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SimplicialComplexes :: star

star -- star of a face in a simplicial complex

Synopsis

Description

The star of a face $f$ in $D$ is the simplicial complex whose faces are the subsets $g$ with $f \cup g$ is a face of $D$.

The bow-tie complex.

i1 : R = QQ[x_1..x_5];
i2 : bowtie = simplicialComplex {x_1*x_2*x_3,x_3*x_4*x_5}

o2 = | x_3x_4x_5 x_1x_2x_3 |

o2 : SimplicialComplex
i3 : star(bowtie,x_3)

o3 = | x_3x_4x_5 x_1x_2x_3 |

o3 : SimplicialComplex
i4 : star(bowtie,x_1*x_2)

o4 = | x_1x_2x_3 |

o4 : SimplicialComplex

The 3-simplex and a copy of its boundary glued along a triangle.

i5 : R = QQ[a..e];
i6 : D = simplicialComplex {a*b*c*d, b*c*e, b*d*e, c*d*e}

o6 = | cde bde bce abcd |

o6 : SimplicialComplex
i7 : star(D,b*c*d)

o7 = | abcd |

o7 : SimplicialComplex
i8 : star(D,b)

o8 = | bde bce abcd |

o8 : SimplicialComplex

See also

Ways to use star :

For the programmer

The object star is a method function.