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addCokerGrading -- Stores a cokernel grading in a polynomial ring.

Synopsis

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 Macaulay2 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

See also

Ways to use addCokerGrading :

For the programmer

The object addCokerGrading is a method function.