id _ SimplicialComplex -- make the identity map from a SimplicialComplex to itself

Scripted functor: id
Usage:

id_Delta
Inputs:
- Delta, an abstract simplicial complex,
Outputs:
- a map of abstract simplicial complexes,

Description

The identity map on the underlying vertex set of an abstract simplicial complex induces the identity map on the entire complex.

The first example is the identity map on a $4$-simplex.

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

i2 : Δ = simplexComplex(4, S)

o2 = simplicialComplex | abcde |

o2 : SimplicialComplex

i3 : f = id_Δ

o3 = | a b c d e |

o3 : SimplicialMap simplicialComplex | abcde | <--- simplicialComplex | abcde |

i4 : assert (isWellDefined f and source f === Δ and
         target f === Δ and matrix f === vars S)

The second example is the identity map on the octahedron.

i5 : R = ZZ[x_0..x_5];

i6 : Γ = simplicialComplex monomialIdeal(x_0*x_5, x_1*x_4, x_2*x_3)

o6 = simplicialComplex | x_3x_4x_5 x_2x_4x_5 x_1x_3x_5 x_1x_2x_5 x_0x_3x_4 x_0x_2x_4 x_0x_1x_3 x_0x_1x_2 |

o6 : SimplicialComplex

i7 : g = id_Γ

o7 = | x_0 x_1 x_2 x_3 x_4 x_5 |

o7 : SimplicialMap simplicialComplex | x_3x_4x_5 x_2x_4x_5 x_1x_3x_5 x_1x_2x_5 x_0x_3x_4 x_0x_2x_4 x_0x_1x_3 x_0x_1x_2 | <--- simplicialComplex | x_3x_4x_5 x_2x_4x_5 x_1x_3x_5 x_1x_2x_5 x_0x_3x_4 x_0x_2x_4 x_0x_1x_3 x_0x_1x_2 |

i8 : assert (isWellDefined g and source g === Γ and
         target g === Γ and matrix g === vars R)

Ways to use this method:

id _ SimplicialComplex -- make the identity map from a SimplicialComplex to itself

The source of this document is in SimplicialComplexes/Documentation.m2:3965:0.

id _ SimplicialComplex -- make the identity map from a SimplicialComplex to itself

Description

See also

Ways to use this method: