universalPresentation -- A presentation of the Stanley-Reisner ring over its universal parameter ring

Usage:

universalPresentation D

universalPresentation F
Inputs:
- D, an abstract simplicial complex,
- F, a list, A list of facets defining a simplicial complex D
Outputs:
- a module, A graded presentation of the Stanley-Reisner ring over its universal parameter ring

Description

Note that M is N-graded.

i1 : S = QQ[a..e];

i2 : F = {a*b*c,c*d,e}

o2 = {a*b*c, c*d, e}

o2 : List

i3 : D = simplicialComplex F

o3 = simplicialComplex | e cd abc |

o3 : SimplicialComplex

i4 : universalPresentation D

o4 = cokernel {0} | 0 0 0 0 |
              {1} | 0 0 0 0 |
              {2} | 0 0 0 0 |
              {3} | 0 0 0 0 |
              {1} | 0 0 0 0 |
              {2} | 0 0 0 0 |
              {1} | 0 d 0 0 |
              {2} | 0 0 d 0 |
              {1} | c 0 0 d |

                                            9
o4 : QQ[b..d]-module, quotient of (QQ[b..d])

i5 : M = universalPresentation F

o5 = cokernel {0} | 0 0 0 0 |
              {1} | 0 0 0 0 |
              {2} | 0 0 0 0 |
              {3} | 0 0 0 0 |
              {1} | 0 0 0 0 |
              {2} | 0 0 0 0 |
              {1} | 0 d 0 0 |
              {2} | 0 0 d 0 |
              {1} | c 0 0 d |

                                            9
o5 : QQ[b..d]-module, quotient of (QQ[b..d])

i6 : degrees M

o6 = {{0}, {1}, {2}, {3}, {1}, {2}, {1}, {2}, {1}}

o6 : List

Ways to use universalPresentation:

universalPresentation(List)
universalPresentation(SimplicialComplex)

For the programmer

The object universalPresentation is a method function.

The source of this document is in ResolutionsOfStanleyReisnerRings.m2:487:0.

universalPresentation -- A presentation of the Stanley-Reisner ring over its universal parameter ring

Description

See also

Ways to use universalPresentation:

For the programmer