net(SimplicialComplex) -- make a symbolic representation of an abstract simplicial complex

Synopsis

Function: net
Usage:

net Delta
Inputs:
- Delta, an abstract simplicial complex,
Outputs:
- a net, a symbolic representation used for printing

Description

The net of an abstract simplicial complex is an expression that lists the monomials representing the facets (also known as the maximal faces). This function is the primary function called upon by << Thing to format for printing.

i1 : S = ZZ[a..f];

i2 : Δ = simplicialComplex monomialIdeal(a*f, b*d, c*e)

o2 = simplicialComplex | def bef cdf bcf ade abe acd abc |

o2 : SimplicialComplex

i3 : net Δ

o3 = simplicialComplex | def bef cdf bcf ade abe acd abc |

i4 : assert instance(net Δ, Net)

The void complex has no facets whereas the irrelevant complex has the empty set as a facet.

i5 : void = simplicialComplex monomialIdeal 1_S

o5 = simplicialComplex 0

o5 : SimplicialComplex

i6 : net void

o6 = simplicialComplex 0

i7 : irrelevant = simplicialComplex {1_S};

i8 : net irrelevant

o8 = simplicialComplex | 1 |

Ways to use this method: