isHomogeneous(FirstOrderDeformation) -- Check whether a deformation is homogeneous.

Synopsis

• Function: isHomogeneous

• Usage:

  isHomogeneous(f)

• Inputs:
  • f, a first order deformation
• Outputs:
  • a Boolean value

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 : isHomogeneous f

o6 = true

See also

• degree(FirstOrderDeformation) -- The small torus degree of a deformation.
• grading -- The grading of a first order deformation or complex or polynomial ring.
• firstOrderDeformation -- Makes a first order deformation.
• addCokerGrading -- Stores a cokernel grading in a polynomial ring.