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SRdeformations :: simplex

simplex -- Simplex in the variables of a polynomial ring.

Synopsis

Description

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

See also

Ways to use simplex :

For the programmer

The object simplex is a method function with options.