"

## For the programmer

The object isRegularMap is .