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complexFromFacets -- Make a complex from its facets.

Description

Make a complex from a list of faces and/or facets.

This is mostly used internally but may be occasionally useful for the end user.

i1 : R=QQ[x_0..x_5]

o1 = R

o1 : PolynomialRing
 
i2 : C=boundaryCyclicPolytope(3,R)

o2 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o2 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1
 
i3 : fC=facets C

o3 = {{}, {}, {}, {x x x , x x x , x x x , x x x , x x x , x x x , x x x ,
                    0 1 2   0 2 3   0 3 4   0 1 5   1 2 5   2 3 5   0 4 5 
     ------------------------------------------------------------------------
     x x x }, {}, {}, {}}
      3 4 5

o3 : List
 
i4 : C1=complexFromFacets(R,fC)

o4 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o4 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial
 
i5 : C1==C

o5 = true
 
i6 : fc C1;
 
i7 : C1

o7 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o7 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1

Caveat

If both the list of faces and facets is specified there is no consistency check.

See also

Ways to use complexFromFacets:

  • complexFromFacets(PolynomialRing,List)
  • complexFromFacets(PolynomialRing,List,PolynomialRing)

For the programmer

The object complexFromFacets is a method function.

The source of this document is in SRdeformations.m2:6938:0.