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

## Synopsis

• Function: isHomogeneous
• Usage:
isHomogeneous(f)
• Inputs:
• Outputs:

## Description

Checks whether a deformation f is homogeneous with respect to the small torus gradin, i.e., the grading added to R = simplexRing f by addCokerGrading.

 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