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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.

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

See also

  • FirstOrderDeformation -- The class of all first order deformations of monomial ideals.
  • raysPPn -- The rays of the standard fan of projective space.

Ways to use addCokerGrading :

  • addCokerGrading(PolynomialRing)
  • addCokerGrading(PolynomialRing,Matrix)