The class of all embedded complexes, not necessarily simplicial or compact or equidimensional. These are complexes with coordinates assigned to their vertices.
Creating complexes:
The following functions return complexes:
simplex  Simplex in the variables of a polynomial ring
boundaryCyclicPolytope  The boundary complex of a cyclic polytope with standard projective space vertices
fullCyclicPolytope  The full cyclic polytope with moment curve vertices
convHull  The convex hull
hull  The positive hull
boundaryOfPolytope  The boundary of a polytope
newEmptyComplex  Generates an empty complex.
idealToComplex  The complex associated to a reduced monomial ideal
dualize  The dual of a cocomplex.
complement  The complement of a cocomplex.
complex  Make a complex from a list of faces
complexFromFacets  Make a complex from a list of facets
embeddingComplex  The complex containing a subcomplex
For examples see the documentation of these functions.
The data stored in a complex C:
C.simplexRing, the polynomial ring of vertices of C.
C.grading, is C.simplexRing.grading, a matrix with the coordinates of the vertices of C in its rows.
C.facets, a list with the facets of C sorted into lists by dimension.
C.edim, the embedding dimension of C, i.e., rank source C.grading.
C.dim, the dimension of the complex.
C.isSimp, a Boolean indicating whether C is simplicial.
C.isEquidimensional, a Boolean indicating whether C is equidimensional.
If not just the facets but the faces of C a known (e.g., after computed with fc) then the following data is present:
C.fc, a ScriptedFunctor with the faces of C sorted and indexed by dimension.
C.fvector, a List with the Fvector of C.
The following may be present (if known due to creation of C or due to calling some function):
C.dualComplex, the dual cocomplex of C in the sense of dual faces of a polytope. See dualize.
C.isPolytope, a Boolean indicating whether C is a polytope.
C.polytopalFacets, a List with the boundary faces of the polytope C.
C.complementComplex, the complement cocomplex of C (if C is a subcomplex of a simplex). See complement.












The object Complex is a type, with ancestor classes MutableHashTable < HashTable < Thing.