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faces -- the i-faces of a simplicial complex

Synopsis

Description

In Macaulay2, every simplicial complex is equipped with a polynomial ring, and the matrix of i-faces is defined over this ring.
loadPackage "SimplicialComplexes";
This triangulation of the real projective plane has 6 vertices, 15 edges and 10 triangles.
R = ZZ[a..f]
D = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f, b*c*d,b*d*e,b*e*f,c*d*f,c*e*f)
faces(-1,D)
faces(0,D)
faces(1,D)
faces(2,D)
fVector D

To avoid repeated computation, the matrix of i-faces is cached at D.cache.faces#i. This function will use this value if it has already been computed.

See also

Ways to use faces :