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# universalSOP -- Universal System of Parameters (USOP)

- Usage:
    `universalSOP D`
    `universalSOP F`
- Inputs:
  - D, an abstract simplicial complex,
  - F, a list, a list of facets defining a simplicial complex
- Outputs:
  - a list, a list of elements from the Stanley-Reisner ring of D

## Description

The following example uses the simplicial complex consisting of a triangle of dimension 2 attached to an edge and a isolated vertex.

    i1 : S = ZZ/2[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 : universalSOP D

    o4 = {a + b + c + d + e, a*b + a*c + b*c + c*d, a*b*c}

    o4 : List

    i5 : universalSOP F

    o5 = {a + b + c + d + e, a*b + a*c + b*c + c*d, a*b*c}

    o5 : List

## See also

- SimplicialComplexes -- exploring abstract simplicial complexes within commutative algebra

## Ways to use universalSOP:

- `universalSOP(List)`
- `universalSOP(SimplicialComplex)`

## For the programmer

The object universalSOP is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ResolutionsOfStanleyReisnerRings.m2:407:0.