Macaulay2 » Documentation
Packages » MultigradedBGG :: differential

next | previous | forward | backward | up | index | toc

differential -- returns the differential of a differential module

Usage:

differential D
Inputs:
- D, a differential module,
Outputs:
- a matrix,

Description

This method returns the differential of a differential module.

i1 : R = QQ[x]/(x^3)

o1 = R

o1 : QuotientRing

i2 : phi = map(R^1, R^1, x^2, Degree=>2)

o2 = | x2 |

             1      1
o2 : Matrix R  <-- R

i3 : D = differentialModule phi

      1      1      1
o3 = R  <-- R  <-- R
                    
     -1     0      1

o3 : DifferentialModule

i4 : differential D

o4 = | x2 |

             1      1
o4 : Matrix R  <-- R

See also

degree(DifferentialModule) -- returns the degree of the differential
image(DifferentialModule) -- computes the image of the differential of a differential module
kernel(DifferentialModule) -- computes the kernel of the differential in a differential module.
HH DifferentialModule -- computes the homology of a differential module

Ways to use differential:

differential(DifferentialModule)

For the programmer

The object differential is a method function.

The source of this document is in MultigradedBGG.m2:444:0.