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singularLocus -- singular locus

Description

singularLocus R -- produce the singular locus of a ring, which is assumed to be integral.

This function can also be applied to an ideal, in which case the singular locus of the quotient ring is returned, or to a variety.

i1 : singularLocus(QQ[x,y] / (x^2 - y^3))

           QQ [x, y]
o1 = ---------------------
         3    2         2
     (- y  + x , 2x, -3y )

o1 : QuotientRing
i2 : singularLocus Spec( QQ[x,y,z] / (x^2 - y^3) )

               QQ [x, y, z]
o2 = Spec(---------------------)
              3    2         2
          (- y  + x , 2x, -3y )

o2 : AffineVariety
i3 : singularLocus Proj( QQ[x,y,z] / (x^2*z - y^3) )

          QQ [x, y, z]
o3 = Proj(------------)
                  2
             (x, y )

o3 : ProjectiveVariety

Ways to use singularLocus :