affineDiscriminant -- affine discriminant

• Usage:

  affineDiscriminant f

• Inputs:
  • f, a ring element, a polynomial
• Optional inputs:
  • Algorithm => ..., default value "Poisson",
• Outputs:
  • a ring element, the discriminant of the polynomial obtained by homogenizing f with respect to a new variable

i1 : ZZ[a,b,c][x]; f = a*x^2+b*x+c

        2
o2 = a*x  + b*x + c

o2 : ZZ[a..c][x]

i3 : affineDiscriminant f

        2
o3 = - b  + 4a*c

o3 : ZZ[a..c]

i4 : ZZ[a,b,c,d][x]; f = a*x^3+b*x^2+c*x+d

        3      2
o5 = a*x  + b*x  + c*x + d

o5 : ZZ[a..d][x]

i6 : affineDiscriminant f

        2 2       3     3                   2 2
o6 = - b c  + 4a*c  + 4b d - 18a*b*c*d + 27a d

o6 : ZZ[a..d]