numeratorMonomial -- The numerator monomial of a deformation.

Synopsis

• Usage:

  numeratorMonomial(f)

• Inputs:
  • f, a first order deformation,
• Outputs:
  • a ring element,

Description

i1 : R=QQ[x_0..x_4];

i2 : addCokerGrading(R);

              5       4
o2 : Matrix ZZ  <-- ZZ

i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)

o3 = ideal (x x , x x , x x , x x , x x )
             0 1   1 2   2 3   3 4   0 4

o3 : Ideal of R

i4 : mg=mingens I;

             1      5
o4 : Matrix R  <-- R

i5 : f=firstOrderDeformation(mg, vector {-1,-1,0,2,0})

       2
      x
       3
o5 = ----
     x x
      0 1

o5 : first order deformation space of dimension 1

i6 : numeratorMonomial f

      2
o6 = x
      3

o6 : R

See also

• FirstOrderDeformation -- The class of all first order deformations of monomial ideals.
• denominatorMonomial -- The denominator monomial of a deformation.
• denominator(FirstOrderDeformation) -- The denominator of a deformation as a vector.
• numerator(FirstOrderDeformation) -- The numerator of a deformation as a vector.
• firstOrderDeformation -- Makes a first order deformation.
• addCokerGrading -- Stores a cokernel grading in a polynomial ring.