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# source(SimplicialMap) -- get the source of the map

## Synopsis

• Function: source
• Usage:
X = source f
• Inputs:
• Outputs:
• X, , that is the source of the map f

## Description

Given a map $f \colon \Delta \to \Gamma$, this method returns the abstract simplicial complex $\Delta$. The source is one of the defining attributes of a simplicial map

For the identity map, the source and target are equal.

 i1 : S = ZZ[x_0..x_5]; i2 : Δ = simplicialComplex monomialIdeal(x_0*x_5, x_1*x_4, x_2*x_3) o2 = 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 | o2 : SimplicialComplex i3 : id_Δ o3 = | x_0 x_1 x_2 x_3 x_4 x_5 | o3 : 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 | i4 : source id_Δ o4 = 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 | o4 : SimplicialComplex i5 : assert(source id_Δ === Δ) i6 : assert(source id_Δ === target id_Δ)

The next map projects an octahedron onto a square.

 i7 : R = ZZ[y_0..y_3]; i8 : Γ = simplicialComplex monomialIdeal(y_1*y_2) o8 = simplicialComplex | y_0y_2y_3 y_0y_1y_3 | o8 : SimplicialComplex i9 : f = map(Γ, Δ, {y_0,y_0,y_1,y_2,y_3,y_3}) o9 = | y_0 y_0 y_1 y_2 y_3 y_3 | o9 : SimplicialMap simplicialComplex | y_0y_2y_3 y_0y_1y_3 | <--- 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 | i10 : assert isWellDefined f i11 : source f o11 = 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 | o11 : SimplicialComplex i12 : assert(source f === Δ) i13 : peek f o13 = SimplicialMap{cache => CacheTable{} } map => map (R, S, {y , y , y , y , y , y }) 0 0 1 2 3 3 source => 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 | target => simplicialComplex | y_0y_2y_3 y_0y_1y_3 |