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TensorComplexes :: pureResES

pureResES -- constructs the Eisenbud--Schreyer pure resolution of a given type

Synopsis

Description

Given a degree sequence d, this function returns the pure resolution of type d constructed in by Eisenbud and Schreyer in Section 5 of “Betti numbers of graded modules and cohomology of vector bundles”. The function operates by resolving the output of pureResES1(d,kk).

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

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

  • pureResES1 -- computes the first map of the Eisenbud--Schreyer pure resolution of a given type

Ways to use pureResES :

  • pureResES(List,Ring) (missing documentation)