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pureResTC -- constructs the balanced tensor complex of a given type

Synopsis

Description

Given a degree sequence $d$, this function returns a balanced tensor complex that is a pure resolution of type $d$, as constructed in Section 3 of the paper ``Tensor Complexes: Multilinear free resolutions constructed from higher tensors by Berkesch-Erman-Kummini-Sam. The function operates by resolving the output of pureResTC1(d,kk).

The code gives an error if d is not strictly increasing with $d_0=0$.

i1 : d={0,2,4,5};
 
i2 : FF=pureResTC(d,ZZ/32003)

        ZZ                                                                                                                                                                                                          3        ZZ                                                                                                                                                                                                          10        ZZ                                                                                                                                                                                                          15        ZZ                                                                                                                                                                                                          8
o2 = (-----[x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       ])  <-- (-----[x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       ])   <-- (-----[x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , x       , 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
      32003  0,0,0,0   0,0,1,0   0,1,0,0   0,1,1,0   1,0,0,0   1,0,1,0   1,1,0,0   1,1,1,0   2,0,0,0   2,0,1,0   2,1,0,0   2,1,1,0   3,0,0,0   3,0,1,0   3,1,0,0   3,1,1,0   4,0,0,0   4,0,1,0   4,1,0,0   4,1,1,0         32003  0,0,0,0   0,0,1,0   0,1,0,0   0,1,1,0   1,0,0,0   1,0,1,0   1,1,0,0   1,1,1,0   2,0,0,0   2,0,1,0   2,1,0,0   2,1,1,0   3,0,0,0   3,0,1,0   3,1,0,0   3,1,1,0   4,0,0,0   4,0,1,0   4,1,0,0   4,1,1,0          32003  0,0,0,0   0,0,1,0   0,1,0,0   0,1,1,0   1,0,0,0   1,0,1,0   1,1,0,0   1,1,1,0   2,0,0,0   2,0,1,0   2,1,0,0   2,1,1,0   3,0,0,0   3,0,1,0   3,1,0,0   3,1,1,0   4,0,0,0   4,0,1,0   4,1,0,0   4,1,1,0          32003  0,0,0,0   0,0,1,0   0,1,0,0   0,1,1,0   1,0,0,0   1,0,1,0   1,1,0,0   1,1,1,0   2,0,0,0   2,0,1,0   2,1,0,0   2,1,1,0   3,0,0,0   3,0,1,0   3,1,0,0   3,1,1,0   4,0,0,0   4,0,1,0   4,1,0,0   4,1,1,0         
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     0                                                                                                                                                                                                                    1                                                                                                                                                                                                                     2                                                                                                                                                                                                                     3

o2 : ChainComplex
 
i3 : betti FF

            0  1  2 3
o3 = total: 3 10 15 8
         0: 3  .  . .
         1: . 10  . .
         2: .  . 15 8

o3 : BettiTally

See also

Ways to use pureResTC :

For the programmer

The object pureResTC is a method function.