SparseDiscriminant Thing -- evaluate a sparse discriminant

Synopsis

• Operator: SPACE

• Usage:

  D(F)

• Inputs:
  • D, an instance of the type SparseDiscriminant, associated to an integral matrix $A$ with $n$ rows.
  • a thing, a Laurent polynomial $F = \sum_{\omega\in \{columns\ of\ A\}} a_{\omega} x^{\omega}$ in $n$ variables $x=(x_1,\ldots,x_n)$.
• Outputs:
  • a ring element, the $A$-discriminant of $F$.

Description

i1 : D = denseDiscriminant(2,2);

o1 : SparseDiscriminant (sparse discriminant associated to | 0 0 0 1 1 2 |)
                                                           | 0 1 2 0 1 0 |

i2 : QQ[a..f][x,y]; F = a*x^2+b*x*y+c*y^2+d*x+e*y+f

        2              2
o3 = a*x  + b*x*y + c*y  + d*x + e*y + f

o3 : QQ[a..f][x..y]

i4 : D(F)

        2              2    2
o4 = c*d  - b*d*e + a*e  + b f - 4a*c*f

o4 : QQ[a..f]

See also

• sparseDiscriminant -- sparse discriminant (A-discriminant)