A free face of a simplicial complex $\Delta$ is a face that is a proper maximal subface of exactly one facet. The elementary collapse is the simplicial complex obtained by removing the free face, and the facet containing it, from $\Delta$. A simplicial complex that can be collapsed to a single vertex is called collapsible. Every collapsible simplicial complex is contractible, but the converse is not true.
i1 : R = ZZ/103[x_0..x_3];
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i2 : Δ = simplicialComplex{R_0*R_1*R_2,R_0*R_2*R_3,R_0*R_1*R_3}
o2 = simplicialComplex | x_0x_2x_3 x_0x_1x_3 x_0x_1x_2 |
o2 : SimplicialComplex
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i3 : C1 = elementaryCollapse(Δ,R_1*R_2)
o3 = simplicialComplex | x_0x_2x_3 x_0x_1x_3 |
o3 : SimplicialComplex
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i4 : C2 = elementaryCollapse(C1,R_2*R_3)
o4 = simplicialComplex | x_0x_2 x_0x_1x_3 |
o4 : SimplicialComplex
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i5 : C3 = elementaryCollapse(C2,R_1*R_3)
o5 = simplicialComplex | x_0x_3 x_0x_2 x_0x_1 |
o5 : SimplicialComplex
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i6 : C4 = elementaryCollapse(C3,R_1)
o6 = simplicialComplex | x_0x_3 x_0x_2 |
o6 : SimplicialComplex
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i7 : C5 = elementaryCollapse(C4,R_2)
o7 = simplicialComplex | x_0x_3 |
o7 : SimplicialComplex
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i8 : C6 = elementaryCollapse(C5,R_3)
o8 = simplicialComplex | x_0 |
o8 : SimplicialComplex
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