Returns a simplex on the variables of R.
If R does not have a coker grading then the standard projective space fan rays are added, see addCokerGrading and raysPPn.
The Option computeFaces=>false suppresses the computation of all faces.
If Rdual is specified it is used for the vertices of the dual simplex, if not a new polynomial ring is created. It is graded by the coordinates of the vertices of the dual simplex.
The dual simplex is always created without face data.
i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing |
i2 : C=simplex(R) o2 = 4: x x x x x 0 1 2 3 4 o2 : complex of dim 4 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0 |
i3 : grading C o3 = | -1 -1 -1 -1 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | 5 4 o3 : Matrix ZZ <--- ZZ |
i4 : dC=C.dualComplex o4 = 4: v v v v v 0 1 2 3 4 o4 : complex of dim 4 embedded in dim 4 (printing facets) equidimensional, simplicial |
i5 : grading dC o5 = | -1 -1 -1 4 | | -1 -1 4 -1 | | -1 4 -1 -1 | | 4 -1 -1 -1 | | -1 -1 -1 -1 | 5 4 o5 : Matrix QQ <--- QQ |
i6 : fc(dC); |
i7 : dC o7 = 4: v v v v v 0 1 2 3 4 o7 : complex of dim 4 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0 |
The object simplex is a method function with options.