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taylorComplex -- gives the Taylor complex of a monomial ideal

Synopsis

Description

Given a monomial ideal I, this function returns the Taylor complex of that ideal. Recall that the Taylor complex is a simplex with vertices labeled by the generators of the ideal.

i1 : S = QQ[x,y,z];
 
i2 : I = monomialIdeal (x^2, y^2, z^2);

o2 : MonomialIdeal of S
 
i3 : T = taylorComplex I

o3 = T

o3 : CellComplex
 
i4 : C = chainComplex T

      1      3      3      1
o4 = S  <-- S  <-- S  <-- S
                           
     -1     0      1      2

o4 : ChainComplex
 
i5 : C.dd

           1                       3
o5 = -1 : S  <------------------- S  : 0
                | -x2 -y2 -z2 |

          3                           3
     0 : S  <----------------------- S  : 1
               {2} | -y2 0   -z2 |
               {2} | x2  -z2 0   |
               {2} | 0   y2  x2  |

          3                   1
     1 : S  <--------------- S  : 2
               {4} | -z2 |
               {4} | -x2 |
               {4} | y2  |

o5 : ChainComplexMap

See also

Ways to use taylorComplex :

For the programmer

The object taylorComplex is a method function.