firstOrderDeformation -- Makes a first order deformation.

Synopsis

• Usage:

  firstOrderDeformation(mg,v)

  firstOrderDeformation(I,v)

• Inputs:
  • I, an ideal, monomial, reduced, in a PolynomialRing, or
  • I, a monomial ideal, reduced
  • mg, a matrix, row, with generators of a reduced monomial ideal.
• Outputs:
  • a first order deformation,

Description

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

i2 : addCokerGrading(R)

o2 = | -1 -1 -1 -1 |
     | 1  0  0  0  |
     | 0  1  0  0  |
     | 0  0  1  0  |
     | 0  0  0  1  |

              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 {-1,1,0,0,0})

     x
      1
o5 = --
     x
      0

o5 : first order deformation space of dimension 1

See also

• FirstOrderDeformation -- The class of all first order deformations of monomial ideals.
• dim(FirstOrderDeformation) -- Compute the dimension of a deformation.
• addCokerGrading -- Stores a cokernel grading in a polynomial ring.