## Synopsis

• Usage:
• Inputs:
• R, ,
• L, a list,
• A, ,
• Outputs:
• , the integer grading matrix.

## Description

Stores a cokernel grading (Cox grading) in a polynomial ring. This data is accessed by FirstOrderDeformation to compute the small torus degree(FirstOrderDeformation) of a deformation, and by Complex and CoComplex to store the vertices.

The number or rows of A has to match the number of variables of R.

If A is not specified, raysPPn R is used.

If L is specified then the grading of a weighted projective space is added.

This command does not change the behaviour of R with respect to the standard Macaualy2 image grading, which we want to use independently.

 i1 : R=QQ[x_0..x_4]; i2 : addCokerGrading(R); 5 4 o2 : Matrix ZZ <--- ZZ i3 : R.grading o3 = | -1 -1 -1 -1 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | 5 4 o3 : Matrix ZZ <--- ZZ

Weighted projective space:

 i4 : R=QQ[x_0..x_4]; i5 : addCokerGrading(R,{1,1,2,2,3}); 5 4 o5 : Matrix ZZ <--- ZZ i6 : R.grading o6 = | -1 -2 -2 -3 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | 5 4 o6 : Matrix ZZ <--- ZZ